# kb

id: sylva-or-a-discourse-of-forest-trees-and-the-propagation-of-timber-20260505-0
file: data/en.wikipedia.org/wiki/Sylva,_or_A_Discourse_of_Forest-Trees_and_the_Propagation_of_Timber-0.md
category: reference
title: Sylva, or A Discourse of Forest-Trees and the Propagation of Timber
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Sylva,_or_A_Discourse_of_Forest-Trees_and_the_Propagation_of_Timber
date_saved: 2026-05-05T08:42:57.589336+00:00
instance: kb-cron
parent: sylva-or-a-discourse-of-forest-trees-and-the-propagation-of-timber-20260505-0
summary:
Sylva, or A Discourse of Forest-Trees and the Propagation of Timber in His Majesty's Dominions by the English writer John Evelyn was first presented in 1662 as a paper to the Royal Society. It was published as a book two years later in 1664, and is recognised as one of the most influential texts on forestry ever published. A second edition with new engravings was published in 1670, and a third edition in 1679 included a geological essay by Evelyn. An expanded fourth edition was published in 1706, with the new segments specifically covering fruit trees and the production of cider. == Editions == 1662 Sylva paper was presented to the Royal Society on 16 February 1662. 1664 Sylva First Edition book printed by publisher John Martyn for the Royal Society, and the first book published after the granting of their Royal Charter as publishers in 1662. 1670 Sylva Second Edition. Various engravings added. 1679 Sylva Third Edition. Included an essay from Evelyn about soils: Terra, a Philosophical Essay of Earth, being a Lecture in Course. 1706 Silva Fourth Edition, now spelt Silva, contained new sections Dendrologia, Pomona; Or, An Appendix concerning Fruit-Trees in relation to CIDER and Kalendarium Hortense.


id: t-rex-and-the-crater-of-doom-20260505-0
file: data/en.wikipedia.org/wiki/T._rex_and_the_Crater_of_Doom-0.md
category: reference
title: T. rex and the Crater of Doom
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/T._rex_and_the_Crater_of_Doom
date_saved: 2026-05-05T08:42:58.785888+00:00
instance: kb-cron
parent: t-rex-and-the-crater-of-doom-20260505-0
summary:
T. rex and the Crater of Doom is a nonfiction book by UC Berkeley professor Walter Alvarez that was published by Princeton University Press in 1997. The book discusses the research and evidence that led to the creation of the Alvarez hypothesis, which explains how an impact event was the main cause that resulted in the Cretaceous–Paleogene extinction event. == Content == The book begins by discussing Alvarez's research in the 1970s, before ever investigating the cause of the Cretaceous–Paleogene extinction event, when he was researching plate tectonics involving the Apennine Mountains with William "Bill" Lowrie. The method of this research was to use the evidence of the Earth's magnetic field to show that the plate upon which the rocks of the mountains rested had rotated over millions of years. While investigating limestone deposits in Gubbio, they discovered that some of the rocks were not aligned with the magnetic north pole, but in the opposite direction, implying the Earth undergoes geomagnetic reversal over time. This, with the plentiful fossilized material of extinct foraminifera, allowed them to date the time differences between each reversal and catalog the species of microscopic life found in each era. In doing so, they discovered that


id: t-rex-and-the-crater-of-doom-20260505-1
file: data/en.wikipedia.org/wiki/T._rex_and_the_Crater_of_Doom-1.md
category: reference
title: T. rex and the Crater of Doom
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/T._rex_and_the_Crater_of_Doom
date_saved: 2026-05-05T08:42:58.785888+00:00
instance: kb-cron
parent: t-rex-and-the-crater-of-doom-20260505-0
summary:
In a review for Geological Magazine, Simon Conway Morris noted that the controversy and debate over the impact hypothesis had led to comments against it that are "querulous, petulant, otiose, and sometimes simply poisonous", but that Alvarez's book "acknowledges the differences that have arisen, but never does he descend to insult and injury", leading to a "gracious and generous book". Timothy Ferris, writing for The New York Times, stated that Alvarez "gets the facts across in a lighthearted, almost playful manner", but still manages to present "solid science" that presents a "clear and efficient exposition that conveys plenty of cogent detail while keeping an eye on the subtle interplay of thought, action and personality that makes scientific research such arresting human behavior." == Critical reception == Clark R. Chapman, writing for Nature, stated that Alvarez's "slim" book can be read "in a single sitting and I recommend it highly – if only as a jumping-off point to other perspectives on this dramatic scientific revolution." In a review for Scientific American of T. rex and the Crater of Doom and the opposing theories presented in The Great Dinosaur Extinction Controversy, Michael Benton advocated reading the book "for an excellent account of


id: theory-of-the-earth-20260505-0
file: data/en.wikipedia.org/wiki/Theory_of_the_Earth-0.md
category: reference
title: Theory of the Earth
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Theory_of_the_Earth
date_saved: 2026-05-05T08:42:59.946789+00:00
instance: kb-cron
parent: theory-of-the-earth-20260505-0
summary:
Theory of the Earth is a publication by James Hutton which laid the foundations for geology. In it he showed that the Earth is the product of natural forces. What could be seen happening today, over long periods of time, could produce what we see in the rocks. It also hypothesized that the age of the Earth was much older than what biblical literalists claim. This idea, uniformitarianism, was used by Charles Lyell in his work, and Lyell's textbook was an important influence on Charles Darwin. The work was first published in 1788 by the Royal Society of Edinburgh, and later in 1795 as two book volumes. Hutton recognized that rocks record the evidence of the past action of processes which still operate today. He also anticipated natural selection, as follows: "Those which depart most from the best adapted constitution, will be the most liable to perish, while, on the other hand, those organised bodies, which most approach to the best constitution for the present circumstances, will be best adapted to continue, in preserving themselves and multiplying the individuals of their race". == History == Hutton's prose hindered his theories. They were not taken seriously until 1802, when Edinburgh University


id: traces-of-catastrophe-20260505-0
file: data/en.wikipedia.org/wiki/Traces_of_Catastrophe-0.md
category: reference
title: Traces of Catastrophe
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Traces_of_Catastrophe
date_saved: 2026-05-05T08:43:01.112862+00:00
instance: kb-cron
parent: traces-of-catastrophe-20260505-0
summary:
Traces of Catastrophe: A Handbook of Shock-Metamorphic Effects in Terrestrial Meteorite Impact Structures is a book written by Bevan M. French of the Smithsonian Institution. It is a comprehensive technical reference on the science of impact craters. It was published in 1998 by the Lunar and Planetary Institute (LPI), which is part of the Universities Space Research Association (USRA). It was originally available in hard copy from LPI, but is now only available as a portable document format (PDF) e-book free download. The book has become very influential in the field of impact crater research, appearing as a common reference for papers and web sites on the topic. The Earth Impact Database lists it among the suggested reading on its introductory page about impact craters. The Impact Field Studies Group Impact Database says it is required reading before submitting an observation of a proposed impact site. NASA's Goddard Space Flight Center (GSFC) lists it among general references relevant to Planetary Science across the Solar System. NASA GSFC also has a Remote Sensing Tutorial site which calls Traces of Catastrophe an "exceptional summary of impact cratering." == Overview == The book is divided into eight chapters. Chapter 1 introduces impact craters,


id: volcano-the-eruption-and-healing-of-mount-st-helens-20260505-0
file: data/en.wikipedia.org/wiki/Volcano:_The_Eruption_and_Healing_of_Mount_St._Helens-0.md
category: reference
title: Volcano: The Eruption and Healing of Mount St. Helens
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Volcano:_The_Eruption_and_Healing_of_Mount_St._Helens
date_saved: 2026-05-05T08:43:02.753090+00:00
instance: kb-cron
parent: volcano-the-eruption-and-healing-of-mount-st-helens-20260505-0
summary:
Volcano: The Eruption and Healing of Mount St. Helens is a 1986 children's science photo book written by Patricia Lauber. Lauber documents the lead-up to the 1980 eruption of Mount St. Helens, the eruption itself, and the aftermath. It received a Newbery Honor in 1987, and reviewers commended the quality and narrative contribution of the color pictures used throughout the book. == Summary == The book explores Mt. St. Helens' geological history and location, as well as the events preceding the eruption, including the gradual development of the bulge on the mountain's north side. The volcano erupts on May 18, 1980, creating lahars, pyroclastic flows, avalanches, and other geological hazards which destroy a 230-square-mile area and kill 57 people. In the aftermath, geologists worked to understand both the cause and ecological impact of the eruption, helping to advance understanding in the fields of seismology and vulcanology. In the aftermath of the destruction from the eruption, surviving underground plants began to colonise the blast area; and burrowing rodents like chipmunks, pocket gophers, and red squirrels returned as well. Over time, the area recovered as more plants and animals returned. The last section of the book explains the process of subduction, the


id: list-of-publications-in-mathematics-20260505-0
file: data/en.wikipedia.org/wiki/List_of_publications_in_mathematics-0.md
category: reference
title: List of publications in mathematics
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/List_of_publications_in_mathematics
date_saved: 2026-05-05T08:43:04.376499+00:00
instance: kb-cron
parent: list-of-publications-in-mathematics-20260505-0
summary:
This is a list of publications in mathematics, organized by field. Some reasons a particular publication might be regarded as important: Topic creator – A publication that created a new topic Breakthrough – A publication that changed scientific knowledge significantly Influence – A publication which has significantly influenced the world or has had a massive impact on the teaching of mathematics. Among published compilations of important publications in mathematics are Landmark writings in Western mathematics 1640–1940 by Ivor Grattan-Guinness and A Source Book in Mathematics by David Eugene Smith. == Algebra == === Theory of equations === ==== Baudhayana Sulba Sutra ==== Baudhayana (8th century BCE) With linguistic evidence suggesting this text to have been written between the 8th and 5th centuries century BCE, this is one of the oldest mathematical texts. It laid the foundations of Indian mathematics and was influential in South Asia. It was primarily a geometrical text and also contained some important developments, including the list of Pythagorean triples, geometric solutions of linear and quadratic equations and square root of 2. ==== The Nine Chapters on the Mathematical Art ==== The Nine Chapters on the Mathematical Art (10th–2nd century BCE) Contains the earliest description of Gaussian


id: list-of-publications-in-mathematics-20260505-1
file: data/en.wikipedia.org/wiki/List_of_publications_in_mathematics-1.md
category: reference
title: List of publications in mathematics
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/List_of_publications_in_mathematics
date_saved: 2026-05-05T08:43:04.376499+00:00
instance: kb-cron
parent: list-of-publications-in-mathematics-20260505-0
summary:
==== Traité des substitutions et des équations algébriques ==== Camille Jordan (1870) Online version: Online version Traité des substitutions et des équations algébriques (Treatise on Substitutions and Algebraic Equations). The first book on group theory, giving a then-comprehensive study of permutation groups and Galois theory. In this book, Jordan introduced the notion of a simple group and epimorphism (which he called isomorphisme mériédrique), proved part of the Jordan–Hölder theorem, and discussed matrix groups over finite fields as well as the Jordan normal form. ==== Theorie der Transformationsgruppen ==== Sophus Lie, Friedrich Engel (1888–1893). Publication data: 3 volumes, B.G. Teubner, Verlagsgesellschaft, mbH, Leipzig, 1888–1893. Volume 1, Volume 2, Volume 3. The first comprehensive work on transformation groups, serving as the foundation for the modern theory of Lie groups. ==== Solvability of groups of odd order ==== Walter Feit and John Thompson (1960) Description: Gave a complete proof of the solvability of finite groups of odd order, establishing the long-standing Burnside conjecture that all finite non-abelian simple groups are of even order. Many of the original techniques used in this paper were used in the eventual classification of finite simple groups. ==== Homological algebra ==== ==== Homological Algebra ==== Henri Cartan and


id: list-of-publications-in-mathematics-20260505-2
file: data/en.wikipedia.org/wiki/List_of_publications_in_mathematics-2.md
category: reference
title: List of publications in mathematics
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/List_of_publications_in_mathematics
date_saved: 2026-05-05T08:43:04.376499+00:00
instance: kb-cron
parent: list-of-publications-in-mathematics-20260505-0
summary:
=== Séminaire de géométrie algébrique === Alexander Grothendieck et al. These seminar notes on Grothendieck's reworking of the foundations of algebraic geometry report on work done at IHÉS starting in the 1960s. SGA 1 dates from the seminars of 1960–1961, and the last in the series, SGA 7, dates from 1967 to 1969. In contrast to EGA, which is intended to set foundations, SGA describes ongoing research as it unfolded in Grothendieck's seminar; as a result, it is quite difficult to read, since many of the more elementary and foundational results were relegated to EGA. One of the major results building on the results in SGA is Pierre Deligne's proof of the last of the open Weil conjectures in the early 1970s. Other authors who worked on one or several volumes of SGA include Michel Raynaud, Michael Artin, Jean-Pierre Serre, Jean-Louis Verdier, Pierre Deligne, and Nicholas Katz. == Number theory == === Brāhmasphuṭasiddhānta === Brahmagupta (628) Brahmagupta's Brāhmasphuṭasiddhānta is the first book that mentions zero as a number, hence Brahmagupta is considered the first to formulate the concept of zero. The current system of the four fundamental operations (addition, subtraction, multiplication and division) based on the Hindu-Arabic number system also


id: list-of-publications-in-mathematics-20260505-3
file: data/en.wikipedia.org/wiki/List_of_publications_in_mathematics-3.md
category: reference
title: List of publications in mathematics
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/List_of_publications_in_mathematics
date_saved: 2026-05-05T08:43:04.376499+00:00
instance: kb-cron
parent: list-of-publications-in-mathematics-20260505-0
summary:
=== "Automorphic Forms on GL(2)" === Hervé Jacquet and Robert Langlands (1970) This publication offers evidence towards Langlands' conjectures by reworking and expanding the classical theory of modular forms and their L-functions through the introduction of representation theory. === "La conjecture de Weil. I." === Pierre Deligne (1974) Proved the Riemann hypothesis for varieties over finite fields, settling the last of the open Weil conjectures. === "Endlichkeitssätze für abelsche Varietäten über Zahlkörpern" === Gerd Faltings (1983) Faltings proves a collection of important results in this paper, the most famous of which is the first proof of the Mordell conjecture (a conjecture dating back to 1922). Other theorems proved in this paper include an instance of the Tate conjecture (relating the homomorphisms between two abelian varieties over a number field to the homomorphisms between their Tate modules) and some finiteness results concerning abelian varieties over number fields with certain properties. === "Modular Elliptic Curves and Fermat's Last Theorem" === Andrew Wiles (1995) This article proceeds to prove a special case of the Shimura–Taniyama conjecture through the study of the deformation theory of Galois representations. This in turn implies the famed Fermat's Last Theorem. The proof's method of identification of a deformation


id: list-of-publications-in-mathematics-20260505-4
file: data/en.wikipedia.org/wiki/List_of_publications_in_mathematics-4.md
category: reference
title: List of publications in mathematics
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/List_of_publications_in_mathematics
date_saved: 2026-05-05T08:43:04.376499+00:00
instance: kb-cron
parent: list-of-publications-in-mathematics-20260505-0
summary:
==== Intégrale, longueur, aire ==== Henri Lebesgue (1901) Lebesgue's doctoral dissertation, summarizing and extending his research to date regarding his development of measure theory and the Lebesgue integral. === Complex analysis === ==== Grundlagen für eine allgemeine Theorie der Functionen einer veränderlichen complexen Grösse ==== Bernhard Riemann (1851) Riemann's doctoral dissertation introduced the notion of a Riemann surface, conformal mapping, simple connectivity, the Riemann sphere, the Laurent series expansion for functions having poles and branch points, and the Riemann mapping theorem. === Functional analysis === ==== Théorie des opérations linéaires ==== Stefan Banach (1932; originally published 1931 in Polish under the title Teorja operacyj.) Banach, Stefan (1932). Théorie des Opérations Linéaires [Theory of Linear Operations] (PDF). Monografie Matematyczne (in French). Vol. 1. Warszawa: Subwencji Funduszu Kultury Narodowej. Zbl 0005.20901. Archived from the original (PDF) on 11 January 2014. Retrieved 11 July 2020. The first mathematical monograph on the subject of linear metric spaces, bringing the abstract study of functional analysis to the wider mathematical community. The book introduced the ideas of a normed space and the notion of a so-called B-space, a complete normed space. The B-spaces are now called Banach spaces and are one of the basic objects of


id: list-of-publications-in-mathematics-20260505-5
file: data/en.wikipedia.org/wiki/List_of_publications_in_mathematics-5.md
category: reference
title: List of publications in mathematics
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/List_of_publications_in_mathematics
date_saved: 2026-05-05T08:43:04.376499+00:00
instance: kb-cron
parent: list-of-publications-in-mathematics-20260505-0
summary:
=== The Nine Chapters on the Mathematical Art === Unknown author This was a Chinese mathematics book, mostly geometric, composed during the Han dynasty, perhaps as early as 200 BC. It remained the most important textbook in China and East Asia for over a thousand years, similar to the position of Euclid's Elements in Europe. Among its contents: Linear problems solved using the principle known later in the West as the rule of false position. Problems with several unknowns, solved by a principle similar to Gaussian elimination. Problems involving the principle known in the West as the Pythagorean theorem. The earliest solution of a matrix using a method equivalent to the modern method. === The Conics === Apollonius of Perga The Conics was written by Apollonius of Perga, a Greek mathematician. His innovative methodology and terminology, especially in the field of conics, influenced many later scholars including Ptolemy, Francesco Maurolico, Isaac Newton, and René Descartes. It was Apollonius who gave the ellipse, the parabola, and the hyperbola the names by which we know them. === Surya Siddhanta === Unknown (400 CE) It describes the archeo-astronomy theories, principles and methods of the ancient Hindus. This siddhanta is supposed to be the


id: list-of-publications-in-mathematics-20260505-6
file: data/en.wikipedia.org/wiki/List_of_publications_in_mathematics-6.md
category: reference
title: List of publications in mathematics
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/List_of_publications_in_mathematics
date_saved: 2026-05-05T08:43:04.376499+00:00
instance: kb-cron
parent: list-of-publications-in-mathematics-20260505-0
summary:
=== L'anneau d'homologie d'une représentation, Structure de l'anneau d'homologie d'une représentation === Jean Leray (1946) These two Comptes Rendus notes of Leray from 1946 introduced the novel concepts of sheafs, sheaf cohomology, and spectral sequences, which he had developed during his years of captivity as a prisoner of war. Leray's announcements and applications (published in other Comptes Rendus notes from 1946) drew immediate attention from other mathematicians. Subsequent clarification, development, and generalization by Henri Cartan, Jean-Louis Koszul, Armand Borel, Jean-Pierre Serre, and Leray himself allowed these concepts to be understood and applied to many other areas of mathematics. Dieudonné would later write that these notions created by Leray "undoubtedly rank at the same level in the history of mathematics as the methods invented by Poincaré and Brouwer". === Quelques propriétés globales des variétés differentiables === René Thom (1954) In this paper, Thom proved the Thom transversality theorem, introduced the notions of oriented and unoriented cobordism, and demonstrated that cobordism groups could be computed as the homotopy groups of certain Thom spaces. Thom completely characterized the unoriented cobordism ring and achieved strong results for several problems, including Steenrod's problem on the realization of cycles. == Category theory == === "General Theory


id: list-of-publications-in-mathematics-20260505-7
file: data/en.wikipedia.org/wiki/List_of_publications_in_mathematics-7.md
category: reference
title: List of publications in mathematics
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/List_of_publications_in_mathematics
date_saved: 2026-05-05T08:43:04.376499+00:00
instance: kb-cron
parent: list-of-publications-in-mathematics-20260505-0
summary:
Kurt Gödel (1931) Online version: Online version In mathematical logic, Gödel's incompleteness theorems are two celebrated theorems proved by Kurt Gödel in 1931. The first incompleteness theorem states: For any formal system such that (1) it is ω {\displaystyle \omega } -consistent (omega-consistent), (2) it has a recursively definable set of axioms and rules of derivation, and (3) every recursive relation of natural numbers is definable in it, there exists a formula of the system such that, according to the intended interpretation of the system, it expresses a truth about natural numbers and yet it is not a theorem of the system. === Systems of Logic Based on Ordinals === Alan Turing's PhD thesis (1938) == Combinatorics == === "On sets of integers containing no k elements in arithmetic progression" === Endre Szemerédi (1975) Settled a conjecture of Paul Erdős and Pál Turán (now known as Szemerédi's theorem) that if a sequence of natural numbers has positive upper density then it contains arbitrarily long arithmetic progressions. Szemerédi's solution has been described as a "masterpiece of combinatorics" and it introduced new ideas and tools to the field including a weak form of the Szemerédi regularity lemma. === Graph theory === ====


id: list-of-publications-in-mathematics-20260505-8
file: data/en.wikipedia.org/wiki/List_of_publications_in_mathematics-8.md
category: reference
title: List of publications in mathematics
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/List_of_publications_in_mathematics
date_saved: 2026-05-05T08:43:04.376499+00:00
instance: kb-cron
parent: list-of-publications-in-mathematics-20260505-0
summary:
==== "Полиномиальный алгоритм в линейном программировании" ==== Khachiyan, Leonid Genrikhovich (1979). Полиномиальный алгоритм в линейном программировании [A polynomial algorithm for linear programming]. Doklady Akademii Nauk SSSR (in Russian). 244: 1093–1096.. Khachiyan's work on the ellipsoid method. This was the first polynomial time algorithm for linear programming. == Early manuscripts == These are publications that are not necessarily relevant to a mathematician nowadays, but are nonetheless important publications in the history of mathematics. === Moscow Mathematical Papyrus === This is one of the earliest mathematical treatises that still survives today. The Papyrus contains 25 problems involving arithmetic, geometry, and algebra, each with a solution given. Written in Ancient Egypt at approximately 1850 BC. === Rhind Mathematical Papyrus === Ahmes (scribe) One of the oldest mathematical texts, dating to the Second Intermediate Period of ancient Egypt. It was copied by the scribe Ahmes (properly Ahmose) from an older Middle Kingdom papyrus. It laid the foundations of Egyptian mathematics and in turn, later influenced Greek and Hellenistic mathematics. Besides describing how to obtain an approximation of π only missing the mark by less than one per cent, Ahmes make use of a kind of an analogue of the cotangent. === Archimedes Palimpsest ===


id: list-of-publications-in-mathematics-20260505-9
file: data/en.wikipedia.org/wiki/List_of_publications_in_mathematics-9.md
category: reference
title: List of publications in mathematics
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/List_of_publications_in_mathematics
date_saved: 2026-05-05T08:43:04.376499+00:00
instance: kb-cron
parent: list-of-publications-in-mathematics-20260505-0
summary:
=== Naive Set Theory === Paul Halmos An undergraduate introduction to not-very-naive set theory which has lasted for decades. It is still considered by many to be the best introduction to set theory for beginners. While the title states that it is naive, which is usually taken to mean without axioms, the book does introduce all the axioms of Zermelo–Fraenkel set theory and gives correct and rigorous definitions for basic objects. Where it differs from a "true" axiomatic set theory book is its character: There are no long-winded discussions of axiomatic minutiae, and there is next to nothing about topics like large cardinals. Instead it aims, and succeeds, in being intelligible to someone who has never thought about set theory before. === Cardinal and Ordinal Numbers === Wacław Sierpiński The nec plus ultra reference for basic facts about cardinal and ordinal numbers. If you have a question about the cardinality of sets occurring in everyday mathematics, the first place to look is this book, first published in the early 1950s but based on the author's lectures on the subject over the preceding 40 years. === Set Theory: An Introduction to Independence Proofs === Kenneth Kunen This book is not really


id: the-math-s-fix-20260505-0
file: data/en.wikipedia.org/wiki/The_Math(s)_Fix-0.md
category: reference
title: The Math(s) Fix
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/The_Math(s)_Fix
date_saved: 2026-05-05T08:43:05.533110+00:00
instance: kb-cron
parent: the-math-s-fix-20260505-0
summary:
The Math(s) Fix: An Education Blueprint for the AI Age is a 2020 book by Conrad Wolfram, a British technologist, entrepreneur, and co-founder of Wolfram Research Europe. The book argues that mathematics education worldwide is fundamentally broken and proposes a comprehensive restructuring centred on real-world problem-solving and computational thinking, rather than manual calculation. == Synopsis == The book's core claim is that school mathematics curricula around the world teach the wrong thing: they overwhelmingly focus on training students to perform hand calculations that computers can now perform far more accurately and quickly. Wolfram contends this conflation of *mathematics* with *calculating by hand* has persisted long past its usefulness and is actively harmful, crowding out the genuinely important mathematical skills of: Problem Definition - translating a real-world situation into a mathematical question Abstraction - identifying the relevant structure of a problem Computation - executing a solution (which in the modern world almost always means using a computer) Interpretation - applying and verifying the answer back in context Wolfram calls these the four steps of the "computational thinking" process, and argues they are what mathematicians, scientists, engineers, and data analysts actually do - yet schools spend nearly all their time on a


id: 99-points-of-intersection-20260505-0
file: data/en.wikipedia.org/wiki/99_Points_of_Intersection-0.md
category: reference
title: 99 Points of Intersection
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/99_Points_of_Intersection
date_saved: 2026-05-05T08:43:06.654180+00:00
instance: kb-cron
parent: 99-points-of-intersection-20260505-0
summary:
99 Points of Intersection: Examples—Pictures—Proofs is a book on constructions in Euclidean plane geometry in which three or more lines or curves meet in a single point of intersection. This book was originally written in German by Hans Walser as 99 Schnittpunkte (Eagle / Ed. am Gutenbergplatz, 2004), translated into English by Peter Hilton and Jean Pedersen, and published by the Mathematical Association of America in 2006 in their MAA Spectrum series (ISBN 978-0-88385-553-9). == Topics and organization == The book is organized into three sections. The first section provides introductory material, describing different mathematical situations in which multiple curves might meet, and providing different possible explanations for this phenomenon, including symmetry, geometric transformations, and membership of the curves in a pencil of curves. The second section shows the 99 points of intersection of the title. Each is given on its own page, as a large figure with three smaller figures showing its construction, with a one-line caption but no explanatory text. The third section provides background material and proofs for some of these points of intersection, as well as extending and generalizing some of these results. Some of these points of intersection are standard; for instance, these include the


id: adventures-among-the-toroids-20260505-0
file: data/en.wikipedia.org/wiki/Adventures_Among_the_Toroids-0.md
category: reference
title: Adventures Among the Toroids
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Adventures_Among_the_Toroids
date_saved: 2026-05-05T08:43:08.969210+00:00
instance: kb-cron
parent: adventures-among-the-toroids-20260505-0
summary:
Adventures Among the Toroids: A study of orientable polyhedra with regular faces is a book on toroidal polyhedra that have regular polygons as their faces. It was written, hand-lettered, and illustrated by mathematician Bonnie Stewart, and self-published under the imprint "Number One Tall Search Book" in 1970. Stewart put out a second edition, again hand-lettered and self-published, in 1980. Although out of print, the Basic Library List Committee of the Mathematical Association of America has recommended its inclusion in undergraduate mathematics libraries. == Topics == The Platonic solids, known to antiquity, have all faces regular polygons, all symmetric to each other (each face can be taken to each other face by a symmetry of the polyhedron). However, if less symmetry is required, a greater number of polyhedra can be formed while having all faces regular. The convex polyhedra with all faces regular were catalogued in 1966 by Norman Johnson (after earlier study e.g. by Martyn Cundy and A. P. Rollett), and have come to be known as the Johnson solids. Adventures Among the Toroids extends the investigation of polyhedra with regular faces to non-convex polyhedra, and in particular to polyhedra of higher genus than the sphere. Many of these polyhedra


id: lgebra-de-baldor-20260505-0
file: data/en.wikipedia.org/wiki/Álgebra_de_Baldor-0.md
category: reference
title: Álgebra de Baldor
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Álgebra_de_Baldor
date_saved: 2026-05-05T08:43:10.080065+00:00
instance: kb-cron
parent: lgebra-de-baldor-20260505-0
summary:
Álgebra, commonly known as Álgebra de Baldor (Spanish: Baldor's Algebra), is a book by the Cuban mathematician, lawyer, and professor Aurelio Baldor. The first edition was published on 19 June 1941. Baldor’s Algebra contains a total of 5,790 exercises, averaging 19 exercises per test. It is considered one of the most comprehensive works on algebra. == Publication history == Rhe first recorded edition of Baldor’s Algebra was published in 1941 by Editorial Cultural in Havana, Cuba. In 1948, Aurelio Baldor sold the rights to the Mexican publisher Publicaciones Culturales in order to invest the proceeds in his educational institute. This publisher continued to publish the book from Mexico. Upon his arrival in Mexico, already in exile, the book was published by Editorial Cultural Mexicana. According to this website, the book was also published in Venezuela, Colombia, and Spain. Publications continue in Mexico, following reorganizations and name changes of the original publishing companies, by Grupo Editorial Patria. == Description == In the early editions of Algebra, the cover was red, and until the 2005 edition the illustrations were originally created by the Cuban artist D.G. Terminel. The cover featured the Persian Muslim mathematician Al-Khwarizmi and, in the background, a depiction of


id: algorithmic-combinatorics-on-partial-words-20260505-0
file: data/en.wikipedia.org/wiki/Algorithmic_Combinatorics_on_Partial_Words-0.md
category: reference
title: Algorithmic Combinatorics on Partial Words
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Algorithmic_Combinatorics_on_Partial_Words
date_saved: 2026-05-05T08:43:12.362150+00:00
instance: kb-cron
parent: algorithmic-combinatorics-on-partial-words-20260505-0
summary:
Algorithmic Combinatorics on Partial Words is a book in the area of combinatorics on words, and more specifically on partial words. It was written by Francine Blanchet-Sadri, and published in 2007 by Chapman & Hall/CRC in their Discrete Mathematics and its Applications book series. == Topics == A partial word is a string whose characters may either belong to a given alphabet or be a wildcard character. Such a word can represent a set of strings over the alphabet without wildcards, by allowing each wildcard character to be replaced by any single character of the alphabet, independently of the replacements of the other wildcard characters. Two partial words are compatible when they agree on their non-wildcard characters, or equivalently when there is a string that they both match; one partial word x {\displaystyle x} contains another partial word y {\displaystyle y} if they are compatible and the non-wildcard positions of x {\displaystyle x} contain those of y {\displaystyle y} ; equivalently, the strings matched by x {\displaystyle x} are a subset of those matched by y {\displaystyle y} . The book has 12 chapters, which can be grouped into five larger parts. The first part consists of two introductory chapters


id: the-analyst-20260505-0
file: data/en.wikipedia.org/wiki/The_Analyst-0.md
category: reference
title: The Analyst
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/The_Analyst
date_saved: 2026-05-05T08:43:13.533929+00:00
instance: kb-cron
parent: the-analyst-20260505-0
summary:
The Analyst: A Discourse Addressed to an Infidel Mathematician: Wherein It Is Examined Whether the Object, Principles, and Inferences of the Modern Analysis Are More Distinctly Conceived, or More Evidently Deduced, Than Religious Mysteries and Points of Faith, is a book by George Berkeley. It was first published in 1734, first by J. Tonson (London), then by S. Fuller (Dublin). The "infidel mathematician" is believed to have been Edmond Halley, though others have speculated that Isaac Newton was intended. The book contains a direct attack on the foundations of calculus, specifically on Isaac Newton's notion of fluxions and on Leibniz's notion of infinitesimal change. == Background and purpose == From his earliest days as a writer, Berkeley had taken up his satirical pen to attack what were then called 'free-thinkers' (secularists, sceptics, agnostics, atheists, etc.—in short, anyone who doubted the truths of received Christian religion or called for a diminution of religion in public life). In 1732, in the latest installment in this effort, Berkeley published his Alciphron, a series of dialogues directed at different types of 'free-thinkers'. One of the archetypes Berkeley addressed was the secular scientist, who discarded Christian mysteries as unnecessary superstitions, and declared his confidence in


id: the-analyst-20260505-1
file: data/en.wikipedia.org/wiki/The_Analyst-1.md
category: reference
title: The Analyst
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/The_Analyst
date_saved: 2026-05-05T08:43:13.533929+00:00
instance: kb-cron
parent: the-analyst-20260505-0
summary:
== Influence == Two years after this publication, Thomas Bayes published anonymously "An Introduction to the Doctrine of Fluxions, and a Defence of the Mathematicians Against the Objections of the Author of the Analyst" (1736), in which he defended the logical foundation of Isaac Newton's calculus against the criticism outlined in The Analyst. Colin Maclaurin's two-volume Treatise of Fluxions published in 1742 also began as a response to Berkeley attacks, intended to show that Newton's calculus was rigorous by reducing it to the methods of Greek geometry. Despite these attempts, calculus continued to be developed using non-rigorous methods until around 1830 when Augustin Cauchy, and later Bernhard Riemann and Karl Weierstrass, redefined the derivative and integral using a rigorous definition of the concept of limit. The idea of using limits as a foundation for calculus had been suggested by d'Alembert, but d'Alembert's definition was not rigorous by modern standards. The concept of limits had already appeared in the work of Newton, but was not stated with sufficient clarity to hold up to the criticism of Berkeley. In 1966, Abraham Robinson introduced Non-standard Analysis, which provided a rigorous foundation for working with infinitely small quantities. This provided another way of putting


id: analytic-combinatorics-book-20260505-0
file: data/en.wikipedia.org/wiki/Analytic_Combinatorics_(book)-0.md
category: reference
title: Analytic Combinatorics (book)
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Analytic_Combinatorics_(book)
date_saved: 2026-05-05T08:43:14.662379+00:00
instance: kb-cron
parent: analytic-combinatorics-book-20260505-0
summary:
Analytic Combinatorics is a book on the mathematics of combinatorial enumeration, using generating functions and complex analysis to understand the growth rates of the numbers of combinatorial objects. It was written by Philippe Flajolet and Robert Sedgewick, and published by the Cambridge University Press in 2009. It won the Leroy P. Steele Prize in 2019. == Topics == The main part of the book is organized into three parts. The first part, covering three chapters and roughly the first quarter of the book, concerns the symbolic method in combinatorics, in which classes of combinatorial objects are associated with formulas that describe their structures, and then those formulas are reinterpreted to produce the generating functions or exponential generating functions of the classes, in some cases using tools such as the Lagrange inversion theorem as part of the reinterpretation process. The chapters in this part divide the material into the enumeration of unlabeled objects, the enumeration of labeled objects, and multivariate generating functions. The five chapters of the second part of the book, roughly half of the text and "the heart of the book", concern the application of tools from complex analysis to the generating function, in order to understand the asymptotics


id: animal-math-20260505-0
file: data/en.wikipedia.org/wiki/Animal_Math-0.md
category: reference
title: Animal Math
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Animal_Math
date_saved: 2026-05-05T08:43:15.889648+00:00
instance: kb-cron
parent: animal-math-20260505-0
summary:
Animal Math is an educational book series featuring baby animals that introduces reader to mathematic principles. The series consists of five books: Tiger Math (2000), Chimp Math (2002), Polar Bear Math (2004), Panda Math (2005), and Cheetah Math (2007). On the right-hand pages, the books tell stories of baby animals cared for at either the Denver Zoo or San Diego Zoo who needed extra care when they were young. The left-hand pages discuss basic mathematic concepts using the animals as examples in problems. Published by Henry Holt and Company, the books are authored by Ann Whitehead Nagda, with support from Cindy Bickel, an assistant at the Denver Zoo, or in collaboration with the San Diego Zoo. == Books == === Tiger Math (2000) === Tiger Math: Learning to Graph from a Baby Tiger (2000), co-written by Ann Whitehead Nagda and Cindy Bickel, teaches students about different types of graphs, including bar graphs, line graphs, picture graphs, and pie charts. The book features the Siberian tiger cub T. J., who was born at the Denver Zoo, then struggled to eat after his mother died. Tiger Math is a Junior Library Guild book. Kirkus Reviews said the book provided "a delightful way


id: the-annotated-turing-20260505-0
file: data/en.wikipedia.org/wiki/The_Annotated_Turing-0.md
category: reference
title: The Annotated Turing
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/The_Annotated_Turing
date_saved: 2026-05-05T08:43:17.061886+00:00
instance: kb-cron
parent: the-annotated-turing-20260505-0
summary:
The Annotated Turing: A Guided Tour Through Alan Turing's Historic Paper on Computability and the Turing Machine is a book by Charles Petzold, published in 2008 by John Wiley & Sons, Inc. Petzold annotates Alan Turing's paper "On Computable Numbers, with an Application to the Entscheidungsproblem". The book takes readers sentence by sentence through Turing's paper, providing explanations, further examples, corrections, and biographical information. == Table of contents == Part I. Foundations Chapter 1: This Tomb Holds Diophantus Chapter 2: The Irrational and the Transcendental Chapter 3: Centuries of Progress Part II. Computable Numbers Chapter 4: The Education of Alan Turing Chapter 5: Machines at Work Chapter 6: Addition and Multiplication Chapter 7: Also Known as Subroutines Chapter 8: Everything is a Number Chapter 9: The Universal Machine Chapter 10: Computers and Computability Chapter 11: Of Machines and Men Part III. Das Entscheidungsproblem Chapter 12: Logic and Computability Chapter 13: Computable Functions Chapter 14: The Major Proof Chapter 15: The Lambda Calculus Chapter 16: Conceiving the Continuum Part IV. And Beyond Chapter 17: Is Everything a Turing Machine? Chapter 18: The Long Sleep of Diophantus == See also == Alan Turing: The Enigma (1983) Prof: Alan Turing Decoded (2015) The


id: antiquarian-science-books-20260505-0
file: data/en.wikipedia.org/wiki/Antiquarian_science_books-0.md
category: reference
title: Antiquarian science books
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Antiquarian_science_books
date_saved: 2026-05-05T08:43:18.246965+00:00
instance: kb-cron
parent: antiquarian-science-books-20260505-0
summary:
Antiquarian science books are original historical works (e.g., books or technical papers) concerning science, mathematics and sometimes engineering. These books are important primary references for the study of the history of science and technology, they can provide valuable insights into the historical development of the various fields of scientific inquiry (History of science, History of mathematics, etc.) The landmark are significant first (or early) editions typically worth hundreds or thousands of dollars (prices may vary widely based on condition, etc.). Reprints of these books are often available, for example from Great Books of the Western World, Dover Publications or Google Books. Incunabula are extremely rare and valuable, but as the Scientific Revolution is only taken to have started around the 1540s, such works of Renaissance literature (including alchemy, Renaissance magic, etc.) are not usually included under the notion of "scientific" literature. Printed originals of the beginning Scientific Revolution thus date to the 1540s or later, notably beginning with the original publication of Copernican heliocentrism. Nicolaus Copernicus' De revolutionibus orbium coelestium of 1543 sold for more than US$2 million at auctions. == List of notable books == === 16th century === Tartaglia, Niccolò. Nova Scientia (A New Science). Venice, 1537. Ballistics.


id: antiquarian-science-books-20260505-1
file: data/en.wikipedia.org/wiki/Antiquarian_science_books-1.md
category: reference
title: Antiquarian science books
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Antiquarian_science_books
date_saved: 2026-05-05T08:43:18.246965+00:00
instance: kb-cron
parent: antiquarian-science-books-20260505-0
summary:
=== 19th century === Gauss, Carl Friedrich (Germany). Disquisitiones Arithmeticae. Leipzig, 1801. Number theory Young, Thomas (England). Experiments and Calculations Relative to Physical Optics, 1803. Light Argand, Jean-Robert (Switzerland). Essai sur une maniere de representer les quantities imaginaries dans les constructions geometriques, 1806. Imaginary numbers. Dalton, John (England). A New System of Chemical Philosophy. London, 1808. Atomic theory Berzelius, Jöns Jacob (Sweden). Läroboken i kemien, 1808. Chemistry Cayley, George (England). On Aerial Navigation. Brompton, 3 Vol, 1809. Aeronautics. Ørsted, Hans Christian (Denmark). Experimenta circa effectum conflictus electrici in acum magneticam. Copenhagen, 1820. Electromagnetism. Fourier, Joseph (France). Théorie Analytique de la Chaleur. Paris, 1822. Fourier series. Fresnel, Augustin-Jean (France). Mémoire Sur Un Nouveau Système D'Éclairage Des Phares Lu À L'Académie Des Sciences. Paris, 1822. Wave optics Babbage, Charles (England). Mr. Babbage's invention: Application of machinery to the purpose of calculating and printing mathematical tables. London, 1823. Computing Lobachevsky, Nikolai (Russia). Geometriya. 1823. Non-Euclidean geometry Cauchy, Augustin-Louis (France). Le calcul infinitesimal. Paris, 1823. Mathematical analysis Carnot, Sadi (France). Réflexions sur la Puissance Motrice du Feu et sur les machines propres à déveloper cette puissance. Paris, 1824. Thermodynamics Ampère, André-Marie (France). Mémoire sur la théorie mathématique des phénomènes électrodynamiques, 1827. Electromagnetism Laplace, Pierre-Simon


id: antiquarian-science-books-20260505-2
file: data/en.wikipedia.org/wiki/Antiquarian_science_books-2.md
category: reference
title: Antiquarian science books
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Antiquarian_science_books
date_saved: 2026-05-05T08:43:18.246965+00:00
instance: kb-cron
parent: antiquarian-science-books-20260505-0
summary:
=== 20th century (pre-Cold War) === Planck, Max (Germany). Zur Theorie des Gesetzes der Energieverteilung im Normalspectrum. Leipzig, 1900. Quantum mechanics Tsiolkovsky, Konstantin Eduardovich (Russia). The Exploration of Cosmic Space by Means of Reaction Devices. Kaluga, 1903. Rockets Rutherford, Ernest (New Zealand). Radio-activity. Cambridge, 1904. Nuclear physics Lorentz, Hendrik (Netherlands). Electromagnetic phenomena in a system moving with any velocity smaller than that of light. Amsterdam, 1904. Special relativity Einstein, Albert (Germany). Zur Elektrodynamik bewegter Körper ("On the Electrodynamics of Moving Bodies") Leipzig, 1905. Special relativity Einstein, Albert (Germany). Does the Inertia of a Body Depend Upon Its Energy Content? Leipzig, 1905. Physics Richardson, Lewis (England). The Approximate Arithmetical Solution by Finite Differences of Physical Problems Involving Differential Equations, with an Application to the Stresses in a Masonry Dam. London, 1910. Computational mechanics Boas, Franz (Germany/America). The Mind of Primitive Man. New York, 1911. Anthropology Bohr, Niels (Denmark). On the Constitution of Atoms and Molecules. London, 1913. Quantum mechanics Einstein, Albert (Germany). Die Grundlage Der Allgemeinen Relativitätstheorie (Foundations of the General Theory of Relativity). Leipzig, 1916. Physics. Goddard, Robert Hutchings (America). A Method of Reaching Extreme Altitudes. Washington, D.C, 1919. Rockets de Broglie, Louis (France). Recherches sur la théorie des quanta


id: arithmetica-universalis-20260505-0
file: data/en.wikipedia.org/wiki/Arithmetica_Universalis-0.md
category: reference
title: Arithmetica Universalis
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Arithmetica_Universalis
date_saved: 2026-05-05T08:43:21.752199+00:00
instance: kb-cron
parent: arithmetica-universalis-20260505-0
summary:
Arithmetica Universalis ("Universal Arithmetic") is a mathematics text by Isaac Newton. Written in Latin, it was edited and published by William Whiston, Newton's successor as Lucasian Professor of Mathematics at the University of Cambridge. The Arithmetica was based on Newton's lecture notes. == Publication history == Whiston's original edition was published in 1707. It was translated into English by Joseph Raphson, who published it in 1720 as the Universal Arithmetick. John Machin published a second Latin edition in 1722. == Lack of credit for the writer == None of these editions credit Newton as author; Newton was unhappy with the publication of the Arithmetica, and so refused to have his name appear. In fact, when Whiston's edition was published, Newton was so upset he considered purchasing all of the copies so he could destroy them. == Content == The Arithmetica touches on algebraic notation, arithmetic, the relationship between geometry and algebra, and the solution of equations. Newton also applied Descartes' rule of signs to imaginary roots. He also offered, without proof, a rule to determine the number of imaginary roots of polynomial equations. A rigorous proof of Newton's counting formula for equations up to and including the fifth degree was


id: ars-magna-cardano-book-20260505-0
file: data/en.wikipedia.org/wiki/Ars_Magna_(Cardano_book)-0.md
category: reference
title: Ars Magna (Cardano book)
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Ars_Magna_(Cardano_book)
date_saved: 2026-05-05T08:43:22.876678+00:00
instance: kb-cron
parent: ars-magna-cardano-book-20260505-0
summary:
The Ars Magna (The Great Art, 1545) is an important Latin-language book on algebra written by Gerolamo Cardano. It was first published in 1545 under the title Artis Magnae, Sive de Regulis Algebraicis, Lib. unus (The Great Art, or The Rules of Algebra, Book one). There was a second edition in Cardano's lifetime, published in 1570. It is considered one of the three greatest scientific treatises of the early Renaissance, together with Copernicus' De revolutionibus orbium coelestium and Vesalius' De humani corporis fabrica. The first editions of these three books were published within a two-year span (1543–1545). == History == In 1535, Niccolò Fontana Tartaglia became famous for having solved cubics of the form x3 + ax = b (with a,b > 0). However, he chose to keep his method secret. In 1539, Cardano, then a lecturer in mathematics at the Piatti Foundation in Milan, published his first mathematical book, Pratica Arithmeticæ et mensurandi singularis (The Practice of Arithmetic and Simple Mensuration). That same year, he asked Tartaglia to explain to him his method for solving cubic equations. After some reluctance, Tartaglia did so, but he asked Cardano not to share the information until he published it. Cardano submerged himself


id: art-gallery-theorems-and-algorithms-20260505-0
file: data/en.wikipedia.org/wiki/Art_Gallery_Theorems_and_Algorithms-0.md
category: reference
title: Art Gallery Theorems and Algorithms
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Art_Gallery_Theorems_and_Algorithms
date_saved: 2026-05-05T08:43:24.102157+00:00
instance: kb-cron
parent: art-gallery-theorems-and-algorithms-20260505-0
summary:
Art Gallery Theorems and Algorithms is a mathematical monograph on topics related to the art gallery problem, on finding positions for guards within a polygonal museum floorplan so that all points of the museum are visible to at least one guard, and on related problems in computational geometry concerning polygons. It was written by Joseph O'Rourke, and published in 1987 in the International Series of Monographs on Computer Science of the Oxford University Press. Only 1000 copies were produced before the book went out of print, so to keep this material accessible O'Rourke has made a pdf version of the book available online. == Topics == The art gallery problem, posed by Victor Klee in 1973, asks for the number of points at which to place guards inside a polygon (representing the floor plan of a museum) so that each point within the polygon is visible to at least one guard. Václav Chvátal provided the first proof that the answer is at most ⌊ n / 3 ⌋ {\displaystyle \lfloor n/3\rfloor } for a polygon with n {\displaystyle n} corners, but a simplified proof by Steve Fisk based on graph coloring and polygon triangulation is more widely known. This is


id: automorphic-forms-on-gl-2-20260505-0
file: data/en.wikipedia.org/wiki/Automorphic_Forms_on_GL(2)-0.md
category: reference
title: Automorphic Forms on GL(2)
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Automorphic_Forms_on_GL(2)
date_saved: 2026-05-05T08:43:25.244788+00:00
instance: kb-cron
parent: automorphic-forms-on-gl-2-20260505-0
summary:
Automorphic Forms on GL(2) is a mathematics book by H. Jacquet and Robert Langlands (1970) where they rewrite Erich Hecke's theory of modular forms in terms of the representation theory of GL(2) over local fields and adele rings of global fields and prove the Jacquet–Langlands correspondence. A second volume by Jacquet (1972) gives an interpretation of some results by Rankin and Selberg in terms of the representation theory of GL(2) × GL(2). == References == Godement, R. (1970), Notes on Jacquet–Langlands' theory, Institute for Advanced Study Jacquet, H; Langlands, R. P. (1970), Automorphic Forms on GL (2), Lecture Notes in Mathematics, vol. 114, Berlin-New York: Springer-Verlag, doi:10.1007/BFb0058988, ISBN 978-3540049036, MR 0401654, S2CID 122773458 Jacquet, Hervé (1972), Automorphic Forms on GL(2) Part II, Lecture Notes in Mathematics, vol. 278, Berlin-New York: Springer-Verlag, doi:10.1007/BFb0058503, ISBN 978-3-540-05931-8, MR 0562503 Langlands, R. (1971), "Automorphic forms on GL(2)" (PDF), Actes du Congrès International des Mathématiciens (Nice, 1970), vol. 2, Paris: Gauthier-Villars, pp. 327–329, MR 0562505 == External links == Buzzard, Kevin (2012), What is in the book Automorphic forms on GL(2) by Jacquet and Langlands? (PDF)


id: the-banach-tarski-paradox-book-20260505-0
file: data/en.wikipedia.org/wiki/The_Banach–Tarski_Paradox_(book)-0.md
category: reference
title: The Banach–Tarski Paradox (book)
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/The_Banach–Tarski_Paradox_(book)
date_saved: 2026-05-05T08:43:26.367041+00:00
instance: kb-cron
parent: the-banach-tarski-paradox-book-20260505-0
summary:
The Banach–Tarski Paradox is a book in mathematics on the Banach–Tarski paradox, the fact that a unit ball can be partitioned into a finite number of subsets and reassembled to form two unit balls. It was written by Stan Wagon and published in 1985 by the Cambridge University Press as volume 24 of their Encyclopedia of Mathematics and its Applications book series. A second printing in 1986 added two pages as an addendum, and a 1993 paperback printing added a new preface. In 2016 the Cambridge University Press published a second edition, adding Grzegorz Tomkowicz as a co-author, as volume 163 of the same series. The Basic Library List Committee of the Mathematical Association of America has recommended its inclusion in undergraduate mathematics libraries. == Topics == The Banach–Tarski paradox, proved by Stefan Banach and Alfred Tarski in 1924, states that it is possible to partition a three-dimensional unit ball into finitely many pieces and reassemble them into two unit balls, a single ball of larger or smaller area, or any other bounded set with a non-empty interior. Although it is a mathematical theorem, it is called a paradox because it is so counter-intuitive; in the preface to the book,


id: basic-number-theory-20260505-0
file: data/en.wikipedia.org/wiki/Basic_Number_Theory-0.md
category: reference
title: Basic Number Theory
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Basic_Number_Theory
date_saved: 2026-05-05T08:43:27.589697+00:00
instance: kb-cron
parent: basic-number-theory-20260505-0
summary:
Basic Number Theory is an influential book by André Weil, an exposition of algebraic number theory and class field theory with particular emphasis on valuation-theoretic methods. Based in part on a course taught at Princeton University in 1961–62, it appeared as Volume 144 in Springer's Grundlehren der mathematischen Wissenschaften series. The approach handles all 'A-fields' or global fields, meaning finite algebraic extensions of the field of rational numbers and of the field of rational functions of one variable with a finite field of constants. The theory is developed in a uniform way, starting with topological fields, properties of Haar measure on locally compact fields, the main theorems of adelic and idelic number theory, and class field theory via the theory of simple algebras over local and global fields. The word `basic’ in the title is closer in meaning to `foundational’ rather than `elementary’, and is perhaps best interpreted as meaning that the material developed is foundational for the development of the theories of automorphic forms, representation theory of algebraic groups, and more advanced topics in algebraic number theory. The style is austere, with a narrow concentration on a logically coherent development of the theory required, and essentially no examples. ==


id: basic-number-theory-20260505-1
file: data/en.wikipedia.org/wiki/Basic_Number_Theory-1.md
category: reference
title: Basic Number Theory
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Basic_Number_Theory
date_saved: 2026-05-05T08:43:27.589697+00:00
instance: kb-cron
parent: basic-number-theory-20260505-0
summary:
== Contents == Roughly speaking, the first half of the book is modern in its consistent use of adelic and idèlic methods and the simultaneous treatment of algebraic number fields and rational function fields over finite fields. The second half is arguably pre-modern in its development of simple algebras and class field theory without the language of cohomology, and without the language of Galois cohomology in particular. The author acknowledges this as a trade-off, explaining that “to develop such an approach systematically would have meant loading a great deal of unnecessary machinery on a ship which seemed well equipped for this particular voyage; instead of making it more seaworthy, it might have sunk it.” The treatment of class field theory uses analytic methods on both commutative fields and simple algebras. These methods show their power in giving the first unified proof that if K/k is a finite normal extension of A-fields, then any automorphism of K over k is induced by the Frobenius automorphism for infinitely many places of K. This approach also allows for a significantly simpler and more logical proof of algebraic statements, for example the result that a simple algebra over an A-field splits (globally) if and


id: the-beauty-of-fractals-20260505-0
file: data/en.wikipedia.org/wiki/The_Beauty_of_Fractals-0.md
category: reference
title: The Beauty of Fractals
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/The_Beauty_of_Fractals
date_saved: 2026-05-05T08:43:28.808626+00:00
instance: kb-cron
parent: the-beauty-of-fractals-20260505-0
summary:
The Beauty of Fractals is a 1986 book by Heinz-Otto Peitgen and Peter Richter which publicises the fields of complex dynamics, chaos theory and the concept of fractals. It is lavishly illustrated and as a mathematics book became an unusual success. The book includes a total of 184 illustrations, including 88 full-colour pictures of Julia sets. Although the format suggests a coffee table book, the discussion of the background of the presented images addresses some sophisticated mathematics which would not be found in popular science books. In 1987 the book won an Award for distinguished technical communication. == Summary == The book starts with a general introduction to Complex Dynamics, Chaos and fractals. In particular the Feigenbaum scenario and the relation to Julia sets and the Mandelbrot set is discussed. The following special sections provide in depth detail for the shown images: Verhulst Dynamics, Julia Sets and Their Computergraphical Generation, Sullivan's Classification of Critical Points, The Mandelbrot Set, External Angles and Hubbard Trees, Newton's Method for Complex Polynomials: Cayley's Problem, Newtons's Method for Real Equations, A Discrete Volterra-Lotka System, Yang-Lee Zeros, Renormalization (Magnetism and Complex Boundaries). The book also includes invited Contributions by Benoît Mandelbrot, Adrien Douady, Gert Eilenberger and


id: black-mathematicians-and-their-works-20260505-0
file: data/en.wikipedia.org/wiki/Black_Mathematicians_and_Their_Works-0.md
category: reference
title: Black Mathematicians and Their Works
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Black_Mathematicians_and_Their_Works
date_saved: 2026-05-05T08:43:31.112492+00:00
instance: kb-cron
parent: black-mathematicians-and-their-works-20260505-0
summary:
Black Mathematicians and Their Works is an edited volume of works in and about mathematics, by African-American mathematicians. It was edited by Virginia Newell, Joella Gipson, L. Waldo Rich, and Beauregard Stubblefield, with a foreword by Wade Ellis, and published in 1980 by Dorrance & Company. The Basic Library List Committee of the Mathematical Association of America has recommended its inclusion in undergraduate mathematics libraries. == Contents == The book celebrates the achievements of black mathematicians and also records their struggle against racism. It includes reprints of 23 papers of mathematics research and three more on mathematics education, by black mathematicians. It provides brief biographies and photographs of 62 black mathematicians, all long-established at the time of publication (having doctorates prior to 1973). It also reproduces several letters by Lee Lorch documenting racist behavior in mathematical societies, such as exclusion from conferences and their associated social gatherings. An appendix lists universities that have worked with black mathematicians, by the number of doctorates conferred and the number of faculty hired. As well as two of the editors (Gipson and Stubblefield), the authors whose works are reproduced in the book include Albert Turner Bharucha-Reid, David Blackwell, Lillian K. Bradley, Marjorie Lee Browne,


id: the-book-of-numbers-math-book-20260505-0
file: data/en.wikipedia.org/wiki/The_Book_of_Numbers_(math_book)-0.md
category: reference
title: The Book of Numbers (math book)
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/The_Book_of_Numbers_(math_book)
date_saved: 2026-05-05T08:43:32.292880+00:00
instance: kb-cron
parent: the-book-of-numbers-math-book-20260505-0
summary:
The Book of Numbers is a 1996 mathematics book by John H. Conway and Richard K. Guy. It discusses individual numbers, and types of number, that have proved conceptually significant. Topics include the origin of the nursery rhyme "Hickory Dickory Dock", figurate numbers, the Fibonacci sequence, transcendental numbers, the Metonic cycle, combinatorics, the complex plane, nimbers, and surreal numbers. The Basic Library List Committee of the Mathematical Association of America has recommended that it be included in undergraduate mathematics libraries. == Reception == Andrew Bremner called the book "a delight" and opined that readers of Martin Gardner would appreciate it. A. Robert Pargeter found it "fascinating" both for systematic reading and for browsing, and he recommended that school and college libraries carry it. Sarah Gourlie called the book "organized and enlightening", while observing that some topics were considerably more demanding than others. Likewise, reviewing the book for the Mathematical Association of America, Allen Stenger noted that while the book only presumed knowledge of high-school algebra and trigonometry, it also in places demanded a "high level of mathematical reasoning". Stenger expected that many readers would be unable to follow all of the explanations unaided. A retrospective by Ezra Brown also commented


id: the-book-of-squares-20260505-0
file: data/en.wikipedia.org/wiki/The_Book_of_Squares-0.md
category: reference
title: The Book of Squares
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/The_Book_of_Squares
date_saved: 2026-05-05T08:43:33.488575+00:00
instance: kb-cron
parent: the-book-of-squares-20260505-0
summary:
The Book of Squares, (Liber Quadratorum in the original Latin) is a book on algebra by Leonardo Fibonacci, published in 1225. It was dedicated to Frederick II, Holy Roman Emperor. After being brought to Pisa by Master Dominick to the feet of your celestial majesty, most glorious prince, Lord F., The Liber quadratorum has been passed down by a single 15th-century manuscript, the so-called ms. E 75 Sup. of the Biblioteca Ambrosiana (Milan, Italy), ff. 19r–39v. During the 19th century, the work was published for the first time in a printed edition by Baldassarre Boncompagni Ludovisi, prince of Piombino. Appearing in the book is Fibonacci's identity, establishing that the set of all sums of two squares is closed under multiplication. The book anticipated the works of later mathematicians such as Fermat and Euler. The book examines several topics in number theory, among them an inductive method for finding Pythagorean triples based on the sequence of odd integers, the fact that the sum of the first n {\displaystyle n} odd integers is n 2 {\displaystyle n^{2}} , and the solution to the congruum problem. == Notes == == Further reading == B. Boncompagni Ludovisi, Opuscoli di Leonardo Pisano secondo un codice


id: book-on-numbers-and-computation-20260505-0
file: data/en.wikipedia.org/wiki/Book_on_Numbers_and_Computation-0.md
category: reference
title: Book on Numbers and Computation
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Book_on_Numbers_and_Computation
date_saved: 2026-05-05T08:43:34.610392+00:00
instance: kb-cron
parent: book-on-numbers-and-computation-20260505-0
summary:
The Book on Numbers and Computation (Chinese: 筭數書; pinyin: Suàn shù shū), or the Writings on Reckoning, is one of the earliest known Chinese mathematical treatises. It was written during the early Western Han dynasty, sometime between 202 BC and 186 BC. It was preserved among the Zhangjiashan Han bamboo texts and contains similar mathematical problems and principles found in the later Eastern Han period text of The Nine Chapters on the Mathematical Art. == Discovery == The text was found in tomb M247 of the burial grounds near Zhangjiashan, Jiangling County, in Hubei province, excavated in December–January 1983–1984. This tomb belonged to an anonymous civil servant in early West Han dynasty. In the tomb were 1200 bamboo strips written in ink. Originally the strips were bound together with string, but the string had rotted away and it took Chinese scholars 17 years to piece together the strips. As well as the mathematical work the strips covered government statutes, law reports and therapeutic gymnastics. On the back of the sixth strip, the top has a black square mark, followed by the three characters 筭數書, which serve as the title of the rolled up book. == Content == The Suàn shù


id: braids-links-and-mapping-class-groups-20260505-0
file: data/en.wikipedia.org/wiki/Braids,_Links,_and_Mapping_Class_Groups-0.md
category: reference
title: Braids, Links, and Mapping Class Groups
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Braids,_Links,_and_Mapping_Class_Groups
date_saved: 2026-05-05T08:43:35.756825+00:00
instance: kb-cron
parent: braids-links-and-mapping-class-groups-20260505-0
summary:
Braids, Links, and Mapping Class Groups is a mathematical monograph on braid groups and their applications in low-dimensional topology. It was written by Joan Birman, and published in 1974 by the Princeton University Press and University of Tokyo Press, as volume 82 of the book series Annals of Mathematics Studies. Although braid groups had been introduced in 1891 by Adolf Hurwitz and formalized in 1925 by Emil Artin, this was the first book devoted to them. It has been described as a "seminal work", one that "laid the foundations for several new subfields in topology". == Topics == Braids, Links, and Mapping Class Groups is organized into five chapters and an appendix. The first introductory chapter defines braid groups, configuration spaces, and the use of configuration spaces to define braid groups on arbitrary two-dimensional manifolds. It provides a solution to the word problem for braids, the question of determining whether two different-looking braid presentations really describe the same group element. It also describes the braid groups as automorphism groups of free groups and of multiply-punctured disks. The next three chapters present connections of braid groups to three different areas of mathematics. Chapter 2 concerns applications to knot theory, via Alexander's


id: the-calculating-machines-20260505-0
file: data/en.wikipedia.org/wiki/The_Calculating_Machines-0.md
category: reference
title: The Calculating Machines
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/The_Calculating_Machines
date_saved: 2026-05-05T08:43:36.966881+00:00
instance: kb-cron
parent: the-calculating-machines-20260505-0
summary:
Die Rechenmaschinen, by Ernst Martin, and its English translation, The Calculating Machines (Die Rechenmaschinen): Their History and Development, are books on mechanical desktop calculators from prior to World War II. == Publication history == Die Rechenmaschinen, the original book by Martin, was published in 1925, and revised in 1937. Both editions are very rare. Little is known about Martin beyond these books. The 1925 edition was edited and translated into English by Peggy A. Kidwell and Michael R. Williams, and published in 1992 by the MIT Press as the final 16th volume of its The Charles Babbage Institute Reprint Series for the History of Computing (ISBN 0-262-13278-8). Kidwell and Williams chose this edition, rather than the revised edition, because of "the rarity of the books and the poor condition of the illustrations in extant copies". Indeed, they were only able to locate three copies of Martin's book. The book and its translation includes many illustrations, and the translation preserves some idiosyncrasies of the original work, including a set of advertisements for calculating machines at the end of the book. == Topics == After an introduction grouping calculating machines into seven types, the book describes over 200 machines, comprising "almost every


id: calendrical-calculations-20260505-0
file: data/en.wikipedia.org/wiki/Calendrical_Calculations-0.md
category: reference
title: Calendrical Calculations
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Calendrical_Calculations
date_saved: 2026-05-05T08:43:38.156804+00:00
instance: kb-cron
parent: calendrical-calculations-20260505-0
summary:
Calendrical Calculations is a book on calendar systems and algorithms for computers to convert between them. It was written by computer scientists Nachum Dershowitz and Edward Reingold and published in 1997 by the Cambridge University Press. A second "millennium" edition with a CD-ROM of software was published in 2001, a third edition in 2008, and a fourth "ultimate" edition in 2018. == Topics == There have been many different calendars in different societies, and there is much difficulty in converting between them, largely because of the impossibility of reconciling the irrational ratios of the daily, monthly, and yearly astronomical cycle lengths using integers. The 14 calendars discussed in the first edition of the book included the Gregorian calendar, ISO week date, Julian calendar, Coptic calendar, Ethiopian calendar, Islamic calendar, modern Iranian calendar, Baháʼí calendar, French Republican calendar, old and modern Hindu calendars, Maya calendar, and modern Chinese calendar. Later editions expanded it to many more calendars. They are divided into two groups: "arithmetical" calendars, whose calculations can be performed purely mathematically, independently from the positions of the moon and sun, and "astronomical" calendars, based in part on those positions. The authors design individual calendrical calculation algorithms for converting each of


id: canon-arithmeticus-20260505-0
file: data/en.wikipedia.org/wiki/Canon_arithmeticus-0.md
category: reference
title: Canon arithmeticus
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Canon_arithmeticus
date_saved: 2026-05-05T08:43:39.276631+00:00
instance: kb-cron
parent: canon-arithmeticus-20260505-0
summary:
The Canon arithmeticus is a set of mathematical tables of indices and powers with respect to primitive roots for prime powers less than 1000, originally published by Carl Gustav Jacob Jacobi (1839), with introductory text in Latin. The tables were at one time used for arithmetical calculations modulo prime powers, though like many mathematical tables, they have now been replaced by digital computers. Jacobi also reproduced Burkhardt's table of the periods of decimal fractions of 1/p and Ostrogradsky's tables of primitive roots of primes less than 200 and gave tables of indices of some odd numbers modulo powers of 2 with respect to the base 3 (Dickson 2005, p. 185–186). Although the second edition of 1956 has Jacobi's name on the title, it has little in common with the first edition apart from the topic: the tables were completely recalculated, usually with a different choice of primitive root, by Wilhelm Patz. Jacobi's original tables use 10 or −10 or a number with a small power of this form as the primitive root whenever possible, while the second edition uses the smallest possible positive primitive root (Fletcher 1958). The term "canon arithmeticus" is occasionally used to mean any table of indices


id: cardinal-and-ordinal-numbers-20260505-0
file: data/en.wikipedia.org/wiki/Cardinal_and_Ordinal_Numbers-0.md
category: reference
title: Cardinal and Ordinal Numbers
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Cardinal_and_Ordinal_Numbers
date_saved: 2026-05-05T08:43:40.431703+00:00
instance: kb-cron
parent: cardinal-and-ordinal-numbers-20260505-0
summary:
Cardinal and Ordinal Numbers is a book on transfinite numbers, by Polish mathematician Wacław Sierpiński. It was published in 1958 by Państwowe Wydawnictwo Naukowe, as volume 34 of the series Monografie Matematyczne of the Institute of Mathematics of the Polish Academy of Sciences. Sierpiński wrote on the same topic earlier, in his 1928 book Leçons sur les nombres transfinis, but his 1958 book on the topic was completely rewritten and significantly longer. A second edition of Cardinal and Ordinal Numbers was published in 1965. == Topics == After five introductory chapters on naive set theory and set-theoretic notation, and a sixth chapter on the axiom of choice, the book has four chapters on cardinal numbers, their arithmetic, and series and products of cardinal numbers, comprising approximately 50 pages. Following this, four longer chapters (totalling roughly 180 pages) cover orderings of sets, order types, well-orders, ordinal numbers, ordinal arithmetic, and the Burali-Forti paradox according to which the collection of all ordinal numbers cannot be a set. Three final chapters concern aleph numbers and the continuum hypothesis, statements equivalent to the axiom of choice, and consequences of the axiom of choice. The second edition makes only minor changes to the first except


id: chases-and-escapes-20260505-0
file: data/en.wikipedia.org/wiki/Chases_and_Escapes-0.md
category: reference
title: Chases and Escapes
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Chases_and_Escapes
date_saved: 2026-05-05T08:43:41.600966+00:00
instance: kb-cron
parent: chases-and-escapes-20260505-0
summary:
Chases and Escapes: The Mathematics of Pursuit and Evasion is a mathematics book on continuous pursuit–evasion problems. It was written by Paul J. Nahin, and published by the Princeton University Press in 2007. It was reissued as a paperback reprint in 2012. The Basic Library List Committee of the Mathematical Association of America has rated this book as essential for inclusion in undergraduate mathematics libraries. == Topics == The book has four chapters, covering the solutions to 21 continuous pursuit–evasion problems, with an additional 10 "challenge problems" left for readers to solve, with solutions given in an appendix. The problems are presented as entertaining stories that "breathe life into the mathematics and invite wider engagement", and their solutions use varied methods, including the computer calculation of numerical solutions for differential equations whose solutions have no closed form. Most of the material was previously known, but is collected here for the first time. The book also provides background material on the history of the problems it describes, although this is not its main focus. Even before beginning its main content, the preface of the book begins with an example of pure evasion from known pursuit, the path used by the Enola


id: chicka-chicka-1-2-3-20260505-0
file: data/en.wikipedia.org/wiki/Chicka_Chicka_1,_2,_3-0.md
category: reference
title: Chicka Chicka 1, 2, 3
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Chicka_Chicka_1,_2,_3
date_saved: 2026-05-05T08:43:43.953353+00:00
instance: kb-cron
parent: chicka-chicka-1-2-3-20260505-0
summary:
Chicka Chicka 1, 2, 3 is the title of a children's picture book written by Bill Martin, Jr. and Michael Sampson, and illustrated by Lois Ehlert in 2004. It was published by Simon & Schuster. It is a sequel to 1989's Chicka Chicka Boom Boom. == Plot == Anthropomorphic numbers from 1 to 20 consecutively (including 5 wearing a top hat), then 30 to 90 by tens (including 70 with long hair), and finally 99, climb up an apple tree. While watching them climb, the number 0 tries to find a place available for him in the tree. However, 0 soon realizes there is no more room left for him, until a colony of bumblebees make everyone in the tree (except 10 who hides) fall out, counting backwards. While this happens, a few of the numbers are revealed to have suffered certain injuries from the fall. The number 0 finally finds his place in the tree and goes to the top, joining with 10 and forming the large number 100 to scare the bees away. Then all the other numbers return and climb back up the apple tree, cheering for 10 and 0's bravery. == Development == The publisher, Simon


id: the-classical-groups-20260505-0
file: data/en.wikipedia.org/wiki/The_Classical_Groups-0.md
category: reference
title: The Classical Groups
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/The_Classical_Groups
date_saved: 2026-05-05T08:43:46.222532+00:00
instance: kb-cron
parent: the-classical-groups-20260505-0
summary:
The Classical Groups: Their Invariants and Representations is a mathematics book by Hermann Weyl published in 1939. The book describes classical invariant theory in terms of representation theory. It is largely responsible for the revival of interest in invariant theory, which had been almost killed off by David Hilbert's solution of its main problems in the 1890s. The second edition was published in 1946. Weyl gave an informal talk about the topic of his book in 1939. == Reception == Roger Howe called the book "wonderful and terrible". == References == Howe, Roger (1988), "The classical groups and invariants of binary forms", in Wells, R. O. Jr. (ed.), The mathematical heritage of Hermann Weyl (Durham, NC, 1987), Proc. Sympos. Pure Math., vol. 48, Providence, R.I.: American Mathematical Society, pp. 133–166, ISBN 978-0-8218-1482-6, MR 0974333 Howe, Roger (1989), "Remarks on classical invariant theory.", Transactions of the American Mathematical Society, 313 (2), American Mathematical Society: 539–570, doi:10.2307/2001418, ISSN 0002-9947, JSTOR 2001418, MR 0986027 Jacobson, Nathan (1940), "Book Review: The Classical Groups", Bulletin of the American Mathematical Society, 46 (7): 592–595, doi:10.1090/S0002-9904-1940-07236-2, ISSN 0002-9904, MR 1564136 Weyl, Hermann (1939), The Classical Groups. Their Invariants and Representations, Princeton University Press, ISBN 978-0-691-05756-9, MR 0000255


id: clavis-mathematicae-20260505-0
file: data/en.wikipedia.org/wiki/Clavis_mathematicae-0.md
category: reference
title: Clavis mathematicae
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Clavis_mathematicae
date_saved: 2026-05-05T08:43:47.337039+00:00
instance: kb-cron
parent: clavis-mathematicae-20260505-0
summary:
Clavis mathematicae (English: The Key of Mathematics) is a mathematics book written by William Oughtred, originally published in 1631 in Latin. It was an attempt to communicate the contemporary mathematical practices, and the European history of mathematics, into a concise and digestible form. The book contains an addition in its 1647 English edition, "Easy Way of Delineating Sun-Dials by Geometry", which had been written by Oughtred earlier in life. The original edition brought the autodidactic Oughtred acclaim amongst mathematicians, but the English-language reissue brought him celebrity, especially amongst tradesman who made use of the arithmetic in their labors. The book is also notable for using the symbol "x" for multiplication, a method invented by Oughtred. == References ==


id: color-and-symmetry-20260505-0
file: data/en.wikipedia.org/wiki/Color_and_Symmetry-0.md
category: reference
title: Color and Symmetry
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Color_and_Symmetry
date_saved: 2026-05-05T08:43:48.503230+00:00
instance: kb-cron
parent: color-and-symmetry-20260505-0
summary:
Color and Symmetry is a book by Arthur L. Loeb published by Wiley Interscience in 1971. The author adopts an unconventional algorithmic approach to generating the line and plane groups based on the concept of "rotocenter" (the invariant point of a rotation). He then introduces the concept of two or more colors to derive all of the plane dichromatic symmetry groups and some of the polychromatic symmetry groups. == Structure and topics == The book is divided into three parts. In the first part, chapters 1–7, the author introduces his "algorismic" (algorithmic) method based on "rotocenters" and "rotosimplexes" (a set of congruent rotocenters). He then derives the 7 frieze groups and the 17 wallpaper groups. In the second part, chapters 8–10, the dichromatic (black-and-white, two-colored) patterns are introduced and the 17 dichromatic line groups and the 46 black-and-white dichromatic plane groups are derived. In the third part, chapters 11–22, polychromatic patterns (3 or more colors), polychromatic line groups, and polychromatic plane groups are derived and illustrated. Loeb's synthetic approach does not enable a comparison of colour symmetry concepts and definitions by other authors, and it is therefore not surprising that the number of polychromatic patterns he identifies are different from


id: colored-symmetry-20260505-0
file: data/en.wikipedia.org/wiki/Colored_Symmetry-0.md
category: reference
title: Colored Symmetry
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Colored_Symmetry
date_saved: 2026-05-05T08:43:49.656087+00:00
instance: kb-cron
parent: colored-symmetry-20260505-0
summary:
Colored Symmetry is a book by A.V. Shubnikov and N.V. Belov and published by Pergamon Press in 1964. The book contains translations of materials originally written in Russian and published between 1951 and 1958. The book was notable because it gave English-language speakers access to new work in the fields of dichromatic and polychromatic symmetry. == Structure and topics == The book is divided into two parts. The first part is a translation into English of A.V. Shubnikov's book Symmetry and antisymmetry of finite figures (Russian: Симметрия и антисимметрия конечных фигур) originally published in 1951. As the editor says in his preface, this book rekindled interest in the field of antisymmetry after a break of 20 years. The book defines symmetry elements, operations and groups; it then introduces the concept of antisymmetry, and derives the full set of dichromatic three-dimensional point groups. A paper entitled Antisymmetry of textures is appended to part 1; it analyzes the antisymmetry of groups containing infinity-fold axes. The second part, entitled Infinite groups of colored symmetry, consists of translations of six papers by N.V. Belov and his co-workers in the new field of polychromatic symmetry. These papers cover the derivation of the 42 magnetic Bravais


id: complexities-women-in-mathematics-20260505-0
file: data/en.wikipedia.org/wiki/Complexities:_Women_in_Mathematics-0.md
category: reference
title: Complexities: Women in Mathematics
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Complexities:_Women_in_Mathematics
date_saved: 2026-05-05T08:43:50.805469+00:00
instance: kb-cron
parent: complexities-women-in-mathematics-20260505-0
summary:
Complexities: Women in Mathematics is an edited volume on women in mathematics that "contains the stories and insights of more than eighty female mathematicians". It was edited by Bettye Anne Case and Anne M. Leggett, based on a collection of material from the Newsletter of the Association for Women in Mathematics, and published by Princeton University Press in 2005 (ISBN 0-691-11462-5). == Topics == The book contains over 100 articles, by over 70 authors, divided into five sections. The first of these, "Inspiration", discusses the work of famous women in mathematics (such as Sofya Kovalevskaya, Julia Robinson, and Emmy Noether) and of women mathematicians from the 18th and 19th centuries, offering insights into their personal life as well as their mathematics. Next, "Joining Together" covers the history of the Association for Women in Mathematics and related topics in the organization of women in mathematics including European Women in Mathematics and the participation of women at the International Congress of Mathematicians. The middle section, "Choices and Challenges", covers the problems facing women in contemporary mathematics, and includes a statistical quantification of these problems by Case and Leggett. "Celebration" is a collection of plenary talks and other materials from the Olga Taussky-Todd


id: complexity-and-real-computation-20260505-0
file: data/en.wikipedia.org/wiki/Complexity_and_Real_Computation-0.md
category: reference
title: Complexity and Real Computation
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Complexity_and_Real_Computation
date_saved: 2026-05-05T08:43:51.906904+00:00
instance: kb-cron
parent: complexity-and-real-computation-20260505-0
summary:
Complexity and Real Computation is a book on the computational complexity theory of real computation. It studies algorithms whose inputs and outputs are real numbers, using the Blum–Shub–Smale machine as its model of computation. For instance, this theory is capable of addressing a question posed in 1991 by Roger Penrose in The Emperor's New Mind: "is the Mandelbrot set computable?" The book was written by Lenore Blum, Felipe Cucker, Michael Shub and Stephen Smale, with a foreword by Richard M. Karp, and published by Springer-Verlag in 1998 (doi:10.1007/978-1-4612-0701-6, ISBN 0-387-98281-7). == Purpose == Stephen Vavasis observes that this book fills a significant gap in the literature: although theoretical computer scientists working on discrete algorithms had been studying models of computation and their implications for the complexity of algorithms since the 1970s, researchers in numerical algorithms had for the most part failed to define their model of computation, leaving their results on a shaky foundation. Beyond the goal of making this aspect of the topic more well-founded, the book also has the aims of presenting new results in the complexity theory of real-number computation, and of collecting previously-known results in this theory. == Topics == The introduction of the book reprints


id: computability-in-analysis-and-physics-20260505-0
file: data/en.wikipedia.org/wiki/Computability_in_Analysis_and_Physics-0.md
category: reference
title: Computability in Analysis and Physics
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Computability_in_Analysis_and_Physics
date_saved: 2026-05-05T08:43:53.082106+00:00
instance: kb-cron
parent: computability-in-analysis-and-physics-20260505-0
summary:
Computability in Analysis and Physics is a monograph on computable analysis by Marian Pour-El and J. Ian Richards. It was published by Springer-Verlag in their Perspectives in Mathematical Logic series in 1989, and reprinted by the Association for Symbolic Logic and Cambridge University Press in their Perspectives in Logic series in 2016. == Topics == The book concerns computable analysis, a branch of mathematical analysis founded by Alan Turing and concerned with the computability of constructions in analysis. This area is connected to, but distinct from, constructive analysis, reverse mathematics, and numerical analysis. The early development of the field was summarized in a book by Oliver Aberth, Computable Analysis (1980), and Computability in Analysis and Physics provides an update, incorporating substantial developments in this area by its authors. In contrast to the Russian school of computable analysis led by Andrey Markov Jr., it views computability as a distinguishing property of mathematical objects among others, rather than developing a theory that concerns only computable objects. After an initial section of the book, introducing computable analysis and leading up to an example of John Myhill of a computable continuously differentiable function whose derivative is not computable, the remaining two parts of the


id: concepts-of-modern-mathematics-20260505-0
file: data/en.wikipedia.org/wiki/Concepts_of_Modern_Mathematics-0.md
category: reference
title: Concepts of Modern Mathematics
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Concepts_of_Modern_Mathematics
date_saved: 2026-05-05T08:43:54.236463+00:00
instance: kb-cron
parent: concepts-of-modern-mathematics-20260505-0
summary:
Concepts of Modern Mathematics is a book by mathematician and science popularizer Ian Stewart about then-recent developments in mathematics. It was originally published by Penguin Books in 1975, updated in 1981, and reprinted by Dover publications in 1995 and 2015. == Overview == The book arose out of an extramural class that Ian Stewart taught at the University of Warwick about "Modern mathematics". In the 1995 Dover edition Stewart wrote that the aim of the class was: to explain why the underlying abstract point of view had gained currency among research mathematicians, and to examine how it opened up entirely new realms of mathematical thought. The book is aimed at non-mathematicians. However, there are frequent equations and diagrams and the level of presentation is more technical than some of Stewart's other popular books such as Flatterland. Topics covered include analytic geometry, set theory, abstract algebra, group theory, topology, and probability. == References ==


id: the-construction-and-principal-uses-of-mathematical-instruments-20260505-0
file: data/en.wikipedia.org/wiki/The_Construction_and_Principal_Uses_of_Mathematical_Instruments-0.md
category: reference
title: The Construction and Principal Uses of Mathematical Instruments
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/The_Construction_and_Principal_Uses_of_Mathematical_Instruments
date_saved: 2026-05-05T08:43:55.455451+00:00
instance: kb-cron
parent: the-construction-and-principal-uses-of-mathematical-instruments-20260505-0
summary:
The Construction and Principal Uses of Mathematical Instruments (French: Traité de la construction et des principaux usages des instrumens de mathématique) is a book by Nicholas Bion, first published in 1709. It was translated into English in 1723 by Edmund Stone. The book describes ways to construct mathematical instruments. It was described as "the most famous book devoted to instruments" by historian of science David M. Knight. == Nicholas Bion == Nicholas Bion (French: Nicolas Bion [bjɔ̃]; 1652–1733) was a French instrument maker and author with workshops in Paris. He was king's engineer for mathematical instruments. He died in Paris in 1733 aged 81. === Bibliography === Bion is the author of the following: L'usage des Globes Célestes et Terrestres et des sphères suivant les differents systèmes du Monde (Amsterdam, 1700) Usage des Astrolabes Traité de la construction et des principaux usages des instrumens de mathématique (Paris, 1709) (online version) == References == == Further reading == Complete Dictionary of Scientific Biography. Vol. 1. Detroit: Charles Scribner's Sons. 2008. ISBN 978-0-684-31559-1. Kern, Ralf (2010). Wissenschaftliche Instrumente in ihrer Zeit. Vom 15. – 19. Jahrhundert. Köln: König, Walther. ISBN 978-3-86560-772-0. == External links == Online edition Bell Book Collection at the


id: convex-polyhedra-book-20260505-0
file: data/en.wikipedia.org/wiki/Convex_Polyhedra_(book)-0.md
category: reference
title: Convex Polyhedra (book)
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Convex_Polyhedra_(book)
date_saved: 2026-05-05T08:43:56.619640+00:00
instance: kb-cron
parent: convex-polyhedra-book-20260505-0
summary:
Convex Polyhedra is a book on the mathematics of convex polyhedra, written by Soviet mathematician Aleksandr Danilovich Aleksandrov, and originally published in Russian in 1950, under the title Выпуклые многогранники. It was translated into German by Wilhelm Süss as Konvexe Polyeder in 1958. An updated edition, translated into English by Nurlan S. Dairbekov, Semën Samsonovich Kutateladze and Alexei B. Sossinsky, with added material by Victor Zalgaller, L. A. Shor, and Yu. A. Volkov, was published as Convex Polyhedra by Springer-Verlag in 2005. == Topics == The main focus of the book is on the specification of geometric data that will determine uniquely the shape of a three-dimensional convex polyhedron, up to some class of geometric transformations such as congruence or similarity. It considers both bounded polyhedra (convex hulls of finite sets of points) and unbounded polyhedra (intersections of finitely many half-spaces). The 1950 Russian edition of the book included 11 chapters. The first chapter covers the basic topological properties of polyhedra, including their topological equivalence to spheres (in the bounded case) and Euler's polyhedral formula. After a lemma of Augustin Cauchy on the impossibility of labeling the edges of a polyhedron by positive and negative signs so that each vertex


id: crocheting-adventures-with-hyperbolic-planes-20260505-0
file: data/en.wikipedia.org/wiki/Crocheting_Adventures_with_Hyperbolic_Planes-0.md
category: reference
title: Crocheting Adventures with Hyperbolic Planes
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Crocheting_Adventures_with_Hyperbolic_Planes
date_saved: 2026-05-05T08:43:58.864644+00:00
instance: kb-cron
parent: crocheting-adventures-with-hyperbolic-planes-20260505-0
summary:
Crocheting Adventures with Hyperbolic Planes is a book on crochet and hyperbolic geometry by Daina Taimiņa. It was published in 2009 by A K Peters, with a 2018 second edition by CRC Press. == Topics == The book is on the use of crochet to make physical surfaces with the geometry of the hyperbolic plane. The full hyperbolic plane cannot be embedded smoothly into three-dimensional space, but pieces of it can. Past researchers had made models of these surfaces out of paper, but Taimiņa's work is the first work to do so using textile arts. She had previously described these models in a research paper and used them as illustrations for an undergraduate geometry textbook, but this book describes more of the background for the project, makes it more widely accessible, and provides instructions for others to follow in making these models. The book has nine chapters. The first chapter introduces the notion of the curvature of a surface, provides instructions for an introductory project in crocheting a patch of the hyperbolic plane, and provides an initial warning about the exponential growth in the area of this plane as a function of its radius, which will cause larger crochet projects


id: the-cube-made-interesting-20260505-0
file: data/en.wikipedia.org/wiki/The_Cube_Made_Interesting-0.md
category: reference
title: The Cube Made Interesting
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/The_Cube_Made_Interesting
date_saved: 2026-05-05T08:43:59.993538+00:00
instance: kb-cron
parent: the-cube-made-interesting-20260505-0
summary:
The Cube Made Interesting is a geometry book aimed at high school mathematics students, on the geometry of the cube. It was originally written in Polish by Aniela Ehrenfeucht (née Miklaszewska, 1905–2000), titled Ciekawy Sześcian [the interesting cube], and published by Polish Scientific Publishers PWN in 1960. Wacław Zawadowski translated it into English, and the translation was published in 1964 by the Pergamon Press and Macmillan Inc., in their "Popular Lectures in Mathematics" series. == Topics == The book begins with Euler's polyhedral formula, and includes material on the symmetries of their cube and their realization as geometric rotations, and on the shape of plane sections through cubes. It describes the 30 combinatorially distinct colorings of the six faces of the cube by six different colors, and discusses arrangements of colored cubes that match pairs of equal-colored faces. The final chapter of the book concerns Prince Rupert's cube, the problem of fitting a cube through a hole drilled through a smaller cube without breaking the smaller cube into pieces. An unusual feature of the book is its heavy illustration with red-blue anaglyphs; provided with the book are red-blue glasses allowing readers to see these images as three-dimensional shapes. == Audience


id: davenport-schinzel-sequences-and-their-geometric-applications-20260505-0
file: data/en.wikipedia.org/wiki/Davenport–Schinzel_Sequences_and_Their_Geometric_Applications-0.md
category: reference
title: Davenport–Schinzel Sequences and Their Geometric Applications
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Davenport–Schinzel_Sequences_and_Their_Geometric_Applications
date_saved: 2026-05-05T08:44:01.151538+00:00
instance: kb-cron
parent: davenport-schinzel-sequences-and-their-geometric-applications-20260505-0
summary:
Davenport–Schinzel Sequences and Their Geometric Applications is a book in discrete geometry. It was written by Micha Sharir and Pankaj K. Agarwal, and published by Cambridge University Press in 1995, with a paperback reprint in 2010. == Topics == Davenport–Schinzel sequences are named after Harold Davenport and Andrzej Schinzel, who applied them to certain problems in the theory of differential equations. They are finite sequences of symbols from a given alphabet, constrained by forbidding pairs of symbols from appearing in alternation more than a given number of times (regardless of what other symbols might separate them). In a Davenport–Schinzel sequence of order k {\displaystyle k} , the longest allowed alternations have length k {\displaystyle k} . For instance, a Davenport–Schinzel sequence of order three could have two symbols x {\displaystyle x} and y {\displaystyle y} that appear either in the order x … y … x {\displaystyle x\dots y\dots x} or y … x … y {\displaystyle y\dots x\dots y} , but longer alternations like x … y … x … y {\displaystyle x\dots y\dots x\dots y} would be forbidden. The length of such a sequence, for a given choice of k {\displaystyle k} , can be only slightly longer


id: de-arte-supputandi-20260505-0
file: data/en.wikipedia.org/wiki/De_arte_supputandi-0.md
category: reference
title: De arte supputandi
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/De_arte_supputandi
date_saved: 2026-05-05T08:44:02.309998+00:00
instance: kb-cron
parent: de-arte-supputandi-20260505-0
summary:
De arte supputandi libri quattuor was the first printed work on arithmetic published in England. Published in 1522, it was written by Cuthbert Tunstall, Bishop of London, and based on Luca Pacioli's Summa de arithmetica, geometria, proportioni et proportionalità. It is dedicated to Sir Thomas More. == References ==


id: divina-proportione-20260505-0
file: data/en.wikipedia.org/wiki/Divina_proportione-0.md
category: reference
title: Divina proportione
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Divina_proportione
date_saved: 2026-05-05T08:44:03.564557+00:00
instance: kb-cron
parent: divina-proportione-20260505-0
summary:
Divina proportione (15th century Italian for Divine proportion), later also called De divina proportione (converting the Italian title into a Latin one) is a book on mathematics written by Luca Pacioli and illustrated by Leonardo da Vinci, completed by February 9th, 1498 in Milan and first printed in 1509. Its subject was mathematical proportions (the title refers to the golden ratio) and their applications to geometry, to visual art through perspective, and to architecture. The clarity of the written material and Leonardo's excellent diagrams helped the book to achieve an impact beyond mathematical circles, popularizing contemporary geometric concepts and images. Some of its content was plagiarised from an earlier book by Piero della Francesca, De quinque corporibus regularibus. == Contents of the book == The book consists of three separate manuscripts, which Pacioli worked on between 1496 and 1498. He credits Fibonacci as the main source for the mathematics he presents. === Compendio divina proportione === The first part, Compendio divina proportione (Compendium on the Divine Proportion), studies the golden ratio from a mathematical perspective (following the relevant work of Euclid), giving mystical and religious meanings to this ratio, in seventy-one chapters. Pacioli points out that golden rectangles can be


id: de-quinque-corporibus-regularibus-20260505-0
file: data/en.wikipedia.org/wiki/De_quinque_corporibus_regularibus-0.md
category: reference
title: De quinque corporibus regularibus
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/De_quinque_corporibus_regularibus
date_saved: 2026-05-05T08:44:04.742568+00:00
instance: kb-cron
parent: de-quinque-corporibus-regularibus-20260505-0
summary:
De quinque corporibus regularibus (sometimes called Libellus de quinque corporibus regularibus) is a book on the geometry of polyhedra written in the 1480s or early 1490s by Italian painter and mathematician Piero della Francesca. It is a manuscript, in the Latin language; its title means [the little book] on the five regular solids. It is one of three books known to have been written by della Francesca. Along with the Platonic solids, De quinque corporibus regularibus includes descriptions of five of the thirteen Archimedean solids, and of several other irregular polyhedra coming from architectural applications. It was the first of what would become many books connecting mathematics to art through the construction and perspective drawing of polyhedra, including Luca Pacioli's 1509 Divina proportione (which incorporated without credit an Italian translation of della Francesca's work). Lost for many years, De quinque corporibus regularibus was rediscovered in the 19th century in the Vatican Library and the Vatican copy has since been republished in facsimile. == Background == The five Platonic solids (the regular tetrahedron, cube, octahedron, dodecahedron, and icosahedron) were known to della Francesca through two classical sources: Timaeus, in which Plato theorizes that four of them correspond to the classical elements


id: de-quinque-corporibus-regularibus-20260505-1
file: data/en.wikipedia.org/wiki/De_quinque_corporibus_regularibus-1.md
category: reference
title: De quinque corporibus regularibus
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/De_quinque_corporibus_regularibus
date_saved: 2026-05-05T08:44:04.742568+00:00
instance: kb-cron
parent: de-quinque-corporibus-regularibus-20260505-0
summary:
The fourth and final part of the book concerns other shapes than the Platonic solids. These include six Archimedean solids: the truncated tetrahedron (which appears also in an exercise in his Trattato d'abaco), and the truncations of the other four Platonic solids. The cuboctahedron, another Archimedean solid, is described in the Trattato but not in De quinque corporibus regularibus; since De quinque corporibus regularibus appears to be a later work than the Trattato, this omission appears to be deliberate, and a sign that della Francesca was not aiming for a complete listing of these polyhedra. The fourth part of De quinque corporibus regularibus also includes domed shapes like the domes of the Pantheon, Rome or the (at the time newly constructed) Santa Maria presso San Satiro in Milan formed from a ring of triangles surrounded by concentric rings of irregular quadrilaterals, and other shapes arising in architectural applications. The result that Peterson (1997) calls della Francesca's "most sophisticated" is the derivation of the volume of a Steinmetz solid (the intersection of two cylinders, the shape of a cloister vault), which della Francesca had illustrated in his book on perspective. Despite its curves, this shape has a simple but non-obvious formula


id: descriptive-complexity-20260505-0
file: data/en.wikipedia.org/wiki/Descriptive_Complexity-0.md
category: reference
title: Descriptive Complexity
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Descriptive_Complexity
date_saved: 2026-05-05T08:44:05.899385+00:00
instance: kb-cron
parent: descriptive-complexity-20260505-0
summary:
Descriptive Complexity is a book in mathematical logic and computational complexity theory by Neil Immerman. It concerns descriptive complexity theory, an area in which the expressibility of mathematical properties using different types of logic is shown to be equivalent to their computability in different types of resource-bounded models of computation. It was published in 1999 by Springer-Verlag in their book series Graduate Texts in Computer Science. == Topics == The book has 15 chapters, roughly grouped into five chapters on first-order logic, three on second-order logic, and seven independent chapters on advanced topics. The first two chapters provide background material in first-order logic (including first-order arithmetic, the BIT predicate, and the notion of a first-order query) and complexity theory (including formal languages, resource-bounded complexity classes, and complete problems). Chapter three begins the connection between logic and complexity, with a proof that the first-order-recognizable languages can be recognized in logarithmic space, and the construction of complete languages for logarithmic space, nondeterministic logarithmic space, and polynomial time. The fourth chapter concerns inductive definitions, fixed-point operators, and the characterization of polynomial time in terms of first-order logic with the least fixed-point operator. The part of the book on first-order topics ends with a


id: the-design-of-experiments-20260505-0
file: data/en.wikipedia.org/wiki/The_Design_of_Experiments-0.md
category: reference
title: The Design of Experiments
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/The_Design_of_Experiments
date_saved: 2026-05-05T08:44:07.114263+00:00
instance: kb-cron
parent: the-design-of-experiments-20260505-0
summary:
The Design of Experiments is a 1935 book by the English statistician, Ronald Fisher, on experimental design, considered to be a foundational work in modern statistics and experimental methodology. The book introduced concepts such as randomization, replication, blocking, and contains Fisher’s influential discussion of the null hypothesis, illustrated in the context of the Lady tasting tea experiment. The book has had a lasting impact on the development of statistical science, shaping diverse fields such as agriculture, psychology, and medical research. It remains an important reference in the history of applied statistics and the philosophy of scientific testing. == Background == At the time of publication, Fisher was a statistician at Rothamsted Research (formally known as Rothamsted Experimental Station) where he developed statistical methods to analyze agricultural data. His broader career included fundamental contributions to statistics, genetics, and evolutionary biology. The Design of Experiments built on Fisher’s earlier work, including his book Statistical Methods for Research Workers (1925), and laid the groundwork for the practical application of statistical tests in experimental science. Much of Fisher’s approach grew out of earlier studies at Rothamsted, particularly a 1923 paper with Winifred Mackenzie on crop variation. In this work, Fisher tied the validity of


id: disquisitiones-arithmeticae-20260505-0
file: data/en.wikipedia.org/wiki/Disquisitiones_Arithmeticae-0.md
category: reference
title: Disquisitiones Arithmeticae
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Disquisitiones_Arithmeticae
date_saved: 2026-05-05T08:44:09.351017+00:00
instance: kb-cron
parent: disquisitiones-arithmeticae-20260505-0
summary:
Disquisitiones Arithmeticae (Latin for Arithmetical Investigations) is a textbook on number theory written in Latin by Carl Friedrich Gauss in 1798, when Gauss was 21, and published in 1801, when he was 24. It had a revolutionary impact on number theory by making the field truly rigorous and systematic and paved the path for modern number theory. In this book, Gauss brought together and reconciled results in number theory obtained by such eminent mathematicians as Fermat, Euler, Lagrange, and Legendre, while adding profound and original results of his own. == Scope == The Disquisitiones covers both elementary number theory and parts of the area of mathematics now called algebraic number theory. Gauss did not explicitly recognize the concept of a group, which is central to modern algebra, so he did not use this term. His own title for his subject was Higher Arithmetic. In his Preface to the Disquisitiones, Gauss describes the scope of the book as follows: The inquiries which this volume will investigate pertain to that part of Mathematics which concerns itself with integers. Gauss also writes, "When confronting many difficult problems, derivations have been suppressed for the sake of brevity when readers refer to this work." ("Quod,


id: divine-proportions-rational-trigonometry-to-universal-geometry-20260505-0
file: data/en.wikipedia.org/wiki/Divine_Proportions:_Rational_Trigonometry_to_Universal_Geometry-0.md
category: reference
title: Divine Proportions: Rational Trigonometry to Universal Geometry
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Divine_Proportions:_Rational_Trigonometry_to_Universal_Geometry
date_saved: 2026-05-05T08:44:10.549527+00:00
instance: kb-cron
parent: divine-proportions-rational-trigonometry-to-universal-geometry-20260505-0
summary:
Divine Proportions: Rational Trigonometry to Universal Geometry is a 2005 book by the mathematician Norman J. Wildberger on a proposed alternative approach to Euclidean geometry and trigonometry, called rational trigonometry. The book advocates replacing the usual basic quantities of trigonometry, Euclidean distance and angle measure, by squared distance and the square of the sine of the angle, respectively. This is logically equivalent to the standard development (as the replacement quantities can be expressed in terms of the standard ones and vice versa). The author claims his approach holds some advantages, such as avoiding the need for irrational numbers. The book was "essentially self-published" by Wildberger through his publishing company Wild Egg. The formulas and theorems in the book are regarded as correct mathematics but the claims about practical or pedagogical superiority are primarily promoted by Wildberger himself and have received mixed reviews. == Overview == The main idea of Divine Proportions is to replace distances by the squared Euclidean distance, which Wildberger calls the quadrance, and to replace angle measures by the squares of their sines, which Wildberger calls the spread between two lines. Divine Proportions defines both of these concepts directly from the Cartesian coordinates of points that determine


id: divine-proportions-rational-trigonometry-to-universal-geometry-20260505-1
file: data/en.wikipedia.org/wiki/Divine_Proportions:_Rational_Trigonometry_to_Universal_Geometry-1.md
category: reference
title: Divine Proportions: Rational Trigonometry to Universal Geometry
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Divine_Proportions:_Rational_Trigonometry_to_Universal_Geometry
date_saved: 2026-05-05T08:44:10.549527+00:00
instance: kb-cron
parent: divine-proportions-rational-trigonometry-to-universal-geometry-20260505-0
summary:
== Critical reception == The feature of the book that was most positively received by reviewers was its work extending results in distance and angle geometry to finite fields. Reviewer Laura Wiswell found this work impressive, and was charmed by the result that the smallest finite field containing a regular pentagon is F 19 {\displaystyle \mathbb {F} _{19}} . Michael Henle calls the extension of triangle and conic section geometry to finite fields, in part III of the book, "an elegant theory of great generality", and William Barker also writes approvingly of this aspect of the book, calling it "particularly novel" and possibly opening up new research directions. Wiswell raises the question of how many of the detailed results presented without attribution in this work are actually novel. In this light, Michael Henle notes that the use of squared Euclidean distance "has often been found convenient elsewhere"; for instance it is used in distance geometry, least squares statistics, and convex optimization. James Franklin points out that for spaces of three or more dimensions, modelled conventionally using linear algebra, the use of spread by Divine Proportions is not very different from standard methods involving dot products in place of trigonometric functions.


id: do-not-erase-mathematicians-and-their-chalkboards-20260505-0
file: data/en.wikipedia.org/wiki/Do_Not_Erase:_Mathematicians_and_Their_Chalkboards-0.md
category: reference
title: Do Not Erase: Mathematicians and Their Chalkboards
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Do_Not_Erase:_Mathematicians_and_Their_Chalkboards
date_saved: 2026-05-05T08:44:11.731404+00:00
instance: kb-cron
parent: do-not-erase-mathematicians-and-their-chalkboards-20260505-0
summary:
Do Not Erase: Mathematicians and their Chalkboards is a photo-essay book on the blackboards of mathematicians. It was photographed and edited by Jessica Wynne, and published in 2021 by the Princeton University Press. == Background == Wynne is a professor of photography at the Fashion Institute of Technology in New York City. She came to this project through an acquaintance with mathematicians Amie Wilkinson and Benson Farb, neighbors of hers in Cape Cod, and through a trip to India from which she brought back a set of photographs she had taken of school chalkboards in Jaipur. The title of the book harks back to the legend of Archimedes commanding his killer not to erase his circles. In modern times, adding "do not erase" as an annotation on a filled-up chalkboard is a familiar way to request the preservation of its contents. By photographing these chalkboards, Wynne has given them significantly more permanence than they otherwise would have. == Contents == Do Not Erase is formatted as a sequence of 109 two-page spreads, printed unusually in landscape mode: the pages are approximately letter size, but wider than they are tall. Each spread features a full-color photograph of a mathematician's chalkboard, generally


id: does-god-play-dice-20260505-0
file: data/en.wikipedia.org/wiki/Does_God_Play_Dice-0.md
category: reference
title: Does God Play Dice?
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Does_God_Play_Dice?
date_saved: 2026-05-05T08:44:12.875523+00:00
instance: kb-cron
parent: does-god-play-dice-20260505-0
summary:
Does God Play Dice: The New Mathematics of Chaos is a non-fiction book about chaos theory written by British mathematician Ian Stewart. The book was initially published by Blackwell Publishing in 1989. == Summary == In this book, Stewart explains chaos theory to an audience presumably unfamiliar with it. As the book progresses the writing changes from simple explanations of chaos theory to in-depth, rigorous mathematical study. Stewart covers mathematical concepts such as differential equations, resonance, nonlinear dynamics, and probability. The book is illustrated with diagrams and graphs of mathematical concepts and equations when applicable. The back of the book, and a summary of its content, reads, "The science of chaos is forcing scientists to rethink Einstein's fundamental assumptions regarding the way the universe behaves. Chaos theory has already shown that simple systems, obeying precise laws, can nevertheless act in a random manner. Perhaps God plays dice within a cosmic game of complete law and order. Does God Play Dice? reveals a strange universe in which nothing may be as it seems. Familiar geometric shapes such as circles and ellipses give way to infinitely complex structures known as fractals, the fluttering of a butterfly's wings can change the weather, and


id: l-ments-de-g-om-trie-alg-brique-20260505-0
file: data/en.wikipedia.org/wiki/Éléments_de_géométrie_algébrique-0.md
category: reference
title: Éléments de géométrie algébrique
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Éléments_de_géométrie_algébrique
date_saved: 2026-05-05T08:44:14.455832+00:00
instance: kb-cron
parent: l-ments-de-g-om-trie-alg-brique-20260505-0
summary:
The Éléments de géométrie algébrique (EGA; from French: "Elements of Algebraic Geometry") by Alexander Grothendieck (assisted by Jean Dieudonné) is a rigorous treatise on algebraic geometry that was published (in eight parts or fascicles) from 1960 through 1967 by the Institut des Hautes Études Scientifiques. In it, Grothendieck established systematic foundations of algebraic geometry, building upon the concept of schemes, which he defined. The work is now considered the foundation and basic reference of modern algebraic geometry. == Editions == Initially thirteen chapters were planned, but only the first four (making a total of approximately 1500 pages) were published. Much of the material which would have been found in the following chapters can be found, in a less polished form, in the Séminaire de géométrie algébrique (known as SGA). Indeed, as explained by Grothendieck in the preface of the published version of SGA, by 1970 it had become clear that incorporating all of the planned material in EGA would require significant changes in the earlier chapters already published, and that therefore the prospects of completing EGA in the near term were limited. An obvious example is provided by derived categories, which became an indispensable tool in the later SGA volumes,


id: l-ments-de-math-matique-20260505-0
file: data/en.wikipedia.org/wiki/Éléments_de_mathématique-0.md
category: reference
title: Éléments de mathématique
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Éléments_de_mathématique
date_saved: 2026-05-05T08:44:15.713125+00:00
instance: kb-cron
parent: l-ments-de-math-matique-20260505-0
summary:
Éléments de mathématique (English: Elements of Mathematics) is a series of mathematics books written by the pseudonymous French collective Nicolas Bourbaki. Begun in 1939, the series has been published in several volumes, and remains in progress. The series is noted as a large-scale, self-contained, formal treatment of mathematics. The members of the Bourbaki group originally intended the work as a textbook on analysis, with the working title Traité d'analyse (Treatise on Analysis). While planning the structure of the work they became more ambitious, expanding its scope to cover several branches of modern mathematics. Once the plan of the work was expanded to treat other fields in depth, the title Éléments de mathématique was adopted. Topics treated in the series include set theory, abstract algebra, topology, analysis, Lie groups and Lie algebras. The unusual singular "mathématique" (mathematic) of the title is deliberate, meant to convey the authors' belief in the unity of mathematics. A companion volume, Éléments d'histoire des mathématiques (Elements of the History of Mathematics), collects and reproduces several of the historical notes that previously appeared in the work. == History == In late 1934, a group of mathematicians including André Weil resolved to collectively write a textbook on mathematical


id: l-ments-de-math-matique-20260505-1
file: data/en.wikipedia.org/wiki/Éléments_de_mathématique-1.md
category: reference
title: Éléments de mathématique
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Éléments_de_mathématique
date_saved: 2026-05-05T08:44:15.713125+00:00
instance: kb-cron
parent: l-ments-de-math-matique-20260505-0
summary:
== Structure == Éléments de mathématique is divided into books, volumes, and chapters. A book refers to a broad area of investigation or branch of mathematics (Algebra, Integration); a given book is sometimes published in multiple volumes (physical books) or else in a single volume. The work is further subdivided into chapters with some volumes consisting of a single chapter. Typically of mathematics textbooks, the Éléments' chapters present definitions, mathematical notation, proofs of theorems and exercises, forming the core mathematical content of the work. The chapters are supplemented by historical notes and summaries of results. The former usually appear after a given chapter to contextualize the development of its topics, and the latter are occasionally used sections in which a book's major results are collected and stated without proof. Eléments d'histoire des mathématiques is a compilation volume of several of the historical note sections previously published in the Éléments proper, through the book on Lie groups and Lie algebras. When Bourbaki's founders originally planned the Treatise on Analysis, they conceived of an introductory and foundational section of the text, which would describe all prerequisite concepts from scratch. This proposed area of the text was referred to as the "Abstract Packet"


id: encyclopedic-dictionary-of-mathematics-20260505-0
file: data/en.wikipedia.org/wiki/Encyclopedic_Dictionary_of_Mathematics-0.md
category: reference
title: Encyclopedic Dictionary of Mathematics
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Encyclopedic_Dictionary_of_Mathematics
date_saved: 2026-05-05T08:44:19.213869+00:00
instance: kb-cron
parent: encyclopedic-dictionary-of-mathematics-20260505-0
summary:
The Encyclopedic Dictionary of Mathematics is a translation of the Japanese Iwanami Sūgaku Jiten (岩波数学辞典). The editor of the first and second editions was Shokichi Iyanaga; the editor of the third edition was Kiyosi Itô; the fourth edition was edited by the Mathematical Society of Japan. == Editions == Iyanaga, Shōkichi, ed. (1954), Iwanami Sūgaku Jiten (in Japanese) (1st ed.), Tokyo: Iwanami Shoten, MR 0062668 Iyanaga, Shōkichi, ed. (1960), Iwanami mathematical dictionary, Edited by the Mathematical Society of Japan. Revised and enlarged (in Japanese), Tokyo: Iwanami Shoten, MR 0130788 Iyanaga, Shōkichi, ed. (1968), Iwanami Sūgaku Jiten (in Japanese) (2nd ed.), Iwanami Shoten Publishers, Tokyo, MR 0241228 Iyanaga, Shōkichi, ed. (1977), Encyclopedic Dictionary of Mathematics, Volumes I, II, hardback, translated from the 2nd Japanese edition (1st ed.), MIT Press, pp. 1750, ISBN 978-0-262-09016-2, MR 0490100 Iyanaga, Shōkichi; Kawada, Yukiyosi, eds. (1980) [1977], Encyclopedic Dictionary of Mathematics, Volumes I, II, Translated from the 2nd Japanese edition, paperback version of the 1977 edition (1st ed.), MIT Press, ISBN 978-0-262-59010-5, MR 0591028 Sūgaku Jiten (in Japanese) (3rd ed.), Tokyo: Iwanami Shoten, 1985, ISBN 978-4-00-080016-7, MR 0924841 Itô, Kiyosi, ed. (1987), Encyclopedic Dictionary of Mathematics. Vol. I--IV, Hardback, Translated from the Japanese 3rd edition (2nd


category: reference
tags: science, encyclopedia
date_saved: 2026-05-05T08:44:20.399254+00:00
instance: kb-cron
id:
the-equidistribution-of-lattice-shapes-of-rings-of-integers-of-cubic-quartic-and-quintic-number-fields-20260505-0

file:
data/en.wikipedia.org/wiki/The_Equidistribution_of_Lattice_Shapes_of_Rings_of_Integers_of_Cubic,_Quartic,_and_Quintic_Number_Fields-0.md

title:
The Equidistribution of Lattice Shapes of Rings of Integers of Cubic, Quartic, and Quintic Number Fields

summary:
The Equidistribution of Lattice Shapes of Rings of Integers of Cubic, Quartic, and Quintic Number Fields: An Artist's Rendering is a mathematics book by Piper Harron (also known as Piper H and Piper Harris), based on her Princeton University doctoral thesis of the same title. It has been described as "feminist", "unique", "honest", "generous", and "refreshing". == Thesis and reception == Harron was advised by Fields Medalist Manjul Bhargava, and her thesis deals with the properties of number fields, specifically the shape of their rings of integers. Harron and Bhargava showed that, viewed as a lattice in real vector space, the ring of integers of a random number field does not have any special symmetries. Rather than simply presenting the proof, Harron intended for the thesis and book to explain both the mathematics and the process (and struggle) that was required to reach this result. The writing is accessible and informal, and the book features sections targeting three different audiences: laypeople, people with general mathematical knowledge, and experts in number theory. Harron intentionally departs from the typical academic format as she is writing for a community of mathematicians who "do not feel that they are encouraged to be themselves". Unusually

source_url:
https://en.wikipedia.org/wiki/The_Equidistribution_of_Lattice_Shapes_of_Rings_of_Integers_of_Cubic,_Quartic,_and_Quintic_Number_Fields

parent:
the-equidistribution-of-lattice-shapes-of-rings-of-integers-of-cubic-quartic-and-quintic-number-fields-20260505-0


id: equivalents-of-the-axiom-of-choice-20260505-0
file: data/en.wikipedia.org/wiki/Equivalents_of_the_Axiom_of_Choice-0.md
category: reference
title: Equivalents of the Axiom of Choice
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Equivalents_of_the_Axiom_of_Choice
date_saved: 2026-05-05T08:44:21.545527+00:00
instance: kb-cron
parent: equivalents-of-the-axiom-of-choice-20260505-0
summary:
Equivalents of the Axiom of Choice is a book in mathematics, collecting statements in mathematics that are true if and only if the axiom of choice holds. It was written by Herman Rubin and Jean E. Rubin, and published in 1963 by North-Holland as volume 34 of their Studies in Logic and the Foundations of Mathematics series. An updated edition, Equivalents of the Axiom of Choice, II, was published as volume 116 of the same series in 1985. == Topics == At the time of the book's original publication, it was unknown whether the axiom of choice followed from the other axioms of Zermelo–Fraenkel set theory (ZF), or was independent of them, although it was known to be consistent with them from the work of Kurt Gödel. This book codified the project of classifying theorems of mathematics according to whether the axiom of choice was necessary in their proofs, or whether they could be proven without it. At approximately the same time as the book's publication, Paul Cohen proved that the negation of the axiom of choice is also consistent, implying that the axiom of choice, and all of its equivalent statements in this book, are indeed independent of ZF.


id: euclid-and-his-modern-rivals-20260505-0
file: data/en.wikipedia.org/wiki/Euclid_and_His_Modern_Rivals-0.md
category: reference
title: Euclid and His Modern Rivals
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Euclid_and_His_Modern_Rivals
date_saved: 2026-05-05T08:44:22.731487+00:00
instance: kb-cron
parent: euclid-and-his-modern-rivals-20260505-0
summary:
Euclid and His Modern Rivals is a mathematical book published in 1879 by the English mathematician Charles Lutwidge Dodgson (1832–1898), better known under his literary pseudonym "Lewis Carroll". It considers the pedagogic merit of thirteen contemporary geometry textbooks, demonstrating how each in turn is either inferior to or functionally identical to Euclid's Elements. In it Dodgson supports using Euclid's geometry textbook The Elements as the geometry textbook in schools against more modern geometry textbooks that were replacing it, advocated by the Association for the Improvement of Geometrical Teaching, satirized in the book as the "Association for the Improvement of Things in General". Euclid's ghost returns in the play to defend his book against its modern rivals and tries to demonstrate how all of them are inferior to his book. Despite its scholarly subject and content, the work takes the form of a whimsical dialogue, principally between a mathematician named Minos (taken from Minos, judge of the underworld in Greek mythology) and a "devil's advocate" named Professor Niemand (German for 'nobody') who represents the "Modern Rivals" of the title. == References == Robin Wilson (2008). Lewis Carroll in Numberland. Allen Lane. pp. 91–95. ISBN 978-0-7139-9757-6. == External links == Euclid and


id: euclid-s-optics-20260505-0
file: data/en.wikipedia.org/wiki/Euclid's_Optics-0.md
category: reference
title: Euclid's Optics
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Euclid's_Optics
date_saved: 2026-05-05T08:44:23.896975+00:00
instance: kb-cron
parent: euclid-s-optics-20260505-0
summary:
Optics (Ancient Greek: Ὀπτικά) is a work on the geometry of vision written by the Greek mathematician Euclid around 300 BC. The earliest surviving manuscript of Optics is in Greek and dates from the 10th century AD. The work deals almost entirely with the geometry of vision, with little reference to either the physical or psychological aspects of sight. No Western scientist had previously given such mathematical attention to vision. Euclid's Optics influenced the work of later Greek, Islamic, and Western European Renaissance scientists and artists, and is further credited with laying the foundations of classical optics. == Historical significance == Writers before Euclid had developed theories of vision. However, their works were mostly philosophical in nature and lacked the mathematics that Euclid introduced in his Optics. Efforts by the Greeks prior to Euclid were concerned primarily with the physical dimension of vision. Whereas Plato and Empedocles thought of the visual ray as "luminous and ethereal emanation", Euclid’s treatment of vision in a mathematical way was part of the larger Hellenistic trend to quantify a whole range of scientific fields. Because Optics contributed a new dimension to the study of vision, it influenced later scientists. In particular, Ptolemy used Euclid's


id: euclides-danicus-20260505-0
file: data/en.wikipedia.org/wiki/Euclides_Danicus-0.md
category: reference
title: Euclides Danicus
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Euclides_Danicus
date_saved: 2026-05-05T08:44:25.024623+00:00
instance: kb-cron
parent: euclides-danicus-20260505-0
summary:
Euclides Danicus (lit. 'Danish Euclid') is one of three books of mathematics written by Georg Mohr. It was published in 1672 simultaneously in Copenhagen and Amsterdam, in Danish and Dutch respectively. It contains the first proof of the Mohr–Mascheroni theorem, which states that every geometric construction that can be performed using a compass and straightedge can also be done with compass alone. == Contents == The book is divided into two parts. In the first part, Mohr shows how to perform all of the constructions of Euclid's Elements using a compass alone. In the second part, he includes some other specific constructions, including some related to the mathematics of the sundial. == 1928 rediscovery of the book == Euclides Danicus languished in obscurity, possibly caused by its choice of language, until its rediscovery in 1928 in a bookshop in Copenhagen. Until then, the Mohr–Mascheroni theorem had been credited to Lorenzo Mascheroni, who published a proof in 1797, independently of Mohr's work. Soon after the rediscovery of Mohr's book, publications about it by Florian Cajori and Nathan Altshiller Court made its existence much more widely known. The Danish version was republished in facsimile in 1928 by the Royal Danish Academy of


id: evolution-and-the-theory-of-games-20260505-0
file: data/en.wikipedia.org/wiki/Evolution_and_the_Theory_of_Games-0.md
category: reference
title: Evolution and the Theory of Games
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Evolution_and_the_Theory_of_Games
date_saved: 2026-05-05T08:44:26.180617+00:00
instance: kb-cron
parent: evolution-and-the-theory-of-games-20260505-0
summary:
Evolution and the Theory of Games is a book by the British evolutionary biologist John Maynard Smith on evolutionary game theory. The book was initially published in December 1982 by Cambridge University Press. == Overview == In the book, John Maynard Smith summarises work on evolutionary game theory that had developed in the 1970s, to which he made several important contributions. The main contribution of the book is in introducing the concept of Evolutionarily Stable Strategy (ESS). ESS states that for a set of behaviours to be conserved over evolutionary time, they must be the most beneficial avenue of action when common, so that no alternative behaviour can invade. Supposing, for instance, that in a population of frogs, males fight to the death over breeding ponds. This would be an ESS if any one cowardly frog that does not fight to the death always fares worse (in terms of evolutionary survival fitness). A more likely scenario is one in which fighting to the death is not an ESS because a frog might arise that will stop fighting if it realises that it is going to lose. This frog would thus reap the benefits of fighting, but not the ultimate cost.


id: extensions-of-first-order-logic-20260505-0
file: data/en.wikipedia.org/wiki/Extensions_of_First_Order_Logic-0.md
category: reference
title: Extensions of First Order Logic
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Extensions_of_First_Order_Logic
date_saved: 2026-05-05T08:44:39.252783+00:00
instance: kb-cron
parent: extensions-of-first-order-logic-20260505-0
summary:
Extensions of First Order Logic is a book on mathematical logic. It was written by María Manzano, and published in 1996 by the Cambridge University Press as volume 19 of their book series Cambridge Tracts in Theoretical Computer Science. == Topics == The book concerns forms of logic that go beyond first-order logic, and in particular (following the work of Leon Henkin) the project of unifying them by translating all of these extensions into a specific form of logic, many-sorted logic. Beyond many-sorted logic, its topics include second-order logic (including its incompleteness and relation with Peano arithmetic), second-order arithmetic, type theory (in relational, functional, and equational forms), modal logic, and dynamic logic. It is organized into seven chapters. The first concerns second-order logic in its standard form, and it proves several foundational results for this logic. The second chapter introduces the sequent calculus, a method of making sound deductions in second-order logic, and its incompleteness. The third continues the topic of second-order logic, showing how to formulate Peano arithmetic in it, and using Gödel's first incompleteness theorem to provide a second proof of incompleteness of second-order logic. Chapter four formulates a non-standard semantics for second-order logic (from Henkin), in which


id: felix-klein-and-sophus-lie-20260505-0
file: data/en.wikipedia.org/wiki/Felix_Klein_and_Sophus_Lie-0.md
category: reference
title: Felix Klein and Sophus Lie
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Felix_Klein_and_Sophus_Lie
date_saved: 2026-05-05T08:44:40.437862+00:00
instance: kb-cron
parent: felix-klein-and-sophus-lie-20260505-0
summary:
Felix Klein and Sophus Lie: Evolution of the Idea of Symmetry in the Nineteenth Century is a 1988 book by I. M. Yaglom, translated from the Russian into English by Sergei Sossinsky, on the history of the notion of symmetry and the mathematical works of Felix Klein and Sophus Lie besides other mathematicians, such as Camille Jordan, without focusing on biographical details, but on their ideas. It was published by Birkhäuser. == Editions == The original Russian edition of the book was published in 1977 and translated into English by Sergei Sossinky and edited by Hardy Grant and Abe Shenitzer in 1988. In 2009, the book was republished by Ishi Press as Geometries, Groups and Algebras in the Nineteenth Century. The new edition, designed by Sam Sloan, has a foreword by Richard Bozulich. == Contents == Felix Klein and Sophus Lie examines the evolution of mathematical ideas that converged in Klein and Lie's work. Yaglom based the work on his lectures to graduate-level students at Yaroslavl State University; Douglas Quadling described it as "a sharply-focused (though appropriately discursive) study" rather than "a catalogue of names and dates." The book begins with Camille Jordan, who discovers an unanswered letter from Galois


id: the-fifty-nine-icosahedra-20260505-0
file: data/en.wikipedia.org/wiki/The_Fifty-Nine_Icosahedra-0.md
category: reference
title: The Fifty-Nine Icosahedra
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/The_Fifty-Nine_Icosahedra
date_saved: 2026-05-05T08:44:41.601047+00:00
instance: kb-cron
parent: the-fifty-nine-icosahedra-20260505-0
summary:
The Fifty-Nine Icosahedra is a book written and illustrated by H. S. M. Coxeter, P. Du Val, H. T. Flather, and J. F. Petrie. It enumerates certain stellations of the regular convex or Platonic icosahedron, according to a set of rules put forward by J. C. P. Miller. It was first published by the University of Toronto in 1938, and a Second Edition reprint by Springer-Verlag followed in 1982. Tarquin's 1999 Third Edition included new reference material and photographs by K. and D. Crennell. == Stellating polyhedra == In this book a polyhedron is stellated by extending the face planes of a polyhedron until they meet again to form a new polyhedron or compound. When the face planes of the polyhedron are extended indefinitely the space around the polyhedron is divided into unbounded sub spaces and often a number of bounded polyhedrons or cells. Different sets of cells yield different stellations. For a symmetrical polyhedron, these cells will fall into groups of congruent cells, or sets – we say that the cells in such a set are of the same type. This can still lead to a large number of possible forms, so further criteria are imposed to reduce the


id: the-fifty-nine-icosahedra-20260505-1
file: data/en.wikipedia.org/wiki/The_Fifty-Nine_Icosahedra-1.md
category: reference
title: The Fifty-Nine Icosahedra
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/The_Fifty-Nine_Icosahedra
date_saved: 2026-05-05T08:44:41.601047+00:00
instance: kb-cron
parent: the-fifty-nine-icosahedra-20260505-0
summary:
=== Du Val === Du Val devised a symbolic notation for identifying sets of congruent cells, based on the observation that all the extended face (or boundary) planes together cut the space around the icosahedron in many different finite three dimensional regions that he called cells. A segment between a point in a cell and the centre of the icosahedron intersects a number of (extended) face planes; this number is the power of the point and the cell. All cells with the same power form a shell (or layer). The inner icosahedron (power = 0) is named A, the shell with power 1 b, the shell with power 2 c, and so on. If all cells of a shell are congruent, they are named as the shell itself; if there are different non-congruent cells in a shell, they are numbered like e1 and e2. If an enantiomorphic pair of cells is in a shell, if both are referred then f1 is used, if only one of them is used one is in roman and the other in italic like f1 and f1. For example, there are 3 kinds of cells in the layer with power 5 (shell f): f1, f1


id: the-fifty-nine-icosahedra-20260505-2
file: data/en.wikipedia.org/wiki/The_Fifty-Nine_Icosahedra-2.md
category: reference
title: The Fifty-Nine Icosahedra
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/The_Fifty-Nine_Icosahedra
date_saved: 2026-05-05T08:44:41.601047+00:00
instance: kb-cron
parent: the-fifty-nine-icosahedra-20260505-0
summary:
mainline stellations are the stellations whose name consist of a single capital letterA till (and including) H fully supported stellations: stellations where there are no overhangs, and all visible parts of a face can be seen from the same side. these are those stellations where in the faces column there is no face that has an apostrophe, for example 3'. The only Kepler–Poinsot polyhedron in the list is the great icosahedron G. The Great stellated dodecahedron is an edge-stellated icosahedron but only face-stellated icosahedra are in the list and it is therefore not included in the list. Some images illustrate the mirror-image icosahedron with the f1 rather than the f1 cell. == Subsequent debate == There has subsequently been some debate on Miller's rules, with some writers questioning them. Flather himself made and exhibited models which were "non-Miller". Bridge (1974) obtained stellations of the icosahedron by dualising facettings of the dodecahedron, noting the significance of internal structure in distinguishing between stellations which Miller's rules treat as identical. Hudson and Kingston (1988) adopted a reduced rule set. Inchbald noted two non-Miller stellations, and went on to discuss various related issues. == See also == List of Wenninger polyhedron models – Wenninger's


id: finding-ellipses-20260505-0
file: data/en.wikipedia.org/wiki/Finding_Ellipses-0.md
category: reference
title: Finding Ellipses
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Finding_Ellipses
date_saved: 2026-05-05T08:44:42.735764+00:00
instance: kb-cron
parent: finding-ellipses-20260505-0
summary:
Finding Ellipses: What Blaschke Products, Poncelet’s Theorem, and the Numerical Range Know about Each Other is a mathematics book on "some surprising connections among complex analysis, geometry, and linear algebra", and on the connected ways that ellipses can arise from other subjects of study in all three of these fields. It was written by Ulrich Daepp, Pamela Gorkin, Andrew Shaffer, and Karl Voss, and published in 2019 by the American Mathematical Society and Mathematical Association of America as volume 34 of the Carus Mathematical Monographs, a series of books aimed at presenting technical topics in mathematics to a wide audience. == Topics == Finding Ellipses studies a connection between Blaschke products, Poncelet's closure theorem, and the numerical range of matrices. A Blaschke product is a rational function that maps the unit disk in the complex plane to itself, and maps some given points within the disk to the origin. In the main case considered by the book, there are three distinct given points 0 {\displaystyle 0} , a {\displaystyle a} , and b {\displaystyle b} , and their Blaschke product has the formula B ( z ) = z ⋅ z − a 1 − a ¯ z ⋅ z


id: fondements-de-la-g-ometrie-alg-brique-20260505-0
file: data/en.wikipedia.org/wiki/Fondements_de_la_Géometrie_Algébrique-0.md
category: reference
title: Fondements de la Géometrie Algébrique
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Fondements_de_la_Géometrie_Algébrique
date_saved: 2026-05-05T08:44:44.112183+00:00
instance: kb-cron
parent: fondements-de-la-g-ometrie-alg-brique-20260505-0
summary:
Fondements de la Géometrie Algébrique (FGA) is a book that collected together seminar notes of Alexander Grothendieck. It is an important source for his pioneering work on scheme theory, which laid foundations for algebraic geometry in its modern technical developments. The title is a translation of the title of André Weil's book Foundations of Algebraic Geometry. It contained material on descent theory, and existence theorems including that for the Hilbert scheme. The Technique de descente et théorèmes d'existence en géometrie algébrique is one series of seminars within FGA. Like the bulk of Grothendieck's work of the IHÉS period, duplicated notes were circulated, but the publication was not as a conventional book. == Contents == These are Séminaire Bourbaki notes, by number, from the years 1957 to 1962. Fondements de la géométrie algébrique. Commentaires [Séminaire Bourbaki, t. 14, 1961/62, Complément]; Théorème de dualité pour les faisceaux algébriques cohérents [Séminaire Bourbaki, t. 9, 1956/57, no. 149]; (coherent duality) Géométrie formelle et géométrie algébrique [Séminaire Bourbaki, t. 11, 1958/59, no. 182]; (formal geometry) Technique de descente et théorèmes d'existence en géométrie algébrique. I-VI I. Généralités. Descente par morphismes fidèlement plats [Séminaire Bourbaki, t. 12, 1959/60, no. 190]; II. Le théorème d'existence en théorie


id: formulario-mathematico-20260505-0
file: data/en.wikipedia.org/wiki/Formulario_mathematico-0.md
category: reference
title: Formulario mathematico
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Formulario_mathematico
date_saved: 2026-05-05T08:44:45.297151+00:00
instance: kb-cron
parent: formulario-mathematico-20260505-0
summary:
Formulario Mathematico (Latino sine flexione: Formulary for Mathematics) is a book by Giuseppe Peano which expresses fundamental theorems of mathematics in a symbolic language developed by Peano. The author was assisted by Giovanni Vailati, Mario Pieri, Alessandro Padoa, Giovanni Vacca, Vincenzo Vivanti, Gino Fano and Cesare Burali-Forti. The Formulario was first published in 1894. The fifth and last edition was published in 1908. Nicolas Bourbaki described Peano's notation in the Formulario as "following current mathematical usage, and introducing many well-chosen abbreviating symbols, his language succeeded moreover in being fairly readable, ..." Hubert Kennedy wrote "the development and use of mathematical logic is the guiding motif of the project". He also explains the variety of Peano's publication under the title: the five editions of the Formulario [are not] editions in the usual sense of the word. Each is essentially a new elaboration, although much material is repeated. Moreover, the title and language varied: the first three, titled Formulaire de Mathématiques, and the fourth, titled, Formulaire Mathématique, were written in French, while Latino sine flexione, Peano's own invention, was used for the fifth edition, titled Formulario Mathematico. ... Ugo Cassina lists no less than twenty separately published items as being parts of


id: foundations-of-algebraic-geometry-20260505-0
file: data/en.wikipedia.org/wiki/Foundations_of_Algebraic_Geometry-0.md
category: reference
title: Foundations of Algebraic Geometry
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Foundations_of_Algebraic_Geometry
date_saved: 2026-05-05T08:44:46.432627+00:00
instance: kb-cron
parent: foundations-of-algebraic-geometry-20260505-0
summary:
Foundations of Algebraic Geometry is a book by André Weil (1946, 1962) that develops algebraic geometry over fields of any characteristic. In particular it gives a careful treatment of intersection theory by defining the local intersection multiplicity of two subvarieties. Weil was motivated by the need for a rigorous theory of correspondences on algebraic curves in positive characteristic, which he used in his proof of the Riemann hypothesis for curves over finite fields. Weil introduced abstract rather than projective varieties partly so that he could construct the Jacobian of a curve. (It was not known at the time that Jacobians are always projective varieties.) It was some time before anyone found any examples of complete abstract varieties that are not projective. In the 1950s Weil's work was one of several competing attempts to provide satisfactory foundations for algebraic geometry, all of which were superseded by Grothendieck's development of schemes. == See also == Weil cohomology theory == References == Raynaud, Michel (1999), "André Weil and the foundations of algebraic geometry" (PDF), Notices of the American Mathematical Society, 46 (8): 864–867, MR 1704257 van der Waerden, Bartel Leendert (1971), "The foundation of algebraic geometry from Severi to André Weil", Archive for


id: the-fractal-dimension-of-architecture-20260505-0
file: data/en.wikipedia.org/wiki/The_Fractal_Dimension_of_Architecture-0.md
category: reference
title: The Fractal Dimension of Architecture
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/The_Fractal_Dimension_of_Architecture
date_saved: 2026-05-05T08:44:47.635701+00:00
instance: kb-cron
parent: the-fractal-dimension-of-architecture-20260505-0
summary:
The Fractal Dimension of Architecture is a book that applies the mathematical concept of fractal dimension to the analysis of the architecture of buildings. It was written by Michael J. Ostwald and Josephine Vaughan, both of whom are architecture academics at the University of Newcastle (Australia); it was published in 2016 by Birkhäuser, as the first volume in their Mathematics and the Built Environment book series. == Topics == The book applies the box counting method for computing fractal dimension, via the ArchImage software system, to compute a fractal dimension from architectural drawings (elevations and floor plans) of buildings, drawn at multiple levels of detail. The results of the book suggest that the results are consistent enough to allow for comparisons from one building to another, as long as the general features of the images (such as margins, line thickness, and resolution), parameters of the box counting algorithm, and statistical processing of the results are carefully controlled. The first five chapters of the book introduce fractals and the fractal dimension, and explain the methodology used by the authors for this analysis, also applying the same analysis to classical fractal structures including the Apollonian gasket, Fibonacci word, Koch snowflake, Minkowski sausage,


id: the-fractal-geometry-of-nature-20260505-0
file: data/en.wikipedia.org/wiki/The_Fractal_Geometry_of_Nature-0.md
category: reference
title: The Fractal Geometry of Nature
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/The_Fractal_Geometry_of_Nature
date_saved: 2026-05-05T08:44:48.793264+00:00
instance: kb-cron
parent: the-fractal-geometry-of-nature-20260505-0
summary:
The Fractal Geometry of Nature is a 1982 book by the Franco-American mathematician Benoît Mandelbrot. == Overview == The Fractal Geometry of Nature is a revised and enlarged version of his 1977 book entitled Fractals: Form, Chance and Dimension, which in turn was a revised, enlarged, and translated version of his 1975 French book, Les Objets Fractals: Forme, Hasard et Dimension. American Scientist put the book in its one hundred books of 20th century science. As technology has improved, mathematically accurate, computer-drawn fractals have become more detailed. Early drawings were low-resolution black and white; later drawings were higher resolution and in color. Many examples were created by programmers working with Mandelbrot, primarily at IBM Research. These visualizations have added to persuasiveness of the books and their impact on the scientific community. == See also == Chaos theory == References ==


id: fundamenta-nova-theoriae-functionum-ellipticarum-20260505-0
file: data/en.wikipedia.org/wiki/Fundamenta_nova_theoriae_functionum_ellipticarum-0.md
category: reference
title: Fundamenta nova theoriae functionum ellipticarum
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Fundamenta_nova_theoriae_functionum_ellipticarum
date_saved: 2026-05-05T08:44:49.966123+00:00
instance: kb-cron
parent: fundamenta-nova-theoriae-functionum-ellipticarum-20260505-0
summary:
Fundamenta nova theoriae functionum ellipticarum (from Latin: New Foundations of the Theory of Elliptic Functions) is a treatise on elliptic functions by German mathematician Carl Gustav Jacob Jacobi. The book was first published in 1829, and has been reprinted in volume 1 of his collected works and on several later occasions. The book introduces Jacobi elliptic functions and the Jacobi triple product identity. == References == Citations General Conway, John Horton (1980), "Monsters and moonshine", The Mathematical Intelligencer, 2 (4): 165–171, doi:10.1007/BF03028594, ISSN 0343-6993, MR 0600222, S2CID 121787388 Cooke, Roger (2005), "Chapter 31 C. F. G. Jacobi, book on elliptic functions", in Grattan-Guinness, Ivor (ed.), Landmark writings in western mathematics 1640–1940, Elsevier B. V., Amsterdam, pp. 412–430, ISBN 978-0-444-50871-3, MR 2169816 Jacobi, C. G. J. (1829), Fundamenta nova theoriae functionum ellipticarum (in Latin), Königsberg: Borntraeger, ISBN 978-1-108-05200-9, Reprinted by Cambridge University Press 2012 {{citation}}: ISBN / Date incompatibility (help) Jacobi, C. G. J. (1969) [1881], Gesammelte Werke, Herausgegeben auf Veranlassung der Königlich Preussischen Akademie der Wissenschaften, vol. I–VIII (2nd ed.), New York: Chelsea Publishing Co., MR 0260557, archived from the original on 2013-05-13, retrieved 2012-10-14


id: games-puzzles-and-computation-20260505-0
file: data/en.wikipedia.org/wiki/Games,_Puzzles,_and_Computation-0.md
category: reference
title: Games, Puzzles, and Computation
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Games,_Puzzles,_and_Computation
date_saved: 2026-05-05T08:44:51.099239+00:00
instance: kb-cron
parent: games-puzzles-and-computation-20260505-0
summary:
Games, Puzzles, and Computation is a book on game complexity, written by Robert Hearn and Erik Demaine, and published in 2009 by A K Peters. It is revised from Hearn's doctoral dissertation, which was supervised by Demaine. The Basic Library List Committee of the Mathematical Association of America has recommended it for inclusion in undergraduate mathematics libraries. == Topics == Games, Puzzles, and Computation concerns the computational complexity theory of solving logic puzzles and making optimal decisions in two-player and multi-player combinatorial games. Its focus is on games and puzzles that have seen real-world play, rather than ones that have been invented for a purely mathematical purpose. In this area it is common for puzzles and games such as sudoku, Rush Hour, reversi, and chess (in generalized forms with arbitrarily large boards) to be computationally difficult: sudoku is NP-complete, Rush Hour and reversi are PSPACE-complete, and chess is EXPTIME-complete. Beyond proving new results along these lines, the book aims to provide a unifying framework for proving such results, through the use of nondeterministic constraint logic, an abstract combinatorial problem that more closely resembles game play than the more classical problems previously used for completeness proofs. It is divided into three


id: geometric-and-topological-inference-20260505-0
file: data/en.wikipedia.org/wiki/Geometric_and_Topological_Inference-0.md
category: reference
title: Geometric and Topological Inference
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Geometric_and_Topological_Inference
date_saved: 2026-05-05T08:44:52.312144+00:00
instance: kb-cron
parent: geometric-and-topological-inference-20260505-0
summary:
Geometric and Topological Inference is a monograph in computational geometry, computational topology, geometry processing, and topological data analysis, on the problem of inferring properties of an unknown space from a finite point cloud of noisy samples from the space. It was written by Jean-Daniel Boissonnat, Frédéric Chazal, and Mariette Yvinec, and published in 2018 by the Cambridge University Press in their Cambridge Texts in Applied Mathematics book series. The Basic Library List Committee of the Mathematical Association of America has suggested its inclusion in undergraduate mathematics libraries. == Topics == The book is subdivided into four parts and 11 chapters. The first part covers basic tools from topology needed in the study, including simplicial complexes, Čech complexes and Vietoris–Rips complex, homotopy equivalence of topological spaces to their nerves, filtrations of complexes, and the data structures needed to represent these concepts efficiently in computer algorithms. A second introductory part concerns material of a more geometric nature, including Delaunay triangulations and Voronoi diagrams, convex polytopes, convex hulls and convex hull algorithms, lower envelopes, alpha shapes and alpha complexes, and witness complexes. With these preliminaries out of the way, the remaining two sections show how to use these tools for topological inference. The


id: geometric-exercises-in-paper-folding-20260505-0
file: data/en.wikipedia.org/wiki/Geometric_Exercises_in_Paper_Folding-0.md
category: reference
title: Geometric Exercises in Paper Folding
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Geometric_Exercises_in_Paper_Folding
date_saved: 2026-05-05T08:44:53.464312+00:00
instance: kb-cron
parent: geometric-exercises-in-paper-folding-20260505-0
summary:
Geometric Exercises in Paper Folding is a book on the mathematics of paper folding. It was written by Indian mathematician T. Sundara Row, first published in India in 1893, and later republished in many other editions. Its topics include paper constructions for regular polygons, symmetry, and algebraic curves. According to the historian of mathematics Michael Friedman, it became "one of the main engines of the popularization of folding as a mathematical activity". == Publication history == Geometric Exercises in Paper Folding was first published by Addison & Co. in Madras in 1893. The book became known in Europe through a remark of Felix Klein in his book Vorträge über ausgewählte Fragen der Elementargeometrie (1895) and its translation Famous Problems Of Elementary Geometry (1897). Based on the success of Geometric Exercises in Paper Folding in Germany, the Open Court Press of Chicago published it in the US, with updates by Wooster Woodruff Beman and David Eugene Smith. Although Open Court listed four editions of the book, published in 1901, 1905, 1917, and 1941, the content did not change between these editions. The fourth edition was also published in London by La Salle, and both presses reprinted the fourth edition in 1958.


id: geometric-folding-algorithms-20260505-0
file: data/en.wikipedia.org/wiki/Geometric_Folding_Algorithms-0.md
category: reference
title: Geometric Folding Algorithms
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Geometric_Folding_Algorithms
date_saved: 2026-05-05T08:44:54.562391+00:00
instance: kb-cron
parent: geometric-folding-algorithms-20260505-0
summary:
Geometric Folding Algorithms: Linkages, Origami, Polyhedra is a monograph on the mathematics and computational geometry of mechanical linkages, paper folding, and polyhedral nets, by Erik Demaine and Joseph O'Rourke. It was published in 2007 by Cambridge University Press (ISBN 978-0-521-85757-4). A Japanese-language translation by Ryuhei Uehara was published in 2009 by the Modern Science Company (ISBN 978-4-7649-0377-7). == Audience == Although aimed at computer science and mathematics students, much of the book is accessible to a broader audience of mathematically-sophisticated readers with some background in high-school level geometry. Mathematical origami expert Tom Hull has called it "a must-read for anyone interested in the field of computational origami". It is a monograph rather than a textbook, and in particular does not include sets of exercises. The Basic Library List Committee of the Mathematical Association of America has recommended this book for inclusion in undergraduate mathematics libraries. == Topics and organization == The book is organized into three sections, on linkages, origami, and polyhedra. Topics in the section on linkages include the Peaucellier–Lipkin linkage for converting rotary motion into linear motion, Kempe's universality theorem that any algebraic curve can be traced out by a linkage, the existence of linkages for angle trisection,


id: geometric-origami-20260505-0
file: data/en.wikipedia.org/wiki/Geometric_Origami-0.md
category: reference
title: Geometric Origami
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Geometric_Origami
date_saved: 2026-05-05T08:44:55.725835+00:00
instance: kb-cron
parent: geometric-origami-20260505-0
summary:
Geometric Origami is a book on the mathematics of paper folding, focusing on the ability to simulate and extend classical straightedge and compass constructions using origami. It was written by Austrian mathematician Robert Geretschläger and published by Arbelos Publishing (Shipley, UK) in 2008. The Basic Library List Committee of the Mathematical Association of America has suggested its inclusion in undergraduate mathematics libraries. == Topics == The book is divided into two main parts. The first part is more theoretical. It outlines the Huzita–Hatori axioms for mathematical origami, and proves that they are capable of simulating any straightedge and compass construction. It goes on to show that, in this mathematical model, origami is strictly more powerful than straightedge and compass: with origami, it is possible to solve any cubic equation or quartic equation. In particular, origami methods can be used to trisect angles, and for doubling the cube, two problems that have been proven to have no exact solution using only straightedge and compass. The second part of the book focuses on folding instructions for constructing regular polygons using origami, and on finding the largest copy of a given regular polygon that can be constructed within a given square sheet of


id: la-g-om-trie-20260505-0
file: data/en.wikipedia.org/wiki/La_Géométrie-0.md
category: reference
title: La Géométrie
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/La_Géométrie
date_saved: 2026-05-05T08:44:56.902470+00:00
instance: kb-cron
parent: la-g-om-trie-20260505-0
summary:
La Géométrie (French pronunciation: [la ʒeɔmetʁi]) was published in 1637 as an appendix to Discours de la méthode (Discourse on the Method), written by René Descartes. In the Discourse, Descartes presents his method for obtaining clarity on any subject. La Géométrie and two other appendices, also by Descartes, La Dioptrique (Optics) and Les Météores (Meteorology), were published with the Discourse to give examples of the kinds of successes he had achieved following his method (as well as, perhaps, considering the contemporary European social climate of intellectual competitiveness, to show off a bit to a wider audience). The work was the first to propose the idea of uniting algebra and geometry into a single subject and invented an algebraic geometry called analytic geometry, which involves reducing geometry to a form of arithmetic and algebra and translating geometric shapes into algebraic equations. For its time this was ground-breaking. It also contributed to the mathematical ideas of Leibniz and Newton and was thus important in the development of calculus. == The text == This appendix is divided into three "books". Book I is titled Problems Which Can Be Constructed by Means of Circles and Straight Lines Only. In this book he introduces algebraic


id: geometry-from-africa-20260505-0
file: data/en.wikipedia.org/wiki/Geometry_From_Africa-0.md
category: reference
title: Geometry From Africa
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Geometry_From_Africa
date_saved: 2026-05-05T08:44:58.111842+00:00
instance: kb-cron
parent: geometry-from-africa-20260505-0
summary:
Geometry From Africa: Mathematical and Educational Explorations is a book in ethnomathematics by Paulus Gerdes. It analyzes the mathematics behind geometric designs and patterns from multiple African cultures, and suggests ways of connecting this analysis with the mathematics curriculum. It was published in 1999 by the Mathematical Association of America, in their Classroom Resource Materials book series. == Background == The book's author, Paulus Gerdes (1952–2014), was a mathematician from the Netherlands who became a professor of mathematics at the Eduardo Mondlane University in Mozambique, rector of Maputo University, and chair of the African Mathematical Union Commission on the History of Mathematics in Africa. He was a prolific author, especially of works on the ethnomathematics of Africa. However, as many of his publications were written in Portuguese, German, and French, or published only in Mozambique, this book makes his work in ethnomathematics more accessible to English-speaking mathematicians. == Topics == The book is heavily illustrated, and describes geometric patterns in the carvings, textiles, drawings and paintings of multiple African cultures. Although these are primarily decorative rather than mathematical, Gerdes adds his own mathematical analysis of the patterns, and suggests ways of incorporating this analysis into the mathematical curriculum. It is


id: the-geometry-of-the-octonions-20260505-0
file: data/en.wikipedia.org/wiki/The_Geometry_of_the_Octonions-0.md
category: reference
title: The Geometry of the Octonions
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/The_Geometry_of_the_Octonions
date_saved: 2026-05-05T08:44:59.245218+00:00
instance: kb-cron
parent: the-geometry-of-the-octonions-20260505-0
summary:
The Geometry of the Octonions is a mathematics book on the octonions, a system of numbers generalizing the complex numbers and quaternions, presenting its material at a level suitable for undergraduate mathematics students. It was written by Tevian Dray and Corinne Manogue, and published in 2015 by World Scientific. The Basic Library List Committee of the Mathematical Association of America has suggested its inclusion in undergraduate mathematics libraries. == Topics == The book is subdivided into three parts, with the second part being the most significant. Its contents combine both a survey of past work in this area, and much of its authors' own researches. The first part explains the Cayley–Dickson construction, which constructs the complex numbers from the real numbers, the quaternions from the complex numbers, and the octonions from the quaternions. Related algebras are also discussed, including the sedenions (a 16-dimensional real algebra formed in the same way by taking one more step past the octonions) and the split real unital composition algebras (also called Hurwitz algebras). A particular focus here is on interpreting the multiplication operation of these algebras in a geometric way. Reviewer Danail Brezov notes with disappointment that Clifford algebras, although very relevant to this


id: glossary-of-principia-mathematica-20260505-0
file: data/en.wikipedia.org/wiki/Glossary_of_Principia_Mathematica-0.md
category: reference
title: Glossary of Principia Mathematica
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Glossary_of_Principia_Mathematica
date_saved: 2026-05-05T08:45:01.640169+00:00
instance: kb-cron
parent: glossary-of-principia-mathematica-20260505-0
summary:
This is a list of the notation used in Alfred North Whitehead and Bertrand Russell's Principia Mathematica (1910–1913). The second (but not the first) edition of Volume I has a list of notation used at the end. == Glossary == This is a glossary of some of the technical terms in Principia Mathematica that are no longer widely used or whose meaning has changed. apparent variable bound variable atomic proposition A proposition of the form R(x,y,...) where R is a relation. Barbara A mnemonic for a certain syllogism. class A subset of the members of some type codomain The codomain of a relation R is the class of y such that xRy for some x. compact A relation R is called compact if whenever xRz there is a y with xRy and yRz concordant A set of real numbers is called concordant if all nonzero members have the same sign connected connexity A relation R is called connected if for any 2 distinct members x, y either xRy or yRx. continuous A continuous series is a complete totally ordered set isomorphic to the reals. *275 correlator bijection couple 1. A cardinal couple is a class with exactly two elements 2.


id: god-created-the-integers-20260505-0
file: data/en.wikipedia.org/wiki/God_Created_the_Integers-0.md
category: reference
title: God Created the Integers
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/God_Created_the_Integers
date_saved: 2026-05-05T08:45:02.760295+00:00
instance: kb-cron
parent: god-created-the-integers-20260505-0
summary:
God Created the Integers: The Mathematical Breakthroughs That Changed History is a 2005 anthology, edited by Stephen Hawking, of "excerpts from thirty-one of the most important works in the history of mathematics." Each chapter of the work focuses on a different mathematician and begins with a biographical overview. Within each chapter, Hawking examines the mathematician's key discoveries, presents formal proofs of significant results, and explains their impact on the development of the mathematical field. The title of the book is a reference to a quotation attributed to mathematician Leopold Kronecker, who once wrote that "God made the integers; all else is the work of man." == Content == The works are grouped by author and ordered chronologically. Each section is prefaced by notes on the mathematician's life and work. The anthology includes works by the following mathematicians: Selections from the works of Euler, Bolyai, Lobachevsky and Galois, which are included in the second edition of the book (published in 2007), were not included in the first edition. == Editions == Hawking, Stephen (2005). God Created the Integers: The Mathematical Breakthroughs That Changed History. Running Press Book Publishers. pp. 1160 (Hardback). ISBN 0-7624-1922-9. Hawking, Stephen (2007). God Created the Integers: The


id: the-ground-of-arts-20260505-0
file: data/en.wikipedia.org/wiki/The_Ground_of_Arts-0.md
category: reference
title: The Ground of Arts
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/The_Ground_of_Arts
date_saved: 2026-05-05T08:45:05.145058+00:00
instance: kb-cron
parent: the-ground-of-arts-20260505-0
summary:
Robert Recorde's Arithmetic: or, The Ground of Arts was one of the first printed English textbooks on arithmetic and the most popular of its time. The Ground of Arts appeared in London in 1543, and it was reprinted around 45 more editions until 1700. Editors and contributors of new sections included John Dee, John Mellis, Robert Hartwell, Thomas Willsford, and finally Edward Hatton. The text is in the format of a dialogue between master and student to facilitate learning arithmetic without a teacher. == References == Bregman, Alvan (1 July 2005). "Alligation Alternate and the Composition of Medicines: Arithmetic and Medicine in Early Modern England". Med. Hist. 49 (3): 299–320. doi:10.1017/s0025727300008899. PMC 1172291. PMID 16092789. Karpinski, Louis (1925). The history of arithmetic. Rand McNally. LCC QA21.K3. Recorde, Robert (1543). The Grounde of Artes. London: Reynold Wolff. LCC QA33.R3 1542a. Recorde, Robert (1699) [1543]. Edward Hatton (ed.). Arithmetick, or, The ground of arts. London: J.H. for Charles Harper. == Further reading == John Denniss & Fenny Smith, "Robert Recorde and his remarkable Arithmetic", pages 25 to 38 in Gareth Roberts & Fenny Smith (editors) (2012) Robert Recorde: The Life and Times of a Tudor Mathematician, Cardiff: University of Wales Press ISBN


id: grundlagen-der-mathematik-20260505-0
file: data/en.wikipedia.org/wiki/Grundlagen_der_Mathematik-0.md
category: reference
title: Grundlagen der Mathematik
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Grundlagen_der_Mathematik
date_saved: 2026-05-05T08:45:06.338584+00:00
instance: kb-cron
parent: grundlagen-der-mathematik-20260505-0
summary:
Grundlagen der Mathematik (English: Foundations of Mathematics) is a two-volume work by David Hilbert and Paul Bernays. Originally published in 1934 and 1939, it presents fundamental mathematical ideas and introduced second-order arithmetic. == Publication history == 1934/1939 (Vol. I, II) First German edition, Springer 1944 Reprint of first edition by J. W. Edwards, Ann Arbor, Michigan. 1968/1970 (Vol. I, II) Second revised German edition, Springer 1979/1982 (Vol. I, II) Russian translation of 1968/1970, Nauka Publ., Moscow 2001/2003 (Vol. I, II) French translation, L’Harmattan, Paris 2011/2013 (Parts A and B of Vol. I, prefaces and sections 1-5) English translation of 1968 and 1934, bilingual with German facsimile on the left-hand sides. The Hilbert Bernays Project is producing an English translation. == See also == Hilbert–Bernays paradox == References == Sieg, Wilfried; Ravaglia, Mark (2005), "Chapter 77. David Hilbert and Paul Bernays, Grundlagen der Mathematik" (PDF), in Grattan-Guinness, Ivor (ed.), Landmark writings in western mathematics 1640–1940, Elsevier B. V., Amsterdam, pp. 981–99, doi:10.1016/B978-044450871-3/50158-3, ISBN 978-0-444-50871-3, MR 2169816, archived from the original (PDF) on 2011-05-14, retrieved 2011-02-01 Hilbert, David; Bernays, Paul (1934), Grundlagen der Mathematik. I, Die Grundlehren der mathematischen Wissenschaften, vol. 40, Berlin, New York: Springer-Verlag, ISBN 978-3-540-04134-4, JFM 60.0017.02, MR 0237246,


id: grundz-ge-der-mengenlehre-20260505-0
file: data/en.wikipedia.org/wiki/Grundzüge_der_Mengenlehre-0.md
category: reference
title: Grundzüge der Mengenlehre
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Grundzüge_der_Mengenlehre
date_saved: 2026-05-05T08:45:07.505560+00:00
instance: kb-cron
parent: grundz-ge-der-mengenlehre-20260505-0
summary:
Grundzüge der Mengenlehre (English: Basics of Set Theory) is a book on set theory written by Felix Hausdorff. First published in April 1914, Grundzüge der Mengenlehre was the first comprehensive introduction to set theory. In addition to the systematic treatment of known results in set theory, the book also contains chapters on measure theory and topology, which were then still considered parts of set theory. Hausdorff presented and developed original material that later became the basis for those areas. In 1927, Hausdorff published an extensively revised second edition under the title Mengenlehre (English: Set Theory), omitting many topics from the first edition. In 1935, a third German edition was released, which in 1957 was translated into English by John R. Aumann et al. under the title Set Theory. == References == Blumberg, Henry (1920), "Hausdorff's Grundzüge der Mengenlehre", Bulletin of the American Mathematical Society, 27 (3): 116–129, doi:10.1090/S0002-9904-1920-03378-1. Gehman, H. M. (1927), "Hausdorff's Revised Mengenlehre", Bull. Amer. Math. Soc., 33 (6): 778–781, doi:10.1090/S0002-9904-1927-04478-0 Hausdorff, Felix (1914), Grundzüge der Mengenlehre, Leipzig: Veit, ISBN 978-0-8284-0061-9 {{citation}}: ISBN / Date incompatibility (help) Reprinted by Chelsea Publishing Company in 1944, 1949 and 1965 [1]. Hausdorff, F. (1935) [1927], Mengenlehre (3 ed.), Berlin-Leipzig: de Gruyter


id: the-higher-infinite-20260505-0
file: data/en.wikipedia.org/wiki/The_Higher_Infinite-0.md
category: reference
title: The Higher Infinite
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/The_Higher_Infinite
date_saved: 2026-05-05T08:45:09.938302+00:00
instance: kb-cron
parent: the-higher-infinite-20260505-0
summary:
The Higher Infinite: Large Cardinals in Set Theory from their Beginnings is a monograph in set theory by Akihiro Kanamori, concerning the history and theory of large cardinals, infinite sets characterized by such strong properties that their existence cannot be proven in Zermelo–Fraenkel set theory (ZFC). This book was published in 1994 by Springer-Verlag in their series Perspectives in Mathematical Logic, with a second edition in 2003 in their Springer Monographs in Mathematics series, and a paperback reprint of the second edition in 2009 (ISBN 978-3-540-88866-6). == Topics == Not counting introductory material and appendices, there are six chapters in The Higher Infinite, arranged roughly in chronological order by the history of the development of the subject. The author writes that he chose this ordering "both because it provides the most coherent exposition of the mathematics and because it holds the key to any epistemological concerns". In the first chapter, "Beginnings", the material includes inaccessible cardinals, Mahlo cardinals, measurable cardinals, compact cardinals and indescribable cardinals. The chapter covers the constructible universe and inner models, elementary embeddings and ultrapowers, and a result of Dana Scott that measurable cardinals are inconsistent with the axiom of constructibility. The second chapter, "Partition properties", includes


id: higher-topos-theory-20260505-0
file: data/en.wikipedia.org/wiki/Higher_Topos_Theory-0.md
category: reference
title: Higher Topos Theory
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Higher_Topos_Theory
date_saved: 2026-05-05T08:45:11.067998+00:00
instance: kb-cron
parent: higher-topos-theory-20260505-0
summary:
Higher Topos Theory is a treatise on the theory of ∞-categories written by American mathematician Jacob Lurie. In addition to introducing Lurie's new theory of ∞-topoi, the book is widely considered foundational to higher category theory. Since 2018, Lurie has been transferring the contents of Higher Topos Theory (along with new material) to Kerodon, an "online resource for homotopy-coherent mathematics" inspired by the Stacks Project. == Topics == Higher Topos Theory covers two related topics: ∞-categories and ∞-topoi (which are a special case of the former). The first five of the book's seven chapters comprise a rigorous development of general ∞-category theory in the language of quasicategories, a special class of simplicial set which acts as a model for ∞-categories. The path of this development largely parallels classical category theory, with the notable exception of the ∞-categorical Grothendieck construction; this correspondence, which Lurie refers to as "straightening and unstraightening", gains considerable importance in his treatment. The last two chapters are devoted to ∞-topoi, Lurie's own invention and the ∞-categorical analogue of topoi in classical category theory. The material of these chapters is original, and is adapted from an earlier preprint of Lurie's. There are also appendices discussing background material on


id: history-of-the-theory-of-numbers-20260505-0
file: data/en.wikipedia.org/wiki/History_of_the_Theory_of_Numbers-0.md
category: reference
title: History of the Theory of Numbers
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/History_of_the_Theory_of_Numbers
date_saved: 2026-05-05T08:45:12.238942+00:00
instance: kb-cron
parent: history-of-the-theory-of-numbers-20260505-0
summary:
History of the Theory of Numbers is a three-volume work by Leonard Eugene Dickson summarizing work in number theory up to about 1920. The style is unusual in that Dickson mostly just lists results by various authors, with little further discussion. The central topic of quadratic reciprocity and higher reciprocity laws is barely mentioned; this was apparently going to be the topic of a fourth volume that was never written (Fenster 1999). == Volumes == Volume 1 - Divisibility and Primality - 486 pages Volume 2 - Diophantine Analysis - 803 pages Volume 3 - Quadratic and Higher Forms - 313 pages == References == Carmichael, Robert D. (1919), "Recent Publications: Reviews: History of the Theory of Numbers. Volume I: Divisibility and Primality", The American Mathematical Monthly, 26 (9): 396–403, doi:10.2307/2971917, ISSN 0002-9890, JSTOR 2971917 Carmichael, Robert D. (1921), "Recent Publications: Reviews: History of the Theory of Numbers: History of the Theory of Numbers", The American Mathematical Monthly, 28 (2): 72–78, doi:10.2307/2973042, ISSN 0002-9890, JSTOR 2973042 Carmichael, Robert D. (1923), "Recent Publications: Reviews: History of the Theory of Numbers", The American Mathematical Monthly, 30 (5): 259–262, doi:10.2307/2299094, ISSN 0002-9890, JSTOR 2299094 Dickson, Leonard Eugene (2005) [1919], History of the theory


id: a-history-of-vector-analysis-20260505-0
file: data/en.wikipedia.org/wiki/A_History_of_Vector_Analysis-0.md
category: reference
title: A History of Vector Analysis
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/A_History_of_Vector_Analysis
date_saved: 2026-05-05T08:45:13.416934+00:00
instance: kb-cron
parent: a-history-of-vector-analysis-20260505-0
summary:
A History of Vector Analysis (1967) is a book on the history of vector analysis by Michael J. Crowe, originally published by the University of Notre Dame Press. As a scholarly treatment of a reformation in technical communication, the text is a contribution to the history of science. In 2002, Crowe gave a talk summarizing the book, including an entertaining introduction in which he covered its publication history and related the award of a Jean Scott prize of $4000. Crowe had entered the book in a competition for "a study on the history of complex and hypercomplex numbers" twenty-five years after his book was first published. == Summary of book == The book has eight chapters: the first on the origins of vector analysis including Ancient Greek and 16th and 17th century influences; the second on the 19th century William Rowan Hamilton and quaternions; the third on other 19th and 18th century vectorial systems including equipollence of Giusto Bellavitis and the exterior algebra of Hermann Grassmann. Chapter four is on the general interest in the 19th century on vectorial systems including analysis of journal publications as well as sections on major figures and their views (e.g., Peter Guthrie Tait as


id: ijp-the-book-of-surfaces-20260505-0
file: data/en.wikipedia.org/wiki/IJP_The_Book_of_Surfaces-0.md
category: reference
title: IJP The Book of Surfaces
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/IJP_The_Book_of_Surfaces
date_saved: 2026-05-05T08:45:16.947814+00:00
instance: kb-cron
parent: ijp-the-book-of-surfaces-20260505-0
summary:
IJP the book of surfaces is a book by George L. Legendre, with a foreword by Mohsen Mostafavi. == Overview == IJP the Book of Surfaces was released in 2003 by the publishing arm of the London-based Architectural Association School of Architecture. The book features six essays on the notion of surface written from an architectural, philosophical, literary, mathematical, and computational angle, as well as several lighter asides ranging from cookery to poetry. These threads have been given a particular typographic and graphic design treatment meant to weave them together into a continuous narrative. == Background and literary references == The book addresses some significant developments of the decade, such as the explosion of computational tools; the emergence of the 3D surface as an architectural signifier of the Digital Revolution; the profession's fascination with the formal possibilities of surface cladding; and the rise of innovative manufacturing technologies. It can be compared to contemporary titles like Mohsen Mostafavi’s and David Leatherbarrow’s Surface Architecture, an essay on the phenomenology of architectural façades, and Ellen Lupton’s collection Skin: Surface, Substance + Design, which explores the working metaphor of artificial skin in Materials science, fashion and the visual arts. By comparison, Illa Berman notes


id: in-pursuit-of-the-traveling-salesman-20260505-0
file: data/en.wikipedia.org/wiki/In_Pursuit_of_the_Traveling_Salesman-0.md
category: reference
title: In Pursuit of the Traveling Salesman
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/In_Pursuit_of_the_Traveling_Salesman
date_saved: 2026-05-05T08:45:18.117712+00:00
instance: kb-cron
parent: in-pursuit-of-the-traveling-salesman-20260505-0
summary:
In Pursuit of the Traveling Salesman: Mathematics at the Limits of Computation is a book on the travelling salesman problem, by William J. Cook, published in 2011 by the Princeton University Press, with a paperback reprint in 2014. The Basic Library List Committee of the Mathematical Association of America has suggested its inclusion in undergraduate mathematics libraries. == Topics == The travelling salesman problem asks to find the shortest cyclic tour of a collection of points, in the plane or in more abstract mathematical spaces. Because the problem is NP-hard, algorithms that take polynomial time are unlikely to be guaranteed to find its optimal solution; on the other hand a brute-force search of all permutations would always solve the problem exactly but would take far too long to be usable for all but the smallest problems. Threading a middle ground between these too-fast and too-slow running times, and developing a practical system that can find the exact solution of larger instances, raises difficult questions of algorithm engineering, which have sparked the development of "many of the concepts and techniques of combinatorial optimization". The introductory chapter of the book explores the limits of calculation on the problem, from 49-point problems solved


id: indra-s-pearls-book-20260505-0
file: data/en.wikipedia.org/wiki/Indra's_Pearls_(book)-0.md
category: reference
title: Indra's Pearls (book)
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Indra's_Pearls_(book)
date_saved: 2026-05-05T08:45:19.251800+00:00
instance: kb-cron
parent: indra-s-pearls-book-20260505-0
summary:
Indra's Pearls: The Vision of Felix Klein is a geometry book written by David Mumford, Caroline Series and David Wright, and published by Cambridge University Press in 2002 and 2015. The book explores the patterns created by iterating conformal maps of the complex plane called Möbius transformations, and their connections with symmetry and self-similarity. These patterns were glimpsed by German mathematician Felix Klein, but modern computer graphics allows them to be fully visualised and explored in detail. == Title == The book's title refers to Indra's net, a metaphorical object described in the Buddhist text of the Flower Garland Sutra. Indra's net consists of an infinite array of gossamer strands and pearls. The frontispiece to Indra's Pearls quotes the following description: In the glistening surface of each pearl are reflected all the other pearls ... In each reflection, again are reflected all the infinitely many other pearls, so that by this process, reflections of reflections continue without end. The allusion to Felix Klein's "vision" is a reference to Klein's early investigations of Schottky groups and hand-drawn plots of their limit sets. It also refers to Klein's wider vision of the connections between group theory, symmetry and geometry - see Erlangen


id: international-encyclopedia-of-statistical-science-20260505-0
file: data/en.wikipedia.org/wiki/International_Encyclopedia_of_Statistical_Science-0.md
category: reference
title: International Encyclopedia of Statistical Science
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/International_Encyclopedia_of_Statistical_Science
date_saved: 2026-05-05T08:45:21.535662+00:00
instance: kb-cron
parent: international-encyclopedia-of-statistical-science-20260505-0
summary:
The International Encyclopedia of Statistical Science is a statistical sciences reference published by Springer. It has been described as one of the scientific projects with the largest number of involved countries ever, since it includes contributors coming from 105 countries and six continents. It contains the last papers written by Hirotugu Akaike, Nobel Laureate Sir Clive Granger, John Nelder and Erich Leo Lehmann. The team has been nominated for the 2026 Nobel Peace Prize by qualified nominators from Cambodia and Spain, with additional nominations anticipated . The first edition, in three volumes, was edited by Miodrag Lovrić and appeared in December 2010. It is published by Springer and it is available in print and online form. == See also == Encyclopedia of Statistical Sciences == References == == External links == Publisher's webpage for this Encyclopedia


id: introduction-to-circle-packing-20260505-0
file: data/en.wikipedia.org/wiki/Introduction_to_Circle_Packing-0.md
category: reference
title: Introduction to Circle Packing
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Introduction_to_Circle_Packing
date_saved: 2026-05-05T08:45:22.697059+00:00
instance: kb-cron
parent: introduction-to-circle-packing-20260505-0
summary:
Introduction to Circle Packing: The Theory of Discrete Analytic Functions is a mathematical monograph concerning systems of tangent circles and the circle packing theorem. It was written by Kenneth Stephenson and published in 2005 by the Cambridge University Press. == Topics == Circle packings, as studied in this book, are systems of circles that touch at tangent points but do not overlap, according to a combinatorial pattern of adjacencies specifying which pairs of circles should touch. The circle packing theorem states that a circle packing exists if and only if the pattern of adjacencies forms a planar graph; it was originally proved by Paul Koebe in the 1930s, and popularized by William Thurston, who rediscovered it in the 1970s and connected it with the theory of conformal maps and conformal geometry. As a topic, this should be distinguished from sphere packing, which considers higher dimensions (here, everything is two dimensional) and is more focused on packing density than on combinatorial patterns of tangency. The book is divided into four parts, in progressive levels of difficulty. The first part introduces the subject visually, encouraging the reader to think about packings not just as static objects but as dynamic systems of circles


id: jade-mirror-of-the-four-unknowns-20260505-0
file: data/en.wikipedia.org/wiki/Jade_Mirror_of_the_Four_Unknowns-0.md
category: reference
title: Jade Mirror of the Four Unknowns
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Jade_Mirror_of_the_Four_Unknowns
date_saved: 2026-05-05T08:45:23.909555+00:00
instance: kb-cron
parent: jade-mirror-of-the-four-unknowns-20260505-0
summary:
Jade Mirror of the Four Unknowns, Siyuan yujian (simplified Chinese: 四元玉鉴; traditional Chinese: 四元玉鑒), also referred to as Jade Mirror of the Four Origins, is a 1303 mathematical monograph by Yuan dynasty mathematician Zhu Shijie. The book consists of an introduction and three books, with a total of 288 problems. The first four problems in the introduction illustrate his method of the four unknowns. He showed how to convert a problem stated verbally into a system of polynomial equations (up to the 14th order), by using up to four unknowns: 天 Heaven, 地 Earth, 人 Man, 物 Matter, and then how to reduce the system to a single polynomial equation in one unknown by successive elimination of unknowns. He then solved the high-order equation by Southern Song dynasty mathematician Qin Jiushao's "Ling long kai fang" method published in Shùshū Jiǔzhāng (“Mathematical Treatise in Nine Sections”) in 1247 (more than 570 years before English mathematician William Horner's method using synthetic division). To do this, he makes use of the Pascal triangle, which he labels as the diagram of an ancient method first discovered by Jia Xian before 1050. Zhu also solved square and cube roots problems by solving quadratic and cubic


id: jade-mirror-of-the-four-unknowns-20260505-1
file: data/en.wikipedia.org/wiki/Jade_Mirror_of_the_Four_Unknowns-1.md
category: reference
title: Jade Mirror of the Four Unknowns
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Jade_Mirror_of_the_Four_Unknowns
date_saved: 2026-05-05T08:45:23.909555+00:00
instance: kb-cron
parent: jade-mirror-of-the-four-unknowns-20260505-0
summary:
Successive elimination of unknowns to get 4 x 2 − 7 x − 686 = 0 {\displaystyle 4x^{2}-7x-686=0} Solve this and obtain 14 paces == Book I == === Problems of Right Angle Triangles and Rectangles === There are 18 problems in this section. Problem 18 Obtain a tenth order polynomial equation: 16 x 10 − 64 x 9 + 160 x 8 − 384 x 7 + 512 x 6 − 544 x 5 + 456 x 4 + 126 x 3 + 3 x 2 − 4 x − 177162 = 0 {\displaystyle 16x^{10}-64x^{9}+160x^{8}-384x^{7}+512x^{6}-544x^{5}+456x^{4}+126x^{3}+3x^{2}-4x-177162=0} The root of which is x = 3, multiply by 4, getting 12. That is the final answer. === Problems of Plane Figures === There are 18 problems in this section === Problems of Piece Goods === There are 9 problems in this section === Problems on Grain Storage === There are 6 problems in this section === Problems on Labour === There are 7 problems in this section === Problems of Equations for Fractional Roots === There are 13 problems in this section == Book II == === Mixed Problems === === Containment of Circles and Squares === === Problems on Areas ===


id: journey-into-geometries-20260505-0
file: data/en.wikipedia.org/wiki/Journey_into_Geometries-0.md
category: reference
title: Journey into Geometries
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Journey_into_Geometries
date_saved: 2026-05-05T08:45:25.051504+00:00
instance: kb-cron
parent: journey-into-geometries-20260505-0
summary:
Journey into Geometries is a book on non-Euclidean geometry. It was written by Hungarian-Australian mathematician Márta Svéd and published in 1991 by the Mathematical Association of America in their MAA Spectrum book series. == Topics == Journey into Geometries is written as a conversation between three characters: Alice, from Alice's Adventures in Wonderland (but older and familiar with Euclidean geometry), Lewis Carroll, the author of Alice's adventures, and a modern mathematician named "Dr. Whatif". Its topics include hyperbolic geometry, inversive geometry, and projective geometry, following an arrangement of these topics credited to Australian mathematician Carl Moppert, and possibly based on an earlier German-language textbook on similar topics by F. Gonseth and P. Marti. As in Alice's original adventures, the first part of the book is arranged as a travelogue. This part of the book has six chapters, each ending with a set of exercises. Following these chapters, more conventionally written material covers geometric axiom systems and provides solutions to the exercises. == Audience and reception == Reviewer William E. Fenton is unsure of the audience of the book, writing that it is not suitable as a textbook and would scare most undergraduates, but is too unserious for graduate students. David


id: letters-to-a-german-princess-20260505-0
file: data/en.wikipedia.org/wiki/Letters_to_a_German_Princess-0.md
category: reference
title: Letters to a German Princess
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Letters_to_a_German_Princess
date_saved: 2026-05-05T08:45:26.216400+00:00
instance: kb-cron
parent: letters-to-a-german-princess-20260505-0
summary:
Letters to a German Princess, On Different Subjects in Physics and Philosophy (French: Lettres à une princesse d'Allemagne sur divers sujets de physique et de philosophie) were a series of 234 letters written by the mathematician Leonhard Euler between 1760 and 1762 addressed to Friederike Charlotte of Brandenburg-Schwedt and her younger sister Louise. == Contents == Euler started the first letter with an explanation of the concept of "size". Starting with the definition of a foot, he defined the mile and the diameter of the earth as a unit in terms of foot and then calculated the distance of the planets of the Solar System in terms of the diameter of the earth. == Publication == The first two volumes of the 234 letters originally written in French appeared in print in Saint Petersburg in 1768 and the third in Frankfurt in 1774. The letters were later reprinted in Paris with the first volume in 1787, the second in 1788 and the third in 1789. The publication of the book was supported by empress Catherine II with her personally writing to Count Vorontsov in January 1766: I am certain that the academy will be resurrected from its ashes by such


id: letters-to-a-young-mathematician-20260505-0
file: data/en.wikipedia.org/wiki/Letters_to_a_Young_Mathematician-0.md
category: reference
title: Letters to a Young Mathematician
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Letters_to_a_Young_Mathematician
date_saved: 2026-05-05T08:45:27.375942+00:00
instance: kb-cron
parent: letters-to-a-young-mathematician-20260505-0
summary:
Letters to a Young Mathematician (ISBN 0-465-08231-9) is a 2006 book by Ian Stewart, and is part of Basic Books' Art of Mentoring series. Stewart mentions in the preface that he considers this book an update to G.H. Hardy's A Mathematician's Apology. The book is made up of letters to a fictional correspondent of Stewart's, an aspiring mathematician named Meg. The roughly chronological letters follow Meg from her high school years up to her receiving tenure from an American university. Reviews of the book were generally positive. Fernando Q. Gouvêa's review for the MAA calls it "full of good advice, much of it direct and to the point" and later, that "while it won't change the world, it may well help some young people decide to be (or not to be) mathematicians." In Emma Carberry's review for the AMS, reacted differently, saying that "one does not so much feel the benefit of a ream of practical advice, but rather of exposure to the inner realm of mathematics". A review in Nature was harsher, however, saying that "there is a general lack of information ... [and] too much jargon" and that it "suffers from being written entirely for a US audience",


id: liber-abaci-20260505-0
file: data/en.wikipedia.org/wiki/Liber_Abaci-0.md
category: reference
title: Liber Abaci
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Liber_Abaci
date_saved: 2026-05-05T08:45:28.580605+00:00
instance: kb-cron
parent: liber-abaci-20260505-0
summary:
The Liber Abaci or Liber Abbaci (Latin for "The Book of Calculation") was a 1202 Latin work on arithmetic by Leonardo of Pisa, posthumously known as Fibonacci. It is primarily famous for introducing both base-10 positional notation and the symbols known as Arabic numerals in Europe. == Premise == Liber Abaci was among the first Western books to describe the Hindu–Arabic numeral system and to use symbols resembling modern "Arabic numerals". By addressing the applications of both commercial tradesmen and mathematicians, it promoted the superiority of the system and the use of these glyphs. Although the book's title is sometimes translated as "The Book of the Abacus", Sigler (2002) notes that the word in title does not refer to the abacus as a calculating device. Rather, the word "abacus" was used at the time to refer to calculation in any form; the spelling "abbacus" with two "b"s was, and still is in Italy, used to refer to calculation using Hindu-Arabic numerals. The book describes methods of doing calculations without aid of an abacus, and as Ore (1948) confirms, for centuries after its publication the algorismists (followers of the style of calculation demonstrated in Liber Abaci) remained in conflict with the


id: liber-abaci-20260505-1
file: data/en.wikipedia.org/wiki/Liber_Abaci-1.md
category: reference
title: Liber Abaci
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Liber_Abaci
date_saved: 2026-05-05T08:45:28.580605+00:00
instance: kb-cron
parent: liber-abaci-20260505-0
summary:
Modern notation generally writes a fraction to the right of the whole number to which it is added, for instance 2 1 3 {\displaystyle 2\,{\tfrac {1}{3}}} for 7/3. Fibonacci instead would write the same fraction to the left, i.e., 1 3 2 {\displaystyle {\tfrac {1}{3}}\,2} . Fibonacci used a composite fraction notation in which a sequence of numerators and denominators shared the same fraction bar; each such term represented an additional fraction of the given numerator divided by the product of all the denominators below and to the right of it. That is, b a d c = a c + b c d {\displaystyle {\tfrac {b\,\,a}{d\,\,c}}={\tfrac {a}{c}}+{\tfrac {b}{cd}}} , and c b a f e d = a d + b d e + c d e f {\displaystyle {\tfrac {c\,\,b\,\,a}{f\,\,e\,\,d}}={\tfrac {a}{d}}+{\tfrac {b}{de}}+{\tfrac {c}{def}}} . The notation was read from right to left. For example, 29/30 could be written as 1 2 4 2 3 5 {\displaystyle {\tfrac {1\,\,2\,\,4}{2\,\,3\,\,5}}} , representing the value 4 5 + 2 3 × 5 + 1 2 × 3 × 5 {\displaystyle {\tfrac {4}{5}}+{\tfrac {2}{3\times 5}}+{\tfrac {1}{2\times 3\times 5}}} . This can be viewed as a form of mixed radix notation and was


id: list-of-books-about-polyhedra-20260505-0
file: data/en.wikipedia.org/wiki/List_of_books_about_polyhedra-0.md
category: reference
title: List of books about polyhedra
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/List_of_books_about_polyhedra
date_saved: 2026-05-05T08:45:29.884776+00:00
instance: kb-cron
parent: list-of-books-about-polyhedra-20260505-0
summary:
This is a list of books about polyhedra. == Polyhedral models == === Cut-out kits === Jenkins, Gerald; Bear, Magdalen (1998). Paper Polyhedra in Colour. Tarquin. ISBN 1-899618-23-6. Advanced Polyhedra 1: The Final Stellation, ISBN 1-899618-61-9. Advanced Polyhedra 2: The Sixth Stellation, ISBN 1-899618-62-7. Advanced Polyhedra 3: The Compound of Five Cubes, ISBN 978-1-899618-63-7. Jenkins, Gerald; Wild, Anne (2000). Mathematical Curiosities. Tarquin. ISBN 1-899618-35-X. More Mathematical Curiosities, Tarquin, ISBN 1-899618-36-8. Make Shapes 1, ISBN 0-906212-00-6. Make Shapes 2, ISBN 0-906212-01-4. Smith, A. G. (1986). Cut and Assemble 3-D Geometrical Shapes: 10 Models in Full Color. Dover. Cut and Assemble 3-D Star Shapes, 1997. Easy-To-Make 3D Shapes in Full Color, 2000. Torrence, Eve (2011). Cut and Assemble Icosahedra: Twelve Models in White and Color. Dover. === Origami === Fuse, Tomoko (1990). Unit Origami: Multidimensional Transformations. Japan Publications. ISBN 978-0-87040-852-6. Gurkewitz, Rona; Arnstein, Bennett (1996). 3D Geometric Origami: Modular Origami Polyhedra. Dover. ISBN 9780486135601. Multimodular Origami Polyhedra: Archimedeans, Buckyballs and Duality, 2002. Beginner's Book of Modular Origami Polyhedra: The Platonic Solids, 2008. Modular Origami Polyhedra, also with Lewis Simon, 2nd ed., 1999. Mitchell, David (1997). Mathematical Origami: Geometrical Shapes by Paper Folding. Tarquin. ISBN 978-1-899618-18-7. Montroll, John (2009). Origami Polyhedra Design. A


id: list-of-books-about-polyhedra-20260505-1
file: data/en.wikipedia.org/wiki/List_of_books_about_polyhedra-1.md
category: reference
title: List of books about polyhedra
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/List_of_books_about_polyhedra
date_saved: 2026-05-05T08:45:29.884776+00:00
instance: kb-cron
parent: list-of-books-about-polyhedra-20260505-0
summary:
=== Monographs and special topics === Coxeter, H. S. M.; du Val, P.; Flather, H. T.; Petrie, J. F. (1938). The Fifty-Nine Icosahedra. University of Toronto Studies, Mathematical Series. Vol. 6. University of Toronto Press. 2nd ed., Springer, 1982. 3rd ed., Tarquin, 1999. Coxeter, H. S. M. (1974). Regular Complex Polytopes. Cambridge University Press. 2nd ed., 1991. Demaine, Erik; O'Rourke, Joseph (2007). Geometric Folding Algorithms: Linkages, Origami, Polyhedra. Cambridge University Press. Deza, Michel; Grishukhin, Viatcheslav; Shtogrin, Mikhail (2004). Scale-Isometric Polytopal Graphs in Hypercubes and Cubic Lattices: Polytopes in Hypercubes and Z n {\displaystyle \mathbb {Z} _{n}} . London: Imperial College Press. doi:10.1142/9781860945489. ISBN 1-86094-421-3. Lakatos, Imre (1976). Proofs and Refutations: The Logic of Mathematical Discovery. Cambridge University Press. McMullen, Peter (2020). Geometric Regular Polytopes. Encyclopedia of Mathematics and its Applications. Vol. 172. Cambridge University Press. McMullen, Peter; Schulte, Egon (2002). Abstract Regular Polytopes. Encyclopedia of Mathematics and its Applications. Vol. 92. Cambridge University Press. McMullen, Peter; Shephard, G. C. (1971). Convex Polytopes and the Upper Bound Conjecture. London Mathematical Society Lecture Note Series. Vol. 3. Cambridge University Press. Nef, Walter (1978). Beiträge zur Theorie der Polyeder: Mit Anwendungen in der Computergraphik [Contributions to the theory of the polyhedron, with applications


id: list-of-mathematics-books-20260505-0
file: data/en.wikipedia.org/wiki/List_of_mathematics_books-0.md
category: reference
title: List of mathematics books
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/List_of_mathematics_books
date_saved: 2026-05-05T08:45:31.111931+00:00
instance: kb-cron
parent: list-of-mathematics-books-20260505-0
summary:
This is a list of mathematics books including textbooks, expository works, popular mathematics fields, and historically significant treatises. == General works == Concrete Mathematics — Ronald Graham, Donald Knuth, and Oren Patashnik Concepts of Modern Mathematics — Ian Stewart Mathematics and the Imagination — Edward Kasner and James Newman Mathematics and Plausible Reasoning — George Pólya Mathematics: The Loss of Certainty — Morris Kline The Princeton Companion to Mathematics — Timothy Gowers What Is Mathematics? — Richard Courant and Herbert Robbins == Popular mathematics and biographies == A Mathematician's Apology — G. H. Hardy The Annotated Turing — Charles Petzold The Beauty of Fractals — Heinz-Otto Peitgen and Peter Richter The Emperor's New Mind — Roger Penrose Fermat's Enigma — Simon Singh God Created the Integers — Stephen Hawking Gödel, Escher, Bach — Douglas Hofstadter How Not to Be Wrong — Jordan Ellenberg The Man Who Loved Only Numbers — Paul Hoffman Prime Obsession — John Derbyshire Where Mathematics Comes From — George Lakoff and Rafael E. Núñez == Algebra == Algebra — Serge Lang Algebra: Chapter 0 — Paolo Aluffi == Calculus and analysis == Calculus on Manifolds — Michael Spivak Principles of Mathematical Analysis — Walter Rudin Introduction


id: making-mathematics-with-needlework-20260505-0
file: data/en.wikipedia.org/wiki/Making_Mathematics_with_Needlework-0.md
category: reference
title: Making Mathematics with Needlework
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Making_Mathematics_with_Needlework
date_saved: 2026-05-05T08:45:32.269533+00:00
instance: kb-cron
parent: making-mathematics-with-needlework-20260505-0
summary:
Making Mathematics with Needlework: Ten Papers and Ten Projects is an edited volume on mathematics and fiber arts. It was edited by Sarah-Marie Belcastro and Carolyn Yackel, and published in 2008 by A K Peters, based on a meeting held in 2005 in Atlanta by the American Mathematical Society. == Topics == The book includes ten different mathematical fiber arts projects, by eight contributors. An introduction provides a history of the connections between mathematics, mathematics education, and the fiber arts. Each of its ten project chapters is illustrated by many color photographs and diagrams, and is organized into four sections: an overview of the project, a section on the mathematics connected to it, a section of ideas for using the project as a teaching activity, and directions for constructing the project. Although there are some connections between topics, they can be read independently of each other, in any order. The thesis of the book is that directed exercises in fiber arts construction can help teach both mathematical visualization and concepts from three-dimensional geometry. The book uses knitting, crochet, sewing, and cross-stitch, but deliberately avoids weaving as a topic already well-covered in mathematical fiber arts publications. Projects in the book include


id: math-curse-20260505-0
file: data/en.wikipedia.org/wiki/Math_Curse-0.md
category: reference
title: Math Curse
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Math_Curse
date_saved: 2026-05-05T08:45:33.411156+00:00
instance: kb-cron
parent: math-curse-20260505-0
summary:
Math Curse is a children's picture book written by Jon Scieszka and illustrated by Lane Smith. Published in 1995 through Viking Press, the book tells the story of a student cursed by how mathematics is connected to everyday life. In 2009, Weston Woods Studios, Inc. released a film based on the book. == Plot summary == The nameless student begins with a seemingly innocent statement by her math teacher: "you know, almost everything in life can be considered a math problem." The next morning, the hero finds herself thinking of the time she needs to get up, along the lines of algebra. Next comes the mathematical school of probability, followed by charts and statistics. As the narrator slowly turns into a "math zombie", everything in her life is transformed into a problem. A class treat of cupcakes becomes a study in fractions, while a trip to the store turns into a problem of money. Finally, she is left painstakingly calculating how many minutes of "math madness" will be in her life now that she is a "mathematical lunatic." Her sister asks her what her problem is, and she responds, "365 days x 24 hours x 60 minutes." Finally, she collapses


id: mathematical-cranks-20260505-0
file: data/en.wikipedia.org/wiki/Mathematical_Cranks-0.md
category: reference
title: Mathematical Cranks
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Mathematical_Cranks
date_saved: 2026-05-05T08:45:34.587603+00:00
instance: kb-cron
parent: mathematical-cranks-20260505-0
summary:
Mathematical Cranks is a book on pseudomathematics and the cranks who create it, written by Underwood Dudley. It was published by the Mathematical Association of America in their MAA Spectrum book series in 1992 (ISBN 0-88385-507-0). == Topics == Previously, Augustus De Morgan wrote in A Budget of Paradoxes about cranks in multiple subjects, and Dudley wrote a book about angle trisection. However, this book is the first to focus on mathematical crankery as a whole. The book consists of 57 essays, loosely organized by the most common topics in mathematics for cranks to focus their attention on. The "top ten" of these topics, as listed by reviewer Ian Stewart, are, in order: squaring the circle, angle trisection, Fermat's Last Theorem, non-Euclidean geometry and the parallel postulate, the golden ratio, perfect numbers, the four color theorem, advocacy for duodecimal and other non-standard number systems, Cantor's diagonal argument for the uncountability of the real numbers, and doubling the cube. Other common topics for crankery, collected by Dudley, include calculations for the perimeter of an ellipse, roots of quintic equations, Fermat's little theorem, Gödel's incompleteness theorems, Goldbach's conjecture, magic squares, divisibility rules, constructible polygons, twin primes, set theory, statistics, and the Van


id: mathematical-foundations-of-quantum-mechanics-20260505-0
file: data/en.wikipedia.org/wiki/Mathematical_Foundations_of_Quantum_Mechanics-0.md
category: reference
title: Mathematical Foundations of Quantum Mechanics
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Mathematical_Foundations_of_Quantum_Mechanics
date_saved: 2026-05-05T08:45:35.818465+00:00
instance: kb-cron
parent: mathematical-foundations-of-quantum-mechanics-20260505-0
summary:
Mathematical Foundations of Quantum Mechanics (German: Mathematische Grundlagen der Quantenmechanik) is a quantum mechanics book written by John von Neumann in 1932. It is an important early work in the development of the mathematical formulation of quantum mechanics. The book mainly summarizes results that von Neumann had published in earlier papers. Von Neumann formalized quantum mechanics using the concept of Hilbert spaces and linear operators. He acknowledged the previous work by Paul Dirac on the mathematical formalization of quantum mechanics, but was skeptical of Dirac's use of delta functions. He wrote the book in an attempt to be even more mathematically rigorous than Dirac. It was von Neumann's last book in German, afterwards he started publishing in English. == Publication history == The book was originally published in German in 1932 by Springer. It was translated into French by Alexandru Proca in 1946, and into Spanish in 1949. An English translation by Robert T. Beyer was published in 1955 by Princeton University Press. A Russian translation, edited by Nikolay Bogolyubov, was published by Nauka in 1964. A new English edition, edited by Nicholas A. Wheeler, was published in 2018 by Princeton University Press. == Table of contents == According to


id: mathematical-foundations-of-quantum-mechanics-20260505-1
file: data/en.wikipedia.org/wiki/Mathematical_Foundations_of_Quantum_Mechanics-1.md
category: reference
title: Mathematical Foundations of Quantum Mechanics
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Mathematical_Foundations_of_Quantum_Mechanics
date_saved: 2026-05-05T08:45:35.818465+00:00
instance: kb-cron
parent: mathematical-foundations-of-quantum-mechanics-20260505-0
summary:
if there existed other, as yet undiscovered, physical quantities, in addition to those represented by the operators in quantum mechanics, because the relations assumed by quantum mechanics would have to fail already for the by now known quantities, those that we discussed above. It is therefore not, as is often assumed, a question of a re-interpretation of quantum mechanics, the present system of quantum mechanics would have to be objectively false, in order that another description of the elementary processes than the statistical one be possible. === Rejection === This proof was rejected as early as 1935 by Grete Hermann who found a flaw in the proof. The additive postulate above holds for quantum states, but it does not need to apply for measurements of dispersion-free states, specifically when considering non-commuting observables. Dispersion-free states only require to recover additivity when averaging over the hidden parameters. For example, for a spin-1/2 system, measurements of ( σ x + σ y ) {\displaystyle (\sigma _{x}+\sigma _{y})} can take values ± 2 {\displaystyle \pm {\sqrt {2}}} for a dispersion-free state, but independent measurements of σ x {\displaystyle \sigma _{x}} and σ y {\displaystyle \sigma _{y}} can only take values of ± 1 {\displaystyle


id: mathematical-models-cundy-and-rollett-20260505-0
file: data/en.wikipedia.org/wiki/Mathematical_Models_(Cundy_and_Rollett)-0.md
category: reference
title: Mathematical Models (Cundy and Rollett)
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Mathematical_Models_(Cundy_and_Rollett)
date_saved: 2026-05-05T08:45:38.192969+00:00
instance: kb-cron
parent: mathematical-models-cundy-and-rollett-20260505-0
summary:
Mathematical Models is a book on the construction of physical models of mathematical objects for educational purposes. It was written by Martyn Cundy and A. P. Rollett, and published by the Clarendon Press in 1951, with a second edition in 1961. Tarquin Publications published a third edition in 1981. The vertex configuration of a uniform polyhedron, a generalization of the Schläfli symbol that describes the pattern of polygons surrounding each vertex, was devised in this book as a way to name the Archimedean solids, and has sometimes been called the Cundy–Rollett symbol as a nod to this origin. == Topics == The first edition of the book had five chapters, including its introduction which discusses model-making in general and the different media and tools with which one can construct models. The media used for the constructions described in the book include "paper, cardboard, plywood, plastics, wire, string, and sheet metal". The second chapter concerns plane geometry, and includes material on the golden ratio, the Pythagorean theorem, dissection problems, the mathematics of paper folding, tessellations, and plane curves, which are constructed by stitching, by graphical methods, and by mechanical devices. The third chapter, and the largest part of the book, concerns


id: mathematical-models-fischer-20260505-0
file: data/en.wikipedia.org/wiki/Mathematical_Models_(Fischer)-0.md
category: reference
title: Mathematical Models (Fischer)
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Mathematical_Models_(Fischer)
date_saved: 2026-05-05T08:45:39.351961+00:00
instance: kb-cron
parent: mathematical-models-fischer-20260505-0
summary:
Mathematical Models: From the Collections of Universities and Museums – Photograph Volume and Commentary is a book on the physical models of concepts in mathematics that were constructed in the 19th century and early 20th century and kept as instructional aids at universities. It credits Gerd Fischer as editor, but its photographs of models are also by Fischer. It was originally published by Vieweg+Teubner Verlag for their bicentennial in 1986, both in German (titled Mathematische Modelle. Aus den Sammlungen von Universitäten und Museen. Mit 132 Fotografien. Bildband und Kommentarband) and (separately) in English translation, in each case as a two-volume set with one volume of photographs and a second volume of mathematical commentary. Springer Spektrum reprinted it in a second edition in 2017, as a single dual-language volume. == Topics == The work consists of 132 full-page photographs of mathematical models, divided into seven categories, and seven chapters of mathematical commentary written by experts in the topic area of each category. These categories are: Wire and thread models, of hypercubes of various dimensions, and of hyperboloids, cylinders, and related ruled surfaces, described as "elementary analytic geometry" and explained by Fischer himself. Plaster and wood models of cubic and quartic algebraic


id: a-mathematical-theory-of-communication-20260505-0
file: data/en.wikipedia.org/wiki/A_Mathematical_Theory_of_Communication-0.md
category: reference
title: A Mathematical Theory of Communication
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/A_Mathematical_Theory_of_Communication
date_saved: 2026-05-05T08:45:40.516645+00:00
instance: kb-cron
parent: a-mathematical-theory-of-communication-20260505-0
summary:
"A Mathematical Theory of Communication" is an article by mathematician Claude Shannon published in Bell System Technical Journal in 1948. It was renamed The Mathematical Theory of Communication in the 1949 book of the same name, a small but significant title change after realizing the generality of this work. It has tens of thousands of citations, being one of the most influential and cited scientific papers of all time, as it gave rise to the field of information theory, with Scientific American referring to the paper as the "Magna Carta of the Information Age", while the electrical engineer Robert G. Gallager called the paper a "blueprint for the digital era". Historian James Gleick rated the paper as the most important development of 1948, placing the transistor second in the same time period, with Gleick emphasizing that the paper by Shannon was "even more profound and more fundamental" than the transistor. It is also noted that "as did relativity and quantum theory, information theory radically changed the way scientists look at the universe". The paper also formally introduced the term "bit" and serves as its theoretical foundation. == Publication == The article was the founding work of the field of information


id: mathematicall-magick-20260505-0
file: data/en.wikipedia.org/wiki/Mathematicall_Magick-0.md
category: reference
title: Mathematicall Magick
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Mathematicall_Magick
date_saved: 2026-05-05T08:45:41.682100+00:00
instance: kb-cron
parent: mathematicall-magick-20260505-0
summary:
Mathematicall Magick. Or, The Wonders that may be Performed by Mechanicall Geometry is a treatise by the English clergyman, natural philosopher, polymath and author John Wilkins (1614–1672). It was first published in 1648 in London; another edition was printed in 1680 and further editions were published in 1691 and 1707. The work is dedicated to Charles I Louis, the Elector Palatine. The first book describes traditional mechanical devices, speed, siege engines and the modern guns of Wilkins' era. The second book covers Wilkins' theories and observations on land yachts, submarines, flying machines, and perpetual motion. Wilkins thought that human aviation is feasible, if only sufficient exercise, research and development is directed towards it. He envisioned flying machines that would be large enough to carry several people. The book repeats tales about early attempts at human flight, including Busbequius' 16th-century reports about Turkish flight experiments in Constantinople. Wilkins also mentions Anglo-Saxon flight experiments during the reign of Edward the Confessor. The researcher called "Elmerus" in the text is probably Eilmer of Malmesbury, who experimented with gliding flight in the 11th century. == Abstract == Wilkins dedicated his work to His Highness the Prince Elector Palatine (Charles I Louis) who was in


id: mathematics-and-plausible-reasoning-20260505-0
file: data/en.wikipedia.org/wiki/Mathematics_and_Plausible_Reasoning-0.md
category: reference
title: Mathematics and Plausible Reasoning
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Mathematics_and_Plausible_Reasoning
date_saved: 2026-05-05T08:45:42.860670+00:00
instance: kb-cron
parent: mathematics-and-plausible-reasoning-20260505-0
summary:
Mathematics and Plausible Reasoning is a two-volume book by the mathematician George Pólya describing various methods for being a good guesser of new mathematical results. In the Preface to Volume 1 of the book Pólya exhorts all interested students of mathematics thus: "Certainly, let us learn proving, but also let us learn guessing." P. R. Halmos reviewing the book summarised the central thesis of the book thus: ". . . a good guess is as important as a good proof." == Outline == === Volume I: Induction and analogy in mathematics === Polya begins Volume I with a discussion on induction, not mathematical induction, but as a way of guessing new results. He shows how the chance observations of a few results of the form 4 = 2 + 2, 6 = 3 + 3, 8 = 3 + 5, 10 = 3 + 7, etc., may prompt a sharp mind to formulate the conjecture that every even number greater than 4 can be represented as the sum of two odd prime numbers. This is the well known Goldbach's conjecture. The first problem in the first chapter is to guess the rule according to which the successive terms of the


id: mathematics-made-difficult-20260505-0
file: data/en.wikipedia.org/wiki/Mathematics_Made_Difficult-0.md
category: reference
title: Mathematics Made Difficult
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Mathematics_Made_Difficult
date_saved: 2026-05-05T08:45:44.083466+00:00
instance: kb-cron
parent: mathematics-made-difficult-20260505-0
summary:
Mathematics Made Difficult is a book by Carl E. Linderholm that uses advanced mathematical methods to prove results normally shown using elementary proofs. Although the aim is largely satirical, it also shows the non-trivial mathematics behind operations normally considered obvious, such as numbering, counting, and factoring integers. Linderholm discusses these seemingly obvious ideas using concepts like categories and monoids. As an example, the proof that 2 is a prime number starts: It is easily seen that the only numbers between 0 and 2, including 0 but excluding 2, are 0 and 1. Thus the remainder left by any number on division by 2 is either 0 or 1. Hence the quotient ring Z/2Z, where 2Z is the ideal in Z generated by 2, has only the elements [0] and [1], where these are the images of 0 and 1 under the canonical quotient map. Since [1] must be the unit of this ring, every element of this ring except [0] is a unit, and the ring is a field ... == References ==


id: mathematics-form-and-function-20260505-0
file: data/en.wikipedia.org/wiki/Mathematics,_Form_and_Function-0.md
category: reference
title: Mathematics, Form and Function
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Mathematics,_Form_and_Function
date_saved: 2026-05-05T08:45:45.216076+00:00
instance: kb-cron
parent: mathematics-form-and-function-20260505-0
summary:
Mathematics, Form and Function, a book published in 1986 by Springer-Verlag, is a survey of the whole of mathematics, including its origins and deep structure, by the American mathematician Saunders Mac Lane. == Mathematics and human activities == Throughout his book, and especially in chapter I.11, Mac Lane informally discusses how mathematics is grounded in more ordinary concrete and abstract human activities. The following table is adapted from one given on p. 35 of Mac Lane (1986). The rows are very roughly ordered from most to least fundamental. For a bullet list that can be compared and contrasted with this table, see section 3 of Where Mathematics Comes From. Also see the related diagrams appearing on the following pages of Mac Lane (1986): 149, 184, 306, 408, 416, 422-28. Mac Lane (1986) cites a related monograph by Lars Gårding (1977). == Mac Lane's relevance to the philosophy of mathematics == Mac Lane cofounded category theory with Samuel Eilenberg, which enables a unified treatment of mathematical structures and of the relations among them, at the cost of breaking away from their cognitive grounding. Nevertheless, his views—however informal—are a valuable contribution to the philosophy and anthropology of mathematics. His views anticipate, in


id: mechanica-20260505-0
file: data/en.wikipedia.org/wiki/Mechanica-0.md
category: reference
title: Mechanica
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Mechanica
date_saved: 2026-05-05T08:45:47.561752+00:00
instance: kb-cron
parent: mechanica-20260505-0
summary:
Mechanica (Latin: Mechanica sive motus scientia analytice exposita; 1736) is a two-volume work published by mathematician Leonhard Euler which describes analytically the mathematics governing movement. Euler both developed the techniques of analysis and applied them to numerous problems in mechanics, notably in later publications the calculus of variations. Euler's laws of motion expressed scientific laws of Galileo and Newton in terms of points in reference frames and coordinate systems making them useful for calculation when the statement of a problem or example is slightly changed from the original. Newton–Euler equations express the dynamics of a rigid body. Euler has been credited with contributing to the rise of Newtonian mechanics especially in topics other than gravity. == References == == External links == Mechanica Vol. 1 [E015] – Latin. Mechanica Vol. 1 – English translation by Ian Bruce. Mechanica Vol. 2 [E016] – Latin. Mechanica Vol. 2 – English translation by Ian Bruce.


id: method-of-fluxions-20260505-0
file: data/en.wikipedia.org/wiki/Method_of_Fluxions-0.md
category: reference
title: Method of Fluxions
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Method_of_Fluxions
date_saved: 2026-05-05T08:45:48.700102+00:00
instance: kb-cron
parent: method-of-fluxions-20260505-0
summary:
Method of Fluxions (Latin: De Methodis Serierum et Fluxionum) is a mathematical treatise by Sir Isaac Newton which served as the earliest written formulation of modern calculus. The book was completed in 1671 and posthumously published in 1736. == Background == Fluxion is Newton's term for a derivative. He originally developed the method at Woolsthorpe Manor during the closing of Cambridge due to the Great Plague of London from 1665 to 1667. Newton did not choose to make his findings known (similarly, his findings which eventually became the Philosophiae Naturalis Principia Mathematica were developed at this time and hidden from the world in Newton's notes for many years). Gottfried Leibniz developed his form of calculus independently around 1673, seven years after Newton had developed the basis for differential calculus, as seen in surviving documents like “the method of fluxions and fluents..." from 1666. Leibniz, however, published his discovery of differential calculus in 1684, nine years before Newton formally published his fluxion notation form of calculus in part during 1693. == Impact == The calculus notation in use today is mostly that of Leibniz, although Newton's dot notation for differentiation x ˙ {\displaystyle {\dot {x}}} is frequently used to denote derivatives


id: methoden-der-mathematischen-physik-20260505-0
file: data/en.wikipedia.org/wiki/Methoden_der_mathematischen_Physik-0.md
category: reference
title: Methoden der mathematischen Physik
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Methoden_der_mathematischen_Physik
date_saved: 2026-05-05T08:45:49.831629+00:00
instance: kb-cron
parent: methoden-der-mathematischen-physik-20260505-0
summary:
Methoden der mathematischen Physik (translated into English with the title Methods of Mathematical Physics) is a 1924 book, in two volumes totalling around 1000 pages, published under the names of Richard Courant and David Hilbert. It was a comprehensive treatment of the "methods of mathematical physics" of the time. The second volume is devoted to the theory of partial differential equations. It contains presages of the finite element method, on which Courant would work subsequently, and which would eventually become basic to numerical analysis. The material of the book was worked up from the content of Hilbert's lectures. While Courant played the major editorial role, many at the University of Göttingen were involved in the writing-up, and in that sense it was a collective production. On its appearance in 1924 it apparently had little direct connection to the quantum theory questions at the centre of the theoretical physics of the time. That changed within two years, since the formulation of the Schrödinger equation made the Hilbert–Courant techniques of immediate relevance to the new wave mechanics. There was a second edition (1931/7), wartime edition in the USA (1943), and a third German edition (1968). The English version Methods of Mathematical Physics


id: a-metric-america-20260505-0
file: data/en.wikipedia.org/wiki/A_Metric_America-0.md
category: reference
title: A Metric America
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/A_Metric_America
date_saved: 2026-05-05T08:45:50.989387+00:00
instance: kb-cron
parent: a-metric-america-20260505-0
summary:
A Metric America: A Decision Whose Time Has Come was a 1971 book by the United States National Bureau of Standards (now the National Institute of Standards and Technology) printed by the Government Printing Office. In 1968, in the Metric Study Act (Pub. L. 90-472, August 9, 1968, 82 Stat. 693), Congress authorized a three-year study of systems of measurement in the U.S., with particular emphasis on the feasibility of adopting the SI. This detailed U.S. Metric Study was conducted by the Department of Commerce. A 45-member advisory panel consulted with and took testimony from hundreds of consumers, business organizations, labor groups, manufacturers, and state and local officials. A Metric America: "A Decision Whose Time Has Come" – For Real (NISTIR 4858) was a June 1992 follow-up to this book. == See also == Metrication in the United States == External links == A Metric America; A Decision Whose Time Has Come A Metric America: A Decision Whose Time Has Come - For Real (NISTIR 4858) at the Wayback Machine (archived November 12, 2011)


id: metric-structures-for-riemannian-and-non-riemannian-spaces-20260505-0
file: data/en.wikipedia.org/wiki/Metric_Structures_for_Riemannian_and_Non-Riemannian_Spaces-0.md
category: reference
title: Metric Structures for Riemannian and Non-Riemannian Spaces
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Metric_Structures_for_Riemannian_and_Non-Riemannian_Spaces
date_saved: 2026-05-05T08:45:52.170085+00:00
instance: kb-cron
parent: metric-structures-for-riemannian-and-non-riemannian-spaces-20260505-0
summary:
Metric Structures for Riemannian and Non-Riemannian Spaces is a book in geometry by Mikhail Gromov. It was originally published in French in 1981 under the title Structures métriques pour les variétés riemanniennes, by CEDIC (Paris). == History == The 1981 edition was edited by Jacques Lafontaine and Pierre Pansu. The English version, considerably expanded, was published in 1999 by Birkhäuser Verlag, with appendices by Pierre Pansu, Stephen Semmes, and Mikhail Katz. The book was well received and has been reprinted several times. == References ==


id: mishnat-ha-middot-20260505-0
file: data/en.wikipedia.org/wiki/Mishnat_ha-Middot-0.md
category: reference
title: Mishnat ha-Middot
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Mishnat_ha-Middot
date_saved: 2026-05-05T08:45:53.273259+00:00
instance: kb-cron
parent: mishnat-ha-middot-20260505-0
summary:
The Mishnat ha-Middot (Hebrew: מִשְׁנַת הַמִּדּוֹת, lit. 'Treatise of Measures') is the earliest known Hebrew treatise on geometry, composed of 49 mishnayot in six chapters. Scholars have dated the work to either the Mishnaic period or the early Islamic era. == History == === Date of composition === Moritz Steinschneider dated the Mishnat ha-Middot to between 800 and 1200 CE. Sarfatti and Langermann have advanced Steinschneider's claim of Arabic influence on the work's terminology, and date the text to the early ninth century. On the other hand, Hermann Schapira argued that the treatise dates from an earlier era, most likely the Mishnaic period, as its mathematical terminology differs from that of the Hebrew mathematicians of the Arab period. Solomon Gandz conjectured that the text was compiled no later than 150 CE (possibly by Rabbi Nehemiah) and intended to be a part of the Mishnah, but was excluded from its final canonical edition because the work was regarded as too secular. The content resembles both the work of Hero of Alexandria (c. 100 CE) and that of al-Khwārizmī (c. 800 CE) and the proponents of the earlier dating therefore see the Mishnat ha-Middot linking Greek and Islamic mathematics. === Modern history


id: murderous-maths-20260505-0
file: data/en.wikipedia.org/wiki/Murderous_Maths-0.md
category: reference
title: Murderous Maths
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Murderous_Maths
date_saved: 2026-05-05T08:45:54.477242+00:00
instance: kb-cron
parent: murderous-maths-20260505-0
summary:
Murderous Maths is a series of British educational books by author Kjartan Poskitt. Most of the books in the series are illustrated by illustrator Philip Reeve, with the exception of "The Secret Life of Codes", which is illustrated by Ian Baker, "Awesome Arithmetricks" illustrated by Daniel Postgate and Rob Davis, and "The Murderous Maths of Everything", also illustrated by Rob Davis. The Murderous Maths books have been published in over 25 countries. The books, which are aimed at children aged 8 and above, teach maths, spanning from basic arithmetic to relatively complex concepts such as the quadratic formula and trigonometry. The books are written in an informal similar style to the Horrible Histories, Horrible Science and Horrible Geography series, involving evil geniuses, gangsters, and a generally comedic tone. == Development == The first two books of the series were originally part of "The Knowledge" (now "Totally") series, itself a spin-off of Horrible Histories. However, these books were eventually redesigned and they, as well as the rest of the titles in the series, now use the Murderous Maths banner. According to Poskitt, "these books have even found their way into schools and proved to be a boost to GCSE studies". The


id: murderous-maths-20260505-1
file: data/en.wikipedia.org/wiki/Murderous_Maths-1.md
category: reference
title: Murderous Maths
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Murderous_Maths
date_saved: 2026-05-05T08:45:54.477242+00:00
instance: kb-cron
parent: murderous-maths-20260505-0
summary:
Professor Fiendish's Book of Diabolical Brain-benders (2002), ISBN 0-439-98226-X (mazes, logic, coin problems, number crosswords, shape cutting/rearranging, number squares.) Professor Fiendish's Book of Brain-benders (a smaller version of the above) (same as above) Sudoku: 100 Fun Number Puzzles (2005), ISBN 0-439-84570-X Kakuro and Other Fiendish Number Puzzles (2006), ISBN 0-439-95164-X One title that covers many different areas of mathematics has also been released: The Most Epic Book of Maths Ever (previously The Murderous Maths of Everything) (2010), ISBN 1-407-10367-9 (prime numbers, Sieve of Eratosthenes, Pythagoras' Theorem, triangular numbers, square numbers, the International Date Line, geometry, geometric constructions, topology, Möbius strips, curves (conic sections and cycloids Golomb Rulers, four-dimensional "Tic Tac Toe", The Golden Ratio, Fibonacci sequence, Logarithmic spirals, musical ratios, Theorems (including Ham sandwich theorem and Fixed point theorem), probability (cards, dice, cluedo etc.), Pascal's Triangle, Sierpinski Triangle, chess board, light years, size and distance of moon and planets, orbit, size of stars, shape of galaxy.) Kjartan has also written a book entitled Everyday Maths for Grown-Ups (2011). == Reviews == A recommendation of the series by Scientific American includes a quote from a Stanford engineer named Stacy F. Bennet, who described the series as "very humorous and engaging introductions


id: a-new-era-of-thought-20260505-0
file: data/en.wikipedia.org/wiki/A_New_Era_of_Thought-0.md
category: reference
title: A New Era of Thought
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/A_New_Era_of_Thought
date_saved: 2026-05-05T08:45:55.623559+00:00
instance: kb-cron
parent: a-new-era-of-thought-20260505-0
summary:
A New Era of Thought is a non-fiction work written by Charles Howard Hinton, published in 1888 and reprinted in 1900 by Swan Sonnenschein & Co. Ltd., London. A New Era of Thought is about four-dimensional space and its implications on human thinking. The preface was written by Alicia Boole and H. John Falk. They also rewrote Part II which Hinton had sketched. The book has xvi and 230 pages. == Context == A New Era of Thought is inspired by Plato's allegory of the cave and is influenced by the works of Immanuel Kant, Carl Friedrich Gauss and Nikolai Lobachevsky. It influenced the work of P.D. Ouspensky, particularly his book Tertium Organum where it is frequently quoted; Scientific American writer Martin Gardner, who mentioned this book in some of his articles; and Rudy Rucker's The Fourth Dimension. == Synopsis == A New Era of Thought consists of two parts. The first part is a collection of philosophical and mathematical essays on the fourth dimension. These essays are somewhat disconnected. They teach the possibility of thinking four-dimensionally and about the religious and philosophical insights thus obtainable. In the second part Hinton develops a system of coloured cubes. These cubes serve


id: number-theory-an-approach-through-history-from-hammurapi-to-legendre-20260505-0
category: reference
title: Number Theory: An Approach Through History from Hammurapi to Legendre
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Number_Theory:_An_Approach_Through_History_from_Hammurapi_to_Legendre
date_saved: 2026-05-05T08:45:58.975469+00:00
instance: kb-cron
parent: number-theory-an-approach-through-history-from-hammurapi-to-legendre-20260505-0
file:
data/en.wikipedia.org/wiki/Number_Theory:_An_Approach_Through_History_from_Hammurapi_to_Legendre-0.md

summary:
Number Theory: An Approach Through History from Hammurapi to Legendre is a book on the history of number theory, written by André Weil and published in 1984. The book reviews over three millennia of research on numbers but the key focus is on mathematicians from the 17th century to the 19th, in particular, on the works of the mathematicians Fermat, Euler, Lagrange, and Legendre paved the way for modern number theory. It does not discuss many of the developments in the field after the work of Gauss in Disquisitiones Arithmeticae. However, it does indicate some of the developments in fields which directly arise from these works, in particular, the theory of elliptic curves. == See also == List of important publications in mathematics == References == === Footnotes === === Bibliography === Number Theory, An Approach Through History from Hammurapi to Legendre by André Weil, Birkhäuser (December 2006) ISBN 978-0-8176-4565-6


id: numerical-recipes-20260505-0
file: data/en.wikipedia.org/wiki/Numerical_Recipes-0.md
category: reference
title: Numerical Recipes
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Numerical_Recipes
date_saved: 2026-05-05T08:46:00.240449+00:00
instance: kb-cron
parent: numerical-recipes-20260505-0
summary:
Numerical Recipes is the generic title of a series of books on algorithms and numerical analysis by William H. Press, Saul A. Teukolsky, William T. Vetterling and Brian P. Flannery. In various editions, the books have been in print since 1986. The most recent edition was published in 2007. == Overview == The Numerical Recipes books cover a range of topics that include both classical numerical analysis (interpolation, integration, linear algebra, differential equations, and so on), signal processing (Fourier methods, filtering), statistical treatment of data, and a few topics in machine learning (hidden Markov model, support vector machines). The writing style is accessible and has an informal tone. The emphasis is on understanding the underlying basics of techniques, not on the refinements that may, in practice, be needed to achieve optimal performance and reliability. Few results are proved with any degree of rigor, although the ideas behind proofs are often sketched, and references are given. Importantly, virtually all methods that are discussed are also implemented in a programming language, with the code printed in the book. Each variant of the book is keyed to a specific language. According to the publisher, Cambridge University Press, the Numerical Recipes books are historically


id: numerical-recipes-20260505-1
file: data/en.wikipedia.org/wiki/Numerical_Recipes-1.md
category: reference
title: Numerical Recipes
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Numerical_Recipes
date_saved: 2026-05-05T08:46:00.240449+00:00
instance: kb-cron
parent: numerical-recipes-20260505-0
summary:
However, Numerical Recipes does include the following statement regarding copyrights on computer programs:Copyright does not protect ideas, but only the expression of those ideas in a particular form. In the case of a computer program, the ideas consist of the program's methodology and algorithm, including the necessary sequence of steps adopted by the programmer. The expression of those ideas is the program source code ... If you analyze the ideas contained in a program, and then express those ideas in your own completely different implementation, then that new program implementation belongs to you. One early motivation for the GNU Scientific Library was that a free library was needed as a substitute for Numerical Recipes. === Style === Another line of criticism centers on the coding style of the books, which strike some modern readers as "Fortran-ish", though written in contemporary, object-oriented C++. The authors have defended their very terse coding style as necessary to the format of the book because of space limitations and for readability. == Titles in the series (partial list) == The books differ by edition (1st, 2nd, and 3rd) and by the computer language in which the code is given. Numerical Recipes. The Art of Scientific


id: on-numbers-and-games-20260505-0
file: data/en.wikipedia.org/wiki/On_Numbers_and_Games-0.md
category: reference
title: On Numbers and Games
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/On_Numbers_and_Games
date_saved: 2026-05-05T08:46:01.406278+00:00
instance: kb-cron
parent: on-numbers-and-games-20260505-0
summary:
On Numbers and Games is a mathematics book by John Horton Conway first published in 1976. The book is written by a pre-eminent mathematician, and is directed at other mathematicians. The material is, however, developed in a playful and unpretentious manner and many chapters are accessible to non-mathematicians. Martin Gardner discussed the book at length, particularly Conway's construction of surreal numbers, in his Mathematical Games column in Scientific American in September 1976. The book is roughly divided into two sections: the first half (or Zeroth Part), on numbers, the second half (or First Part), on games. In the Zeroth Part, Conway provides axioms for arithmetic: addition, subtraction, multiplication, division and inequality. This allows an axiomatic construction of numbers and ordinal arithmetic, namely, the integers, reals, the countable infinity, and entire towers of infinite ordinals. The object to which these axioms apply takes the form {L|R}, which can be interpreted as a specialized kind of set; a kind of two-sided set. By insisting that L<R, this two-sided set resembles the Dedekind cut. The resulting construction yields a field, now called the surreal numbers. The ordinals are embedded in this field. The construction is rooted in axiomatic set theory, and is closely


id: opera-omnia-leonhard-euler-20260505-0
file: data/en.wikipedia.org/wiki/Opera_Omnia_Leonhard_Euler-0.md
category: reference
title: Opera Omnia Leonhard Euler
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Opera_Omnia_Leonhard_Euler
date_saved: 2026-05-05T08:46:02.590672+00:00
instance: kb-cron
parent: opera-omnia-leonhard-euler-20260505-0
summary:
Opera Omnia Leonhard Euler (Leonhardi Euleri Opera omnia) is the compilation of Leonhard Euler's scientific writings. The project of this compilation was undertaken by the Euler Committee of the Swiss Academy of Sciences, established in 1908, and is ongoing as of September 2022. The Committee decided on "the edition of the Collected Works of Leonhard Euler in the original languages, convinced of rendering the entire scientific world a service thereby", and, in 1919, it indicated to collect “All works from Leonhard Euler, hitherto unseen or already printed, coming from St Petersburg or elsewhere need to be integrated. This also includes the scientific letters of Euler”. The project has been supported by the international community, notably the Petersburg Academy of Sciences where Euler taught and which lent out its Euler materials in 1910. Publishing Euler's Opera Omnia has been termed "one of the most extraordinary projects in publishing". The Opera Omnia, excepting correspondences still being compiled in IVA9, was made available online in 2022 via the Opera-Bernoulli-Euler, which is working to make "the entire work of Euler, the Bernoulli family and their environment" freely available online. == Euler's writings == During his life, Euler published about 560 writings. After his death


id: origami-polyhedra-design-20260505-0
file: data/en.wikipedia.org/wiki/Origami_Polyhedra_Design-0.md
category: reference
title: Origami Polyhedra Design
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Origami_Polyhedra_Design
date_saved: 2026-05-05T08:46:04.980941+00:00
instance: kb-cron
parent: origami-polyhedra-design-20260505-0
summary:
Origami Polyhedra Design is a book on origami designs for constructing polyhedra. It was written by the origami artist and mathematician John Montroll, and it was published in 2009 by A K Peters. == Topics == There are two traditional methods for making polyhedra out of paper: polyhedral nets and modular origami. In the net method, the faces of the polyhedron are placed to form an irregular shape on a flat sheet of paper, with some of these faces connected to each other within this shape; it is cut out and folded into the shape of the polyhedron, and the remaining pairs of faces are attached together. In the modular origami method, many similarly-shaped "modules" are each folded from a single sheet of origami paper, and then assembled to form a polyhedron, with pairs of modules connected by the insertion of a flap from one module into a slot in another module. This book does neither of those two things. Instead, it provides designs for folding polyhedra, each out of a single uncut sheet of origami paper. After a brief introduction to the mathematics of polyhedra and the concepts used to design origami polyhedra, book presents designs for folding 72


id: origamics-20260505-0
file: data/en.wikipedia.org/wiki/Origamics-0.md
category: reference
title: Origamics
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Origamics
date_saved: 2026-05-05T08:46:06.100462+00:00
instance: kb-cron
parent: origamics-20260505-0
summary:
Origamics: Mathematical Explorations Through Paper Folding is a book on the mathematics of paper folding by Kazuo Haga, a Japanese retired biology professor. It was edited and translated into English by Josefina C. Fonacier and Masami Isoda, based on material published in several Japanese-language books by Haga, and published in 2008 by World Scientific. The title is a portmanteau of "origami" and "mathematics", coined in the 1990s by Haga to describe the type of paper-folding mathematical exploration that would later be described in this book. == Topics == Although much of its content involves folding square sheets of origami paper, the book focuses on mathematical explorations developing from folding and unfolding paper rather than on the traditional use of origami to create paper figures and artworks. It is divided into ten chapters, exploring concepts in paper folding that are "so simple that they could be discovered by middle- or high-school students". The book begins with the exploration of a single fold of a corner of a square to a midpoint of an opposite edge, and its analysis involving the geometry of the 3–4–5 right triangle. Later explorations (sometimes presented with colorful stories of knights and princesses as motivation) concern folding


id: pasta-by-design-20260505-0
file: data/en.wikipedia.org/wiki/Pasta_by_Design-0.md
category: reference
title: Pasta by Design
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Pasta_by_Design
date_saved: 2026-05-05T08:46:07.271123+00:00
instance: kb-cron
parent: pasta-by-design-20260505-0
summary:
Pasta by Design is a book by George L. Legendre, with a foreword by Paola Antonelli, and photography by Stefano Graziani. It is based on an idea by Marco Guarnieri. == Overview == Pasta by Design spans the fields of architecture, food, and popular science. The book features 92 pasta shapes, each depicted by a photograph, a mathematical equation, a 3D visual, and a short paragraph on geographic provenance and cooking etiquette. It was first published in 2011 by Thames & Hudson, while a German translation was published in 2012 by Springer Verlag. == Taxonomy == Pasta by Design is primarily a work of taxonomy, or classification. The critical inventory of shapes recalls the compilations of building-related knowledge known in the nineteenth century as architectural treatises, in which the source material was systematically drawn and formatted as a catalogue. To organise and classify the large variety of pasta shapes, the book employed principles of phylogenetics. The first application of phylogenetics to architectural criticism appeared in Phylogenesis: FOA’s Ark (2003), an architectural monograph by Foreign Office Architects, the first such publication to catalogue projects exclusively by design property, instead of the commonly used markers of programme, location, and client. Pasta by


id: perspectiva-corporum-regularium-20260505-0
file: data/en.wikipedia.org/wiki/Perspectiva_corporum_regularium-0.md
category: reference
title: Perspectiva corporum regularium
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Perspectiva_corporum_regularium
date_saved: 2026-05-05T08:46:08.403606+00:00
instance: kb-cron
parent: perspectiva-corporum-regularium-20260505-0
summary:
Perspectiva corporum regularium (from Latin: Perspective of the Regular Solids) is a book of perspective drawings of polyhedra by German Renaissance goldsmith Wenzel Jamnitzer, with engravings by Jost Amman, published in 1568. Despite its Latin title, Perspectiva corporum regularium is written mainly in the German language. It was "the most lavish of the perspective books published in Germany in the late sixteenth century" and was included in several royal art collections. It may have been the first work to depict chiral icosahedral symmetry. == Topics == The book focuses on the five Platonic solids, with the subtitles of its title page citing Plato's Timaeus and Euclid's Elements for their history. Each of these five shapes has a chapter, whose title page relates the connection of its polyhedron to the classical elements in medieval cosmology: fire for the tetrahedron, earth for the cube, air for the octahedron, and water for the icosahedron, with the dodecahedron representing the heavens, its 12 faces corresponding to the 12 symbols of the zodiac. Each chapter includes four engravings of polyhedra, each showing six variations of the shape including some of their stellations and truncations, for a total of 120 polyhedra. This great amount of variation,


id: the-petersen-graph-20260505-0
file: data/en.wikipedia.org/wiki/The_Petersen_Graph-0.md
category: reference
title: The Petersen Graph
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/The_Petersen_Graph
date_saved: 2026-05-05T08:46:09.540930+00:00
instance: kb-cron
parent: the-petersen-graph-20260505-0
summary:
The Petersen Graph is a mathematics book about the Petersen graph and its applications in graph theory. It was written by Derek Holton and John Sheehan, and published in 1993 by the Cambridge University Press as volume 7 in their Australian Mathematical Society Lecture Series. == Topics == The Petersen graph is an undirected graph with ten vertices and fifteen edges, commonly drawn as a pentagram within a pentagon, with corresponding vertices attached to each other. It has many unusual mathematical properties, and has frequently been used as a counterexample to conjectures in graph theory. The book uses these properties as an excuse to cover several advanced topics in graph theory where this graph plays an important role. It is heavily illustrated, and includes both open problems on the topics it discusses and detailed references to the literature on these problems. After an introductory chapter, the second and third chapters concern graph coloring, the history of the four color theorem for planar graphs, its equivalence to 3-edge-coloring of planar cubic graphs, the snarks (cubic graphs that have no such colorings), and the conjecture of W. T. Tutte that every snark has the Petersen graph as a graph minor. Two more


id: point-processes-20260505-0
file: data/en.wikipedia.org/wiki/Point_Processes-0.md
category: reference
title: Point Processes
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Point_Processes
date_saved: 2026-05-05T08:46:13.101692+00:00
instance: kb-cron
parent: point-processes-20260505-0
summary:
Point Processes is a book on the mathematics of point processes, randomly located sets of points on the real line or in other geometric spaces. It was written by David Cox and Valerie Isham, and published in 1980 by Chapman & Hall in their Monographs on Applied Probability and Statistics book series. The Basic Library List Committee of the Mathematical Association of America has suggested its inclusion in undergraduate mathematics libraries. == Topics == Although Point Processes covers some of the general theory of point processes, that is not its main focus, and it avoids any discussion of statistical inference involving these processes. Instead, its aim is to present the properties and descriptions of several specific processes arising in applications of this theory, which had not been previously collected in texts in this area. Three of its six chapters concern more general material, while the final three are more specific. The first chapter includes introductory material on standard processes: Poisson point processes, renewal processes, self-exciting processes, and doubly stochastic processes. The second chapter provides some general theory including stationarity, orderliness (meaning that the probability of multiple arrivals in short intervals is sublinear in the interval length), Palm distributions, Fourier analysis,


id: polyhedra-book-20260505-0
file: data/en.wikipedia.org/wiki/Polyhedra_(book)-0.md
category: reference
title: Polyhedra (book)
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Polyhedra_(book)
date_saved: 2026-05-05T08:46:14.235573+00:00
instance: kb-cron
parent: polyhedra-book-20260505-0
summary:
Polyhedra is a book on polyhedra, by Peter R. Cromwell. It was published by in 1997 by the Cambridge University Press, with an unrevised paperback edition in 1999. == Topics == The book covers both the mathematics of polyhedra and its historical development, limiting itself only to three-dimensional geometry. The notion of what it means to be a polyhedron has varied over the history of the subject, as have other related definitions, an issue that the book handles largely by keeping definitions informal and flexible, and by pointing out problematic examples for these intuitive definitions. Many digressions help make the material readable, and the book includes many illustrations, including historical reproductions, line diagrams, and photographs of models of polyhedra. Polyhedra has ten chapters, the first four of which are primarily historical, with the remaining six more technical. The first chapter outlines the history of polyhedra from the ancient world up to Hilbert's third problem on the possibility of cutting polyhedra into pieces and reassembling them into different polyhedra. The second chapter considers the symmetries of polyhedra, the Platonic solids and Archimedean solids, and the honeycombs formed by space-filling polyhedra. Chapter 3 covers the history of geometry in medieval Islam and


id: polyominoes-puzzles-patterns-problems-and-packings-20260505-0
file: data/en.wikipedia.org/wiki/Polyominoes:_Puzzles,_Patterns,_Problems,_and_Packings-0.md
category: reference
title: Polyominoes: Puzzles, Patterns, Problems, and Packings
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Polyominoes:_Puzzles,_Patterns,_Problems,_and_Packings
date_saved: 2026-05-05T08:46:27.385356+00:00
instance: kb-cron
parent: polyominoes-puzzles-patterns-problems-and-packings-20260505-0
summary:
Polyominoes: Puzzles, Patterns, Problems, and Packings is a mathematics book on polyominoes, the shapes formed by connecting some number of unit squares edge-to-edge. It was written by Solomon Golomb, and is "universally regarded as a classic in recreational mathematics". The Basic Library List Committee of the Mathematical Association of America has strongly recommended its inclusion in undergraduate mathematics libraries. == Publication history == The book collects together material previously published by Golomb in various articles and columns, especially in Recreational Mathematics Magazine. It was originally published by Scribner's in 1965, titled simply Polyominoes, and including a plastic set of the twelve pentominoes. The book's title word "polyominoes" was invented for the subject by Golomb in 1954 as a back-formation from "domino". A translation into Russian by I. Yaglom, Полимино, was published by Mir in 1975; it includes also translations of two papers on polyominoes by Golomb and by David A. Klarner. A second English-language edition of the book was published by the Princeton University Press in 1994. It added to the corrected text of the original addition two more chapters on recent developments, an expanded bibliography, and two appendices, one giving an enumeration of polyominoes and a second reprinting a


id: prime-obsession-20260505-0
file: data/en.wikipedia.org/wiki/Prime_Obsession-0.md
category: reference
title: Prime Obsession
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Prime_Obsession
date_saved: 2026-05-05T08:46:28.637361+00:00
instance: kb-cron
parent: prime-obsession-20260505-0
summary:
Prime Obsession: Bernhard Riemann and the Greatest Unsolved Problem in Mathematics (2003) is a historical book on mathematics by John Derbyshire, detailing the history of the Riemann hypothesis, named for Bernhard Riemann, and some of its applications. The book was awarded the Mathematical Association of America's inaugural Euler Book Prize in 2007. == Overview == The book is written such that even-numbered chapters present historical elements related to the development of the conjecture, and odd-numbered chapters deal with the mathematical and technical aspects. Despite the title, the book provides biographical information on many iconic mathematicians including Euler, Gauss, and Lagrange. In chapter 1, "Card Trick", Derbyshire introduces the idea of an infinite series and the ideas of convergence and divergence of these series. He imagines that there is a deck of cards stacked neatly together, and that one pulls off the top card so that it overhangs from the deck. Explaining that it can overhang only as far as the center of gravity allows, the card is pulled so that exactly half of it is overhanging. Then, without moving the top card, he slides the second card so that it is overhanging too at equilibrium. As he does this more


id: the-princeton-companion-to-mathematics-20260505-0
file: data/en.wikipedia.org/wiki/The_Princeton_Companion_to_Mathematics-0.md
category: reference
title: The Princeton Companion to Mathematics
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/The_Princeton_Companion_to_Mathematics
date_saved: 2026-05-05T08:46:29.787993+00:00
instance: kb-cron
parent: the-princeton-companion-to-mathematics-20260505-0
summary:
The Princeton Companion to Mathematics is a book providing an extensive overview of mathematics that was published in 2008 by Princeton University Press. Edited by Timothy Gowers with associate editors June Barrow-Green and Imre Leader, it has been noted for the high caliber of its contributors. The book was the 2011 winner of the Euler Book Prize of the Mathematical Association of America, given annually to "an outstanding book about mathematics". == Topics and organization == The book concentrates primarily on modern pure mathematics rather than applied mathematics, although it does also cover both applications of mathematics and the mathematics that relates to those applications; it provides a broad overview of the significant ideas and developments in research mathematics. It is organized into eight parts: An introduction to mathematics, outlining the major areas of study, key definitions, and the goals and purposes of mathematical research. An overview of the history of mathematics, in seven chapters including the development of important concepts such as number, geometry, mathematical proof, and the axiomatic approach to the foundations of mathematics. A chronology of significant events in mathematical history is also provided later in the book. Three core sections, totalling approximately 600 pages. The first


id: the-principles-of-mathematics-20260505-0
file: data/en.wikipedia.org/wiki/The_Principles_of_Mathematics-0.md
category: reference
title: The Principles of Mathematics
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/The_Principles_of_Mathematics
date_saved: 2026-05-05T08:46:30.914036+00:00
instance: kb-cron
parent: the-principles-of-mathematics-20260505-0
summary:
The Principles of Mathematics (PoM) is a 1903 book by Bertrand Russell, in which the author presented his famous paradox and argued his thesis that mathematics and logic are identical. The book presents a view of the foundations of mathematics and Meinongianism and has become a classic reference. It reported on developments by Giuseppe Peano, Mario Pieri, Richard Dedekind, Georg Cantor, and others. In 1905 Louis Couturat published a partial French translation that expanded the book's readership. In 1937 Russell prepared a new introduction saying, "Such interest as the book now possesses is historical, and consists in the fact that it represents a certain stage in the development of its subject." Further editions were published in 1938, 1951, 1996, and 2009. == Contents == The Principles of Mathematics consists of 59 chapters divided into seven parts: indefinables in mathematics, number, quantity, order, infinity and continuity, space, matter and motion. In chapter one, "Definition of Pure Mathematics", Russell asserts that: The fact that all Mathematics is Symbolic Logic is one of the greatest discoveries of our age; and when this fact has been established, the remainder of the principles of mathematics consists in the analysis of Symbolic Logic itself. Russell deconstructs


id: the-principles-of-mathematics-20260505-1
file: data/en.wikipedia.org/wiki/The_Principles_of_Mathematics-1.md
category: reference
title: The Principles of Mathematics
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/The_Principles_of_Mathematics
date_saved: 2026-05-05T08:46:30.914036+00:00
instance: kb-cron
parent: the-principles-of-mathematics-20260505-0
summary:
The Principles of Mathematics, which I finished on 23 May 1902, turned out to be a crude and rather immature draft of the subsequent work [Principia Mathematica], from which, however, it differed in containing controversy with other philosophies of mathematics. Such self-deprecation from the author after half a century of philosophical growth is understandable. On the other hand, Jules Vuillemin wrote in 1968: The Principles inaugurated contemporary philosophy. Other works have won and lost the title. Such is not the case with this one. It is serious, and its wealth perseveres. Furthermore, in relation to it, in a deliberate fashion or not, it locates itself again today in the eyes of all those that believe that contemporary science has modified our representation of the universe and through this representation, our relation to ourselves and to others. Moreover, in the same reflection, Russell also recounts the singular place the composition of the book had in his intellectual life. He recalls: I finished this first draft of The Principles of Mathematics on the last day of the nineteenth century—i.e. December 31, 1900. The months since the previous July had been an intellectual honeymoon such as I have never experienced before or since.


id: proofs-and-refutations-20260505-0
file: data/en.wikipedia.org/wiki/Proofs_and_Refutations-0.md
category: reference
title: Proofs and Refutations
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Proofs_and_Refutations
date_saved: 2026-05-05T08:46:32.102198+00:00
instance: kb-cron
parent: proofs-and-refutations-20260505-0
summary:
Proofs and Refutations: The Logic of Mathematical Discovery is a 1976 book by philosopher Imre Lakatos expounding his view of the progress of mathematics. The book is written as a series of Socratic dialogues involving a group of students who discuss proposed proofs of Euler's polyhedral formula. A central theme is that definitions are not carved in stone, but often have to be patched up in the light of later insights, in particular failed proofs. This gives mathematics a somewhat experimental flavour. At the end of the Introduction, Lakatos explains that his purpose is to challenge formalism in mathematics, and to show that informal mathematics grows by a logic of "proofs and refutations". == Background == The 1976 book Proofs and Refutations is based on the first three chapters of his 1961 four-chapter doctoral thesis Essays in the Logic of Mathematical Discovery. But its first chapter is Lakatos's own revision of its chapter 1 that was first published as Proofs and Refutations in four parts in 1963–4 in the British Journal for the Philosophy of Science. == Synopsis == Many important logical ideas are explained in the book. For example, the difference between a counterexample to a lemma (a so-called


id: proofs-from-the-book-20260505-0
file: data/en.wikipedia.org/wiki/Proofs_from_THE_BOOK-0.md
category: reference
title: Proofs from THE BOOK
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Proofs_from_THE_BOOK
date_saved: 2026-05-05T08:46:33.272504+00:00
instance: kb-cron
parent: proofs-from-the-book-20260505-0
summary:
Proofs from THE BOOK is a book of mathematical proofs by Martin Aigner and Günter M. Ziegler, first published in 1998. The book is inspired by and named after an expression used by the mathematician Paul Erdős, who often referred to "The Book" in which God kept the best proof of each mathematical theorem. During a lecture in 1985, Erdős said, "You don't have to believe in God, but you should believe in The Book." The greatest praise Erdős gave to mathematical work was to proclaim it "straight from the Book". Aigner and Zeigler proposed to Erdős a real book that would be "a first (and very modest) approximation to 'The Book'". Erdős had many suggestions for proofs that should be included, and would have been a co-author except that he died in 1996. Proofs from THE BOOK is instead dedicated to his memory. Including its original publication, Proofs from THE BOOK has had six editions in English, and has been translated into Persian, French, German, Hungarian, Italian, Japanese, Chinese, Polish, Portuguese, Korean, Turkish, Russian, Spanish and Greek. The American Mathematical Society awarded the 2018 Leroy P. Steele Prize for Mathematical Exposition to Aigner and Ziegler for this book. ==


id: pythagorean-triangles-20260505-0
file: data/en.wikipedia.org/wiki/Pythagorean_Triangles-0.md
category: reference
title: Pythagorean Triangles
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Pythagorean_Triangles
date_saved: 2026-05-05T08:46:35.563939+00:00
instance: kb-cron
parent: pythagorean-triangles-20260505-0
summary:
Pythagorean Triangles is a book on right triangles, the Pythagorean theorem, and Pythagorean triples. It was originally written in the Polish language by Wacław Sierpiński (titled Trójkąty pitagorejskie), and published in Warsaw in 1954. Indian mathematician Ambikeshwar Sharma translated it into English, with some added material from Sierpiński, and published it in the Scripta Mathematica Studies series of Yeshiva University (volume 9 of the series) in 1962. Dover Books republished the translation in a paperback edition in 2003. There is also a Russian translation of the 1954 edition. == Topics == As a brief summary of the book's contents, reviewer Brian Hopkins quotes The Pirates of Penzance: "With many cheerful facts about the square of the hypotenuse." The book is divided into 15 chapters (or 16, if one counts the added material as a separate chapter). The first three of these define the primitive Pythagorean triples (the ones in which the two sides and hypotenuse have no common factor), derive the standard formula for generating all primitive Pythagorean triples, compute the inradius of Pythagorean triangles, and construct all triangles with sides of length at most 100. Chapter 4 considers special classes of Pythagorean triangles, including those with sides in arithmetic


id: quasicrystals-and-geometry-20260505-0
file: data/en.wikipedia.org/wiki/Quasicrystals_and_Geometry-0.md
category: reference
title: Quasicrystals and Geometry
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Quasicrystals_and_Geometry
date_saved: 2026-05-05T08:46:36.726659+00:00
instance: kb-cron
parent: quasicrystals-and-geometry-20260505-0
summary:
Quasicrystals and Geometry is a book on quasicrystals and aperiodic tiling by Marjorie Senechal, published in 1995 by Cambridge University Press (ISBN 0-521-37259-3). One of the main themes of the book is to understand how the mathematical properties of aperiodic tilings such as the Penrose tiling, and in particular the existence of arbitrarily large patches of five-way rotational symmetry throughout these tilings, correspond to the properties of quasicrystals including the five-way symmetry of their Bragg peaks. Neither kind of symmetry is possible for a traditional periodic tiling or periodic crystal structure, and the interplay between these topics led from the 1960s into the 1990s to new developments and new fundamental definitions in both mathematics and crystallography. == Topics == The book is divided into two parts. The first part covers the history of crystallography, the use of X-ray diffraction to study crystal structures through the Bragg peaks formed on their diffraction patterns, and the discovery in the early 1980s of quasicrystals, materials that form Bragg peaks in patterns with five-way symmetry, impossible for a repeating crystal structure. It models the arrangement of atoms in a substance by a Delone set, a set of points in the plane or in Euclidean


id: rabdology-20260505-0
file: data/en.wikipedia.org/wiki/Rabdology-0.md
category: reference
title: Rabdology
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Rabdology
date_saved: 2026-05-05T08:46:37.868793+00:00
instance: kb-cron
parent: rabdology-20260505-0
summary:
In 1617 a treatise in Latin titled Rabdologiæ and written by John Napier was published in Edinburgh. Printed three years after his treatise on the discovery of logarithms and in the same year as his death, it describes three devices to aid arithmetic calculations. The devices themselves don't use logarithms, rather they are tools to reduce multiplication and division of natural numbers to simple addition and subtraction operations. The first device, which by then was already popularly used and known as Napier's bones, was a set of rods inscribed with the multiplication table. Napier coined the word rabdology (from Greek ῥάβδος [rhabdos], rod and λόγoς [logos] calculation or reckoning) to describe this technique. The rods were used to multiply, divide and even find the square roots and cube roots of numbers. The second device was a promptuary (Latin promptuarium meaning storehouse) and consisted of a large set of strips that could multiply multidigit numbers more easily than the bones. In combination with a table of reciprocals, it could also divide numbers. The third device used a checkerboard like grid and counters moving on the board to perform binary arithmetic. Napier termed this technique location arithmetic from the way in which


id: regular-figures-20260505-0
file: data/en.wikipedia.org/wiki/Regular_Figures-0.md
category: reference
title: Regular Figures
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Regular_Figures
date_saved: 2026-05-05T08:46:38.980218+00:00
instance: kb-cron
parent: regular-figures-20260505-0
summary:
Regular Figures is a book on polyhedra and symmetric patterns, by Hungarian geometer László Fejes Tóth. It was published in 1964 by Pergamon in London and Macmillan in New York. == Topics == Regular Figures is divided into two parts, "Systematology of the Regular Figures" and "Genetics of the Regular Figures", each in five chapters. Although the first part represents older and standard material, much of the second part is based on a large collection of research works by Fejes Tóth, published over the course of approximately 25 years, and on his previous exposition of this material in a 1953 German-language text. The first part of the book covers many of the same topics as a previously published book, Regular Polytopes (1947), by H. S. M. Coxeter, but with a greater emphasis on group theory and the classification of symmetry groups. Its first three chapters describe the symmetries that two-dimensional geometric objects can have: the 17 wallpaper groups of the Euclidean plane in the first chapter, with the first English-language presentation of the proof of their classification by Evgraf Fedorov, the regular spherical tilings in chapter two, and the uniform tilings of the hyperbolic plane in chapter three. Also mentioned


id: regular-polytopes-book-20260505-0
file: data/en.wikipedia.org/wiki/Regular_Polytopes_(book)-0.md
category: reference
title: Regular Polytopes (book)
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Regular_Polytopes_(book)
date_saved: 2026-05-05T08:46:40.134422+00:00
instance: kb-cron
parent: regular-polytopes-book-20260505-0
summary:
Regular Polytopes is a geometry book on regular polytopes written by Harold Scott MacDonald Coxeter. It was originally published by Methuen in 1947 and by Pitman Publishing in 1948, with a second edition published by Macmillan in 1963 and a third edition by Dover Publications in 1973. The Basic Library List Committee of the Mathematical Association of America has recommended that it be included in undergraduate mathematics libraries. == Overview == The main topics of the book are the Platonic solids (regular convex polyhedra), related polyhedra, and their higher-dimensional generalizations. It has 14 chapters, along with multiple appendices, providing a more complete treatment of the subject than any earlier work, and incorporating material from 18 of Coxeter's own previous papers. It includes many figures (both photographs of models by Paul Donchian and drawings), tables of numerical values, and historical remarks on the subject. The first chapter discusses regular polygons, regular polyhedra, basic concepts of graph theory, and the Euler characteristic. Using the Euler characteristic, Coxeter derives a Diophantine equation whose integer solutions describe and classify the regular polyhedra. The second chapter uses combinations of regular polyhedra and their duals to generate related polyhedra, including the semiregular polyhedra, and discusses zonohedra


id: reverse-mathematics-proofs-from-the-inside-out-20260505-0
file: data/en.wikipedia.org/wiki/Reverse_Mathematics:_Proofs_from_the_Inside_Out-0.md
category: reference
title: Reverse Mathematics: Proofs from the Inside Out
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Reverse_Mathematics:_Proofs_from_the_Inside_Out
date_saved: 2026-05-05T08:46:41.365740+00:00
instance: kb-cron
parent: reverse-mathematics-proofs-from-the-inside-out-20260505-0
summary:
Reverse Mathematics: Proofs from the Inside Out is a book by John Stillwell on reverse mathematics, the process of examining proofs in mathematics to determine which axioms are required by the proof. It was published in 2018 by the Princeton University Press. == Topics == The book begins with a historical overview of the long struggles with the parallel postulate in Euclidean geometry, and of the foundational crisis of the late 19th and early 20th centuries, Then, after reviewing background material in real analysis and computability theory, the book concentrates on the reverse mathematics of theorems in real analysis, including the Bolzano–Weierstrass theorem, the Heine–Borel theorem, the intermediate value theorem and extreme value theorem, the Heine–Cantor theorem on uniform continuity, the Hahn–Banach theorem, and the Riemann mapping theorem. These theorems are analyzed with respect to three of the "big five" subsystems of second-order arithmetic, namely arithmetical comprehension, recursive comprehension, and the weak Kőnig's lemma. == Audience == The book is aimed at a "general mathematical audience" including undergraduate mathematics students with an introductory-level background in real analysis. It is intended both to excite mathematicians, physicists, and computer scientists about the foundational issues in their fields, and to provide an accessible


id: revolutions-in-mathematics-20260505-0
file: data/en.wikipedia.org/wiki/Revolutions_in_Mathematics-0.md
category: reference
title: Revolutions in Mathematics
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Revolutions_in_Mathematics
date_saved: 2026-05-05T08:46:42.514232+00:00
instance: kb-cron
parent: revolutions-in-mathematics-20260505-0
summary:
Revolutions in Mathematics is a 1992 collection of essays in the history and philosophy of mathematics. == Contents == Michael J. Crowe, Ten "laws" concerning patterns of change in the history of mathematics (1975) (15–20); Herbert Mehrtens, T. S. Kuhn's theories and mathematics: a discussion paper on the "new historiography" of mathematics (1976) (21–41); Herbert Mehrtens, Appendix (1992): revolutions reconsidered (42–48); Joseph Dauben, Conceptual revolutions and the history of mathematics: two studies in the growth of knowledge (1984) (49–71); Joseph Dauben, Appendix (1992): revolutions revisited (72–82); Paolo Mancosu, Descartes's Géométrie and revolutions in mathematics (83–116); Emily Grosholz, Was Leibniz a mathematical revolutionary? (117–133); Giulio Giorello, The "fine structure" of mathematical revolutions: metaphysics, legitimacy, and rigour. The case of the calculus from Newton to Berkeley and Maclaurin (134–168); Yu Xin Zheng, Non-Euclidean geometry and revolutions in mathematics (169–182); Luciano Boi, The "revolution" in the geometrical vision of space in the nineteenth century, and the hermeneutical epistemology of mathematics (183–208); Caroline Dunmore, Meta-level revolutions in mathematics (209–225); Jeremy Gray, The nineteenth-century revolution in mathematical ontology (226–248); Herbert Breger, A restoration that failed: Paul Finsler's theory of sets (249–264); Donald A. Gillies, The Fregean revolution in logic (265–305); Michael Crowe, Afterword (1992): a


id: sacred-mathematics-20260505-0
file: data/en.wikipedia.org/wiki/Sacred_Mathematics-0.md
category: reference
title: Sacred Mathematics
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Sacred_Mathematics
date_saved: 2026-05-05T08:46:44.766570+00:00
instance: kb-cron
parent: sacred-mathematics-20260505-0
summary:
Sacred Mathematics: Japanese Temple Geometry is a book on Sangaku, geometry problems presented on wooden tablets as temple offerings in the Edo period of Japan. It was written by Fukagawa Hidetoshi and Tony Rothman, and published in 2008 by the Princeton University Press. It won the PROSE Award of the Association of American Publishers in 2008 as the best book in mathematics for that year. == Topics == The book begins with an introduction to Japanese culture and how this culture led to the production of Sangaku tablets, depicting geometry problems, their presentation as votive offerings at temples, and their display at the temples. It also includes a chapter on the Chinese origins of Japanese mathematics, and a chapter on biographies of Japanese mathematicians from the time. The Sangaku tablets illustrate theorems in Euclidean geometry, typically involving circles or ellipses, often with a brief textual explanation. They are presented as puzzles for the viewer to prove, and in many cases the proofs require advanced mathematics. In some cases, booklets providing a solution were included separately, but in many cases the original solution has been lost or was never provided. The book's main content is the depiction, explanation, and solution of


id: sequences-book-20260505-0
file: data/en.wikipedia.org/wiki/Sequences_(book)-0.md
category: reference
title: Sequences (book)
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Sequences_(book)
date_saved: 2026-05-05T08:46:45.913883+00:00
instance: kb-cron
parent: sequences-book-20260505-0
summary:
Sequences is a mathematical monograph on integer sequences. It was written by Heini Halberstam and Klaus Roth, published in 1966 by the Clarendon Press, and republished in 1983 with minor corrections by Springer-Verlag. Although planned to be part of a two-volume set, the second volume was never published. == Topics == The book has five chapters, each largely self-contained and loosely organized around different techniques used to solve problems in this area, with an appendix on the background material in number theory needed for reading the book. Rather than being concerned with specific sequences such as the prime numbers or square numbers, its topic is the mathematical theory of sequences in general. The first chapter considers the natural density of sequences, and related concepts such as the Schnirelmann density. It proves theorems on the density of sumsets of sequences, including Mann's theorem that the Schnirelmann density of a sumset is at least the sum of the Schnirelmann densities and Kneser's theorem on the structure of sequences whose lower asymptotic density is subadditive. It studies essential components, sequences that when added to another sequence of Schnirelmann density between zero and one, increase their density, proves that additive bases are essential components,


id: shuli-jingyun-20260505-0
file: data/en.wikipedia.org/wiki/Shuli_jingyun-0.md
category: reference
title: Shuli jingyun
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Shuli_jingyun
date_saved: 2026-05-05T08:46:47.061966+00:00
instance: kb-cron
parent: shuli-jingyun-20260505-0
summary:
The Shuli jingyun (數理精蘊), known in English as the Collected Essential Principles of Mathematics, is a 53-volume mathematical encyclopedia, part of the Siku Quanshu collection, on musical tuning, calculation, and the calendar. It includes three treatises on astronomy, mathematics, and music, compiled under imperial order during the Kangxi reign. The book was completed in 1723. == Production and distribution == The encyclopedia was commissioned by the Kangxi Emperor in 1713 and involved over one hundred scholars studying under the Emperor and Jesuit experts. The compilation of this book was supervised by Prince Yūnlu, with He Guozong (d. 1767) and Mei Gucheng (1681-1746) as main compilers. The book began its creation in 1713 and was finished by 1723. In 1724, the first copy was published by the imperial printing shop. The encyclopedia was intended to be used as an imperial textbook in China. Upon its publication, it has been imported to different countries such as Korea in 1729. The Shuli jingyun is included in the Siku Quanshu collection, commissioned by the Qianlong Emperor. This collection, compiled between 1773 and 1782, includes 3,461 titles and is divided into four treasuries. == Contents == The Shuli jingyun has two parts and an appendix


id: significant-figures-book-20260505-0
file: data/en.wikipedia.org/wiki/Significant_Figures_(book)-0.md
category: reference
title: Significant Figures (book)
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Significant_Figures_(book)
date_saved: 2026-05-05T08:46:48.244917+00:00
instance: kb-cron
parent: significant-figures-book-20260505-0
summary:
Significant Figures: The Lives and Work of Great Mathematicians is a 2017 nonfiction book by British mathematician Ian Stewart , published by Basic Books. In the work, Stewart discusses the lives and contributions of 25 figures who are prominent in the history of mathematics. The 25 mathematicians selected are: Archimedes, Liu Hui, Muḥammad ibn Mūsā al-Khwārizmī, Madhava of Sangamagrama, Gerolamo Cardano, Pierre de Fermat, Isaac Newton, Euler, Fourier, Gauss, Lobachevsky, Galois, Ada Lovelace, Boole, Riemann, Cantor, Sofia Kovalevskaia, Poincaré, Hilbert, Emmy Noether, Ramanujan, Gödel, Turing, Mandelbrot, and Thurston. == Reception == In Kirkus Reviews, it was written that "even a popularizer as skilled and prolific as Stewart cannot expect general readers to fully digest his highly distilled explanations of what these significant figures did to resolve ever more complex conundrums as math advanced." However, the reviewer praised Stewart's sketches of the lives and times of the innovators. The book was described as "a text for teachers, precocious students, and intellectually curious readers unafraid to tread unfamiliar territory". == See also == In Pursuit of the Unknown: 17 Equations That Changed the World == References ==


id: solving-the-riddle-of-phyllotaxis-20260505-0
file: data/en.wikipedia.org/wiki/Solving_the_Riddle_of_Phyllotaxis-0.md
category: reference
title: Solving the Riddle of Phyllotaxis
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Solving_the_Riddle_of_Phyllotaxis
date_saved: 2026-05-05T08:46:49.465367+00:00
instance: kb-cron
parent: solving-the-riddle-of-phyllotaxis-20260505-0
summary:
Solving the Riddle of Phyllotaxis: Why the Fibonacci Numbers and the Golden Ratio Occur in Plants is a book on the mathematics of plant structure, and in particular on phyllotaxis, the arrangement of leaves on plant stems. It was written by Irving Adler, and published in 2012 by World Scientific. The Basic Library List Committee of the Mathematical Association of America has suggested its inclusion in undergraduate mathematics libraries. == Background == Irving Adler (1913–2012) was known as a peace protester, schoolteacher, and children's science book author before, in 1961, earning a doctorate in abstract algebra. Even later in his life, Adler began working on phyllotaxis, the mathematical structure of leaves on plant stems. This book, which collects several of his papers on the subject previously published in journals and edited volumes, is the last of his 85 books to be published before his death. == Topics == Different plants arrange their leaves differently, for instance on alternating sides of the plant stem, or rotated from each other by other fractions of a full rotation between consecutive leaves. In these patterns, rotations by 1/2 of an angle, 1/3 of an angle, 3/8 of an angle, or 5/8 of an angle


id: sphere-packings-lattices-and-groups-20260505-0
file: data/en.wikipedia.org/wiki/Sphere_Packings,_Lattices_and_Groups-0.md
category: reference
title: Sphere Packings, Lattices and Groups
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Sphere_Packings,_Lattices_and_Groups
date_saved: 2026-05-05T08:46:50.644463+00:00
instance: kb-cron
parent: sphere-packings-lattices-and-groups-20260505-0
summary:
Sphere Packings, Lattices and Groups is a book about geometry and group theory by John Conway and Neil Sloane, with contributions by other mathematicians, first published in 1988. H. S. M. Coxeter noted, "Much of the book is inspired by the Leech lattice." The book covers many results that, as Richard K. Guy phrased it, "appear little short of miraculous", such as how the Leech lattice, a set of points in 24-dimensional space, is related via special relativity to stacking cannonballs. The interrelated topics featured in the book include Golay codes, Mathieu groups and Monstrous Moonshine. Many of the chapters are updates of papers that had been published in journals previously. Portions of the text were coauthored by Eiichi Bannai, Richard Borcherds, John Leech, Simon Norton, Andrew M. Odlyzko, Richard A. Parker, Larissa Queen and B. B. Venkov. Francis Fung called it "monumental", and Nick Lord described it as "epochal". Gian-Carlo Rota wrote: This is the best survey of the best work in the best fields of combinatorics written by the best people. It will make the best reading by the best students interested in the best mathematics that is now going on. == Editions == The book is volume


id: the-strange-logic-of-random-graphs-20260505-0
file: data/en.wikipedia.org/wiki/The_Strange_Logic_of_Random_Graphs-0.md
category: reference
title: The Strange Logic of Random Graphs
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/The_Strange_Logic_of_Random_Graphs
date_saved: 2026-05-05T08:46:51.781673+00:00
instance: kb-cron
parent: the-strange-logic-of-random-graphs-20260505-0
summary:
The Strange Logic of Random Graphs is a book on zero-one laws for random graphs. It was written by Joel Spencer and published in 2001 by Springer-Verlag as volume 22 of their book series Algorithms and Combinatorics. == Topics == The random graphs of the book are generated from the Erdős–Rényi–Gilbert model G ( n , p ) {\displaystyle G(n,p)} in which n {\displaystyle n} vertices are given and a random choice is made whether to connect each pair of vertices by an edge, independently for each pair, with probability p {\displaystyle p} of making a connection. A zero-one law is a theorem stating that, for certain properties of graphs, and for certain choices of p {\displaystyle p} , the probability of generating a graph with the property tends to zero or one in the limit as n {\displaystyle n} goes to infinity. A fundamental result in this area, proved independently by Glebskiĭ et al. and by Ronald Fagin, is that there is a zero-one law for G ( n , 1 / 2 ) {\displaystyle G(n,1/2)} for every property that can be described in the first-order logic of graphs. Moreover, the limiting probability is one if and only if


id: sumario-compendioso-20260505-0
file: data/en.wikipedia.org/wiki/Sumario_Compendioso-0.md
category: reference
title: Sumario Compendioso
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Sumario_Compendioso
date_saved: 2026-05-05T08:46:52.962788+00:00
instance: kb-cron
parent: sumario-compendioso-20260505-0
summary:
The Sumario Compendioso was the first mathematics book published in the New World. The book was published in Mexico City in 1556 by a clergyman Juan Diez. == Availability == The book has been digitized and is available on the Internet. Before the Digital Age the only four known surviving copies were preserved at the Huntington Library, San Marino, California, the British Library, London, Duke University Library, and the University of Salamanca in Spain. == Excerpts == In his book The Math Book, Clifford A. Pickover provided the following information about Sumario Compendioso: The Sumario Compendioso, published in Mexico City in 1556, is the first work on mathematics printed in the Americas. The publication of Sumario Compendioso in the New World preceded by many decades the emigration of the Puritans to North America and the settlement in Jamestown, Virginia. The author, Brother Juan Diez, was a companion of Hernando Cortes, the Spanish conquistador, during Cortes's conquests of the Aztec Empire. == References == == External links == Open Library HathiTrust JSTOR Archive.org


id: symmetry-aspects-of-m-c-escher-s-periodic-drawings-20260505-0
file: data/en.wikipedia.org/wiki/Symmetry_aspects_of_M._C._Escher's_periodic_drawings-0.md
category: reference
title: Symmetry aspects of M. C. Escher's periodic drawings
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Symmetry_aspects_of_M._C._Escher's_periodic_drawings
date_saved: 2026-05-05T08:46:55.237869+00:00
instance: kb-cron
parent: symmetry-aspects-of-m-c-escher-s-periodic-drawings-20260505-0
summary:
Symmetry aspects of M. C. Escher's periodic drawings is a book by crystallographer Caroline H. MacGillavry published for the International Union of Crystallography (IUCr) by Oosthoek in 1965. The book analyzes the symmetry of M. C. Escher's colored periodic drawings using the international crystallographic notation. In 1959, MacGillavry met Escher. His work, the regular tiling of the plane, showed obvious links with the symmetry principles of crystallography. After seeking approval from the organisers (Joseph and Gabrielle Donnay), MacGillavry asked Escher to exhibit his lithographic works at the IUCr Congress in Cambridge, U.K. in 1960. The exhibition was a success, and as a consequence the IUCr commissioned MacGillavry to write the book under its auspices. == Structure and topics == The book has three chapters. In the first chapter, entitled Patterns with Classical Symmetry, the author introduces the concepts of motif, symmetry operations, lattice and unit cell, and uses these to analyze the symmetry of 13 of Escher's tiling designs. In the second chapter, Patterns with Black-white Symmetry, the antisymmetry operation (indicated by a prime ') is introduced. The chapter analyzes 22 of Escher's design in terms of black-white symmetry and assigns each a symbol in the international notation describing its


id: symmetry-in-science-and-art-20260505-0
file: data/en.wikipedia.org/wiki/Symmetry_in_Science_and_Art-0.md
category: reference
title: Symmetry in Science and Art
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Symmetry_in_Science_and_Art
date_saved: 2026-05-05T08:46:56.409275+00:00
instance: kb-cron
parent: symmetry-in-science-and-art-20260505-0
summary:
Symmetry in Science and Art is a book by A.V. Shubnikov and V.A. Koptsik published by Plenum Press in 1974. The book is a translation of Simmetrija v nauke i iskusstve (Russian: Симметрия в науке и искусстве) published by Nauka in 1972. The book was notable because it gave English-language speakers access to Russian work in the fields of dichromatic and polychromatic symmetry. == Structure and topics == The book is divided into two parts. The first part is an updated version of A.V. Shubnikov's 1940 book Symmetry: laws of symmetry and their application in science, technology and applied arts (Russian: Симметрия : законы симметрии и их применение в науке, технике и прикладном искусстве). The following types of classical (one-color) and dichromatic (two-color) symmetries are covered in the first part of the book: one-sided rosettes, figures with a singular point, one-sided bands, two-sided bands, rods, network patterns, layers and space groups. The second part consists of three new chapters written by V.A. Koptsik covering the following subjects: group theory, crystallographic groups, antisymmetry, colored symmetry, symmetry in science and art, and conservation laws. == Audience == The book is written for crystallographers, mathematicians and physicists who are interested in the application


id: synopsis-of-pure-mathematics-20260505-0
file: data/en.wikipedia.org/wiki/Synopsis_of_Pure_Mathematics-0.md
category: reference
title: Synopsis of Pure Mathematics
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Synopsis_of_Pure_Mathematics
date_saved: 2026-05-05T08:46:57.582639+00:00
instance: kb-cron
parent: synopsis-of-pure-mathematics-20260505-0
summary:
Synopsis of Pure Mathematics is a book by G. S. Carr, written in 1886. The book attempted to summarize the state of most of the basic mathematics known at the time. The book is noteworthy because it was a major source of information for the legendary and self-taught mathematician Srinivasa Ramanujan who managed to obtain a library loaned copy from a friend in 1903. Ramanujan reportedly studied the contents of the book in detail. The book is generally acknowledged as a key element in awakening the genius of Ramanujan. Carr acknowledged the main sources of his book in its preface: ... In the Algebra, Theory of Equations, and Trigonometry sections, I am largely indebted to Todhunter's well-known treatises ... In the section entitled Elementary Geometry, I have added to simpler propositions a selection of theorems from Townsend's Modern Geometry and Salmon's Conic Sections. In Geometric Conics, the line of demonstration followed agrees, in the main, with that adopted in Drew's treatise on the subject. ... The account of the C. G. S. system given in the preliminary section, has been compiled from a valuable contribution on the subject by Professor Everett, of Belfast, published by the Physical Society of London.


id: theory-of-lie-groups-20260505-0
file: data/en.wikipedia.org/wiki/Theory_of_Lie_groups-0.md
category: reference
title: Theory of Lie groups
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Theory_of_Lie_groups
date_saved: 2026-05-05T08:46:59.850097+00:00
instance: kb-cron
parent: theory-of-lie-groups-20260505-0
summary:
In mathematics, Theory of Lie groups is a series of books on Lie groups by Claude Chevalley (1946, 1951, 1955). The first in the series was one of the earliest books on Lie groups to treat them from the global point of view, and for many years was the standard text on Lie groups. The second and third volumes, on algebraic groups and Lie algebras, were written in French, and later reprinted bound together as one volume. Apparently further volumes were planned but not published, though his lectures (Chevalley 2005) on the classification of semisimple algebraic groups could be considered as a continuation of the series. == References == Chevalley, Claude (1946), Theory of Lie Groups. I, Princeton Mathematical Series, vol. 8, Princeton University Press, ISBN 978-0-691-04990-8, MR 0015396 {{citation}}: ISBN / Date incompatibility (help) Chevalley, Claude (1951), Théorie des groupes de Lie. Tome II. Groupes algébriques, Actualités Sci. Ind., vol. 1152, Hermann & Cie., Paris, MR 0051242 Chevalley, Claude (1955), Théorie des groupes de Lie. Tome III. Théorèmes généraux sur les algèbres de Lie, Actualités Sci. Ind., vol. 1226, Hermann & Cie, Paris, MR 0068552 Chevalley, Claude (1968), Théorie des groupes de Lie : Groupes algébriques, théorèmes généraux sur


id: tilings-and-patterns-20260505-0
file: data/en.wikipedia.org/wiki/Tilings_and_patterns-0.md
category: reference
title: Tilings and patterns
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Tilings_and_patterns
date_saved: 2026-05-05T08:47:01.029296+00:00
instance: kb-cron
parent: tilings-and-patterns-20260505-0
summary:
Tilings and patterns is a book by mathematicians Branko Grünbaum and Geoffrey Colin Shephard published in 1987 by W.H. Freeman. The book was 10 years in development, and upon publication it was widely reviewed and highly acclaimed. == Structure and topics == The book is concerned with tilings—a partition of the plane into regions (the tiles)—and patterns—repetitions of a motif in the plane in a regular manner. The book is divided into two parts. The first seven chapters define concepts and terminology, establish the general theory of tilings, survey tilings by regular polygons, review the theory of patterns, and discuss tilings in which all the tiles, or all the edges, or all the vertices, play the same role. The last five chapters survey a variety of advanced topics in tiling theory: colored patterns and tilings, polygonal tilings, aperiodic tilings, Wang tiles, and tilings with unusual kinds of tiles. Each chapter open with an introduction to the topic, this is followed by the detailed material of the chapter, much previously unpublished, which is always profusely illustrated, and normally includes examples and proofs. Chapters close with exercises, and a section of notes and references which detail the historical development of the topic.


id: a-topological-picturebook-20260505-0
file: data/en.wikipedia.org/wiki/A_Topological_Picturebook-0.md
category: reference
title: A Topological Picturebook
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/A_Topological_Picturebook
date_saved: 2026-05-05T08:47:02.165515+00:00
instance: kb-cron
parent: a-topological-picturebook-20260505-0
summary:
A Topological Picturebook is a book on mathematical visualization in low-dimensional topology by George K. Francis. It was originally published by Springer in 1987, and reprinted in paperback in 2007. The Basic Library List Committee of the Mathematical Association of America has recommended its inclusion in undergraduate mathematics libraries. == Topics == Although the book includes some computer-generated images, most of it is centered on hand drawing techniques. After an introductory chapter on topological surfaces, the cusps in the outlines of surfaces formed when viewing them from certain angles, and the self-intersections of immersed surfaces, the next two chapters are centered on drawing techniques: chapter two concerns ink, paper, cross-hatching, and shading techniques for indicating the curvature of surfaces, while chapter three provides some basic techniques of graphical perspective. The remaining five chapters of the book provide case studies of different visualization problems in mathematics, called by the book "picture stories". The mathematical topics visualized in these chapters include the Penrose triangle and related optical illusions; the Roman surface and Boy's surface, two different immersions of the projective plane, and deformations between them; sphere eversion and the Morin surface; group theory, the mapping class groups of surfaces, and the braid


id: the-tower-of-hanoi-myths-and-maths-20260505-0
file: data/en.wikipedia.org/wiki/The_Tower_of_Hanoi_–_Myths_and_Maths-0.md
category: reference
title: The Tower of Hanoi – Myths and Maths
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/The_Tower_of_Hanoi_–_Myths_and_Maths
date_saved: 2026-05-05T08:47:03.324829+00:00
instance: kb-cron
parent: the-tower-of-hanoi-myths-and-maths-20260505-0
summary:
The Tower of Hanoi – Myths and Maths is a book in recreational mathematics, on the tower of Hanoi, baguenaudier, and related puzzles. It was written by Andreas M. Hinz, Sandi Klavžar, Uroš Milutinović, and Ciril Petr, and published in 2013 by Birkhäuser, with an expanded second edition in 2018. The Basic Library List Committee of the Mathematical Association of America has suggested its inclusion in undergraduate mathematics libraries. == Topics == Although this book is in recreational mathematics, it takes its subject seriously, and brings in material from automata theory, computational complexity, the design and analysis of algorithms, graph theory, and group theory, topology, fractal geometry, chemical graph theory, and even psychology (where related puzzles have applications in psychological testing). The 1st edition of the book had 10 chapters, and the 2nd edition has 11. In both cases they begin with chapter zero, on the background and history of the Tower of Hanoi puzzle, covering its real-world invention by Édouard Lucas and in the mythical backstory he invented for it. Chapter one considers the Baguenaudier puzzle (or, as it is often called, the Chinese rings), related to the tower of Hanoi both in the structure of its state space


id: treatise-on-analysis-20260505-0
file: data/en.wikipedia.org/wiki/Treatise_on_Analysis-0.md
category: reference
title: Treatise on Analysis
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Treatise_on_Analysis
date_saved: 2026-05-05T08:47:05.664536+00:00
instance: kb-cron
parent: treatise-on-analysis-20260505-0
summary:
Treatise on Analysis is a translation by Ian G. Macdonald of the nine-volume work Éléments d'analyse on mathematical analysis by Jean Dieudonné, and is an expansion of his textbook Foundations of Modern Analysis. It is a successor to the various Cours d'Analyse by Augustin-Louis Cauchy, Camille Jordan, and Édouard Goursat. == Contents and publication history == === Volume I === The first volume was originally a stand-alone graduate textbook with a different title. It was first written in English and later translated into French, unlike the other volumes which were first written in French. It has been republished several times and is much more common than the later volumes of the series. The contents include Chapter I: Sets Chapter II Real numbers Chapter III Metric spaces Chapter IV The real line Chapter V Normed spaces Chapter VI Hilbert spaces Chapter VII Spaces of continuous functions Chapter VIII Differential calculus (This uses the Cauchy integral rather than the more common Riemann integral of functions.) Chapter IX Analytic functions (of a complex variable) Chapter X Existence theorems (for ordinary differential equations) Chapter XI Elementary spectral theory Dieudonné, J. (1960), Foundations of modern analysis, Pure and Applied Mathematics, vol. X, New York-London: Academic


id: a-treatise-on-the-circle-and-the-sphere-20260505-0
file: data/en.wikipedia.org/wiki/A_Treatise_on_the_Circle_and_the_Sphere-0.md
category: reference
title: A Treatise on the Circle and the Sphere
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/A_Treatise_on_the_Circle_and_the_Sphere
date_saved: 2026-05-05T08:47:06.833342+00:00
instance: kb-cron
parent: a-treatise-on-the-circle-and-the-sphere-20260505-0
summary:
A Treatise on the Circle and the Sphere is a mathematics book on circles, spheres, and inversive geometry. It was written by Julian Coolidge and published by the Clarendon Press in 1916. The Chelsea Publishing Company published a corrected reprint in 1971. After the American Mathematical Society acquired Chelsea Publishing it was reprinted again in 1997. == Topics == As is now standard in inversive geometry, the book extends the Euclidean plane to its one-point compactification, and considers Euclidean lines to be a degenerate case of circles, passing through the point at infinity. It identifies every circle with the inversion through it, and studies circle inversions as a group, the group of Möbius transformations of the extended plane. Another key tool used by the book are the "tetracyclic coordinates" of a circle, quadruples of complex numbers a , b , c , d {\displaystyle a,b,c,d} describing the circle in the complex plane as the solutions to the equation a z z ¯ + b z + c z ¯ + d = 0 {\displaystyle az{\bar {z}}+bz+c{\bar {z}}+d=0} . It applies similar methods in three dimensions to identify spheres (and planes as degenerate spheres) with the inversions through them, and to


id: treks-into-intuitive-geometry-20260505-0
file: data/en.wikipedia.org/wiki/Treks_into_Intuitive_Geometry-0.md
category: reference
title: Treks into Intuitive Geometry
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Treks_into_Intuitive_Geometry
date_saved: 2026-05-05T08:47:07.944460+00:00
instance: kb-cron
parent: treks-into-intuitive-geometry-20260505-0
summary:
Treks into Intuitive Geometry: The World of Polygons and Polyhedra is a book on geometry, written as a discussion between a teacher and a student in the style of a Socratic dialogue. It was written by Japanese mathematician Jin Akiyama and science writer Kiyoko Matsunaga, and published by Springer-Verlag in 2015 (ISBN 978-4-431-55841-5), with an expanded second edition in 2024 (ISBN 978-981-99-8607-1). == Topics == The term "intuitive geometry" of the title was used by László Fejes Tóth to refer to results in geometry that are accessible to the general public, and the book concerns topics of this type. The book has 16 self-contained chapters, each beginning with an illustrative puzzle or real-world application. It includes material on tessellations, polyhedra, and honeycombs, unfoldings of polyhedra and tessellations of unfoldings, cross sections of polyhedra, measuring boxes, gift wrapping, packing problems, wallpaper groups, pentagonal tilings, the Conway criterion for prototiles and Escher-like tilings of the plane by animal-shaped figures, aperiodic tilings including the Penrose tiling, the art gallery theorem, the Euler characteristic, dissection problems and the Dehn invariant, and the Steiner tree problem. The book is heavily illustrated. And although the results of the book are demonstrated in an accessible way, the


id: treviso-arithmetic-20260505-0
file: data/en.wikipedia.org/wiki/Treviso_Arithmetic-0.md
category: reference
title: Treviso Arithmetic
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Treviso_Arithmetic
date_saved: 2026-05-05T08:47:09.079015+00:00
instance: kb-cron
parent: treviso-arithmetic-20260505-0
summary:
The Treviso Arithmetic, or Arte dell'Abbaco, is an anonymous textbook in commercial arithmetic written in vernacular Venetian and published in Treviso, Italy, in 1478. The author explains the motivation for writing this textbook: I have often been asked by certain youths in whom I have much interest, and who look forward to mercantile pursuits, to put into writing the fundamental principles of arithmetic, commonly called abacus. The Treviso Arithmetic is the earliest known printed mathematics book in the West, and one of the first printed European textbooks dealing with a science. == The Arithmetic as an early printed book == There appears to have been only one edition of the work. David Eugene Smith translated parts of the Treviso Arithmetic for educational purposes in 1907. Frank J. Swetz translated the complete work using Smith's notes in 1987 in his Capitalism & Arithmetic: The New Math of the 15th Century. Swetz used a copy of the Treviso housed in the Manuscript Library at Columbia University. The volume found its way to this collection via a curious route. Maffeo Pinelli (1785), an Italian bibliophile, is the first known owner. After his death his library was purchased by a London book-dealer and sold


id: trigonometric-series-20260505-0
file: data/en.wikipedia.org/wiki/Trigonometric_Series-0.md
category: reference
title: Trigonometric Series
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Trigonometric_Series
date_saved: 2026-05-05T08:47:10.228449+00:00
instance: kb-cron
parent: trigonometric-series-20260505-0
summary:
Antoni Zygmund wrote a classic two-volume set of books entitled Trigonometric Series, which discusses many different aspects of trigonometric series. The first edition was a single volume, published in 1935 (under the slightly different title Trigonometrical Series). The second edition of 1959 was greatly expanded, taking up two volumes, though it was later reprinted as a single volume paperback. The third edition of 2002 is similar to the second edition, with the addition of a preface by Robert A. Fefferman on more recent developments, in particular Carleson's theorem about almost everywhere pointwise convergence for square-integrable functions. == Publication history == Zygmund, Antoni (1935). Trigonometrical series. Monogr. Mat. Vol. 5. Warszawa, Lwow: Subwencji Fundusz Kultury Narodowej. Zbl 0011.01703. At icm.edu.pl: original archived Zygmund, Antoni (1952). Trigonometrical series. New York: Chelsea Publishing Co. MR 0076084. Zygmund, Antoni (1955). Trigonometrical series. New York: Dover Publications. MR 0072976. Zygmund, Antoni (1959). Trigonometric series (2nd ed.). Cambridge University Press. MR 0107776. Volume I, Volume II. Zygmund, Antoni (1968). Trigonometric series. Second edition, reprinted with corrections and some additions. Vol. I and II (2nd ed.). Cambridge University Press. MR 0236587. Zygmund, Antoni (1977). Trigonometric series. Vol. I and II. Cambridge University Press. ISBN 978-0-521-07477-3. MR 0617944.


id: two-sided-matching-20260505-0
file: data/en.wikipedia.org/wiki/Two-Sided_Matching-0.md
category: reference
title: Two-Sided Matching
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Two-Sided_Matching
date_saved: 2026-05-05T08:47:12.555607+00:00
instance: kb-cron
parent: two-sided-matching-20260505-0
summary:
Two-Sided Matching: A Study in Game-Theoretic Modeling and Analysis is a book on matching markets in economics and game theory, particularly concentrating on the stable marriage problem. It was written by Alvin E. Roth and Marilda Sotomayor, with a preface by Robert Aumann, and published in 1990 by the Cambridge University Press as volume 18 in their series of Econometric Society monographs. For this work, Roth and Sotomayor won the 1990 Frederick W. Lanchester Prize of the Institute for Operations Research and the Management Sciences. == Topics == The book's introduction discusses the National Resident Matching Program and its use of stable marriage to assign medical students to hospital positions, and collects the problems in economics that the theory of matching markets is positioned to solve. Following this, it has three main sections. The first of these sections discusses the stable matching problem in its simplest form, in which two equal-sized groups of agents are to be matched one-to-one. It discusses the stability of solutions (the property that no pair of agents both prefer being matched to each other to their assigned matches), the lattice of stable matchings, the Gale–Shapley algorithm for finding stable solutions, and two key properties of


id: urania-propitia-20260505-0
file: data/en.wikipedia.org/wiki/Urania_Propitia-0.md
category: reference
title: Urania Propitia
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Urania_Propitia
date_saved: 2026-05-05T08:47:13.709479+00:00
instance: kb-cron
parent: urania-propitia-20260505-0
summary:
Urania Propitia (lit. 'kind/beneficent Urania') is a book of astronomical tables written by the Silesian astronomer Maria Cunitz and published in 1650. As Maria Cunitz was the daughter of both a physician and mathematician, it was her ability to grasp complex mathematics quickly and transcribe her findings as a polyglot that allowed her to do what few women had done before her. The work served as a simplification of the Rudolphine Tables (1627) by Johannes Kepler, with Cunitz attempting to both increase the accuracy and to simplify the calculations from the original work. While she corrected a number of Kepler's computational errors, her equations also include inaccuracies. Cunitz's work is credited with making astrological tables accessible outside of the era's universities. Cunitz's cosmology combined elements from the cosmologies of both Kepler and Tycho Brahe. Like Brahe, she thought that the Sun and the Moon orbit around the planet Earth, while the rest of the planets in the Solar System orbit around the Sun. In her work, the physics within the cosmos involve ellipticals and aphelions. == Introduction == Urania Propitia was a simplification of the Rudolphine Tables written by Johannes Kepler in 1627. Kepler's dedication to Emperor Ferdinand II which


id: vectors-in-three-dimensional-space-20260505-0
file: data/en.wikipedia.org/wiki/Vectors_in_Three-dimensional_Space-0.md
category: reference
title: Vectors in Three-dimensional Space
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Vectors_in_Three-dimensional_Space
date_saved: 2026-05-05T08:47:14.876227+00:00
instance: kb-cron
parent: vectors-in-three-dimensional-space-20260505-0
summary:
Vectors in Three-dimensional Space (1978) is a book concerned with physical quantities defined in "ordinary" 3-space. It was written by J. S. R. Chisholm, an English mathematical physicist, and published by Cambridge University Press. According to the author, such physical quantities are studied in Newtonian mechanics, fluid mechanics, theories of elasticity and plasticity, non-relativistic quantum mechanics, and many parts of solid state physics. The author further states that "the vector concept developed in two different ways: in a wide variety of physical applications, vector notation and techniques became, by the middle of this century, almost universal; on the other hand, pure mathematicians reduced vector algebra to an axiomatic system, and introduced wide generalisations of the concept of a three-dimensional 'vector space'." Chisholm explains that since these two developments proceeded largely independently, there is a need to show how one can be applied to the other. == Summary == Vectors in Three-Dimensional Space has six chapters, each divided into five or more subsections. The first on linear spaces and displacements including these sections: Introduction, Scalar multiplication of vectors, Addition and subtraction of vectors, Displacements in Euclidean space, Geometrical applications. The second on Scalar products and components including these sections: Scalar products,


id: vorlesungen-ber-zahlentheorie-20260505-0
file: data/en.wikipedia.org/wiki/Vorlesungen_über_Zahlentheorie-0.md
category: reference
title: Vorlesungen über Zahlentheorie
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Vorlesungen_über_Zahlentheorie
date_saved: 2026-05-05T08:47:16.045939+00:00
instance: kb-cron
parent: vorlesungen-ber-zahlentheorie-20260505-0
summary:
Vorlesungen über Zahlentheorie (German pronunciation: [ˈfoːɐ̯ˌleːzʊŋən ˈyːbɐ ˈtsaːlənteoˌʁiː]; German for Lectures on Number Theory) is the name of several different textbooks of number theory. The best known was written by Peter Gustav Lejeune Dirichlet and Richard Dedekind, and published in 1863. Others were written by Leopold Kronecker, Edmund Landau, and Helmut Hasse. They all cover elementary number theory, Dirichlet's theorem, quadratic fields and forms, and sometimes more advanced topics. == Dirichlet and Dedekind's book == Based on Dirichlet's number theory course at the University of Göttingen, the Vorlesungen were edited by Dedekind and published after Lejeune Dirichlet's death. Dedekind added several appendices to the Vorlesungen, in which he collected further results of Lejeune Dirichlet's and also developed his own original mathematical ideas. === Scope === The Vorlesungen cover topics in elementary number theory, algebraic number theory and analytic number theory, including modular arithmetic, quadratic congruences, quadratic reciprocity and binary quadratic forms. === Contents === The contents of Professor John Stillwell's 1999 translation of the Vorlesungen are as follows Chapter 1. On the divisibility of numbers Chapter 2. On the congruence of numbers Chapter 3. On quadratic residues Chapter 4. On quadratic forms Chapter 5. Determination of the class number of


id: where-mathematics-comes-from-20260505-0
file: data/en.wikipedia.org/wiki/Where_Mathematics_Comes_From-0.md
category: reference
title: Where Mathematics Comes From
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Where_Mathematics_Comes_From
date_saved: 2026-05-05T08:47:17.193195+00:00
instance: kb-cron
parent: where-mathematics-comes-from-20260505-0
summary:
Where Mathematics Comes From: How the Embodied Mind Brings Mathematics into Being (hereinafter WMCF) is a book by George Lakoff, a cognitive linguist, and Rafael E. Núñez, a psychologist. Published in 2000, WMCF seeks to found a cognitive science of mathematics, a theory of embodied mathematics based on conceptual metaphor. == WMCF definition of mathematics == Mathematics makes up that part of the human conceptual system that is special in the following way: It is precise, consistent, stable across time and human communities, symbolizable, calculable, generalizable, universally available, consistent within each of its subject matters, and effective as a general tool for description, explanation, and prediction in a vast number of everyday activities, [ranging from] sports, to building, business, technology, and science. - WMCF, pp. 50, 377 Nikolay Lobachevsky said "There is no branch of mathematics, however abstract, which may not some day be applied to phenomena of the real world." A common type of conceptual blending process would seem to apply to the entire mathematical procession. == Human cognition and mathematics == Lakoff and Núñez's avowed purpose is to begin laying the foundations for a truly scientific understanding of mathematics, one grounded in processes common to all human cognition.


id: where-mathematics-comes-from-20260505-1
file: data/en.wikipedia.org/wiki/Where_Mathematics_Comes_From-1.md
category: reference
title: Where Mathematics Comes From
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Where_Mathematics_Comes_From
date_saved: 2026-05-05T08:47:17.193195+00:00
instance: kb-cron
parent: where-mathematics-comes-from-20260505-0
summary:
== Example of metaphorical ambiguity == WMCF (p. 151) includes the following example of what the authors term "metaphorical ambiguity." Take the set A = { { ∅ } , { ∅ , { ∅ } } } . {\displaystyle A=\{\{\emptyset \},\{\emptyset ,\{\emptyset \}\}\}.} Then recall two bits of standard terminology from elementary set theory: The recursive construction of the ordinal natural numbers, whereby 0 is ∅ {\displaystyle \emptyset } , and n + 1 {\displaystyle n+1} is n ∪ { n } . {\displaystyle n\cup \{n\}.} The ordered pair (a,b), defined as { { a } , { a , b } } . {\displaystyle \{\{a\},\{a,b\}\}.} By (1), A is the set {1,2}. But (1) and (2) together say that A is also the ordered pair (0,1). Both statements cannot be correct; the ordered pair (0,1) and the unordered pair {1,2} are fully distinct concepts. Lakoff and Johnson (1999) term this situation "metaphorically ambiguous." This simple example calls into question any Platonistic foundations for mathematics. While (1) and (2) above are admittedly canonical, especially within the consensus set theory known as the Zermelo–Fraenkel axiomatization, WMCF does not let on that they are but one of several definitions that have


id: where-mathematics-comes-from-20260505-2
file: data/en.wikipedia.org/wiki/Where_Mathematics_Comes_From-2.md
category: reference
title: Where Mathematics Comes From
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Where_Mathematics_Comes_From
date_saved: 2026-05-05T08:47:17.193195+00:00
instance: kb-cron
parent: where-mathematics-comes-from-20260505-0
summary:
But their analysis leaves at least a couple of questions insufficiently answered. For one thing, the authors ignore the fact that brains not only observe nature, but also are part of nature. Perhaps the math that brains invent takes the form it does because math had a hand in forming the brains in the first place (through the operation of natural laws in constraining the evolution of life). Furthermore, it's one thing to fit equations to aspects of reality that are already known. It's something else for that math to tell of phenomena never previously suspected. When Paul Dirac's equations describing electrons produced more than one solution, he surmised that nature must possess other particles, now known as antimatter. But scientists did not discover such particles until after Dirac's math told him they must exist. If math is a human invention, nature seems to know what was going to be invented. Lakoff and Núñez tend to dismiss the negative opinions mathematicians have expressed about WMCF, because their critics do not appreciate the insights of cognitive science. Lakoff and Núñez maintain that their argument can only be understood using the discoveries of recent decades about the way human brains process language


id: the-whetstone-of-witte-20260505-0
file: data/en.wikipedia.org/wiki/The_Whetstone_of_Witte-0.md
category: reference
title: The Whetstone of Witte
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/The_Whetstone_of_Witte
date_saved: 2026-05-05T08:47:18.369323+00:00
instance: kb-cron
parent: the-whetstone-of-witte-20260505-0
summary:
The Whetstone of Witte is the shortened title of Robert Recorde's mathematics book published in 1557, the full title being The whetstone of witte, whiche is the seconde parte of Arithmetike: containyng thextraction of Rootes: The Coßike practise, with the rule of Equation: and the woorkes of Surde Nombers. The book covers topics including whole numbers, the extraction of roots and irrational numbers. The work is notable for containing the first recorded use of the equals sign and also for being the first book in English to use the plus and minus signs. Recordian notation for exponentiation, however, differed from the later Cartesian notation p q = p × p × p ⋯ × p {\displaystyle p^{q}=p\times p\times p\cdots \times p} . Recorde expressed indices and surds larger than 3 in a systematic form based on the prime factorization of the exponent: a factor of two he termed a zenzic, and a factor of three, a cubic. Recorde termed the larger prime numbers appearing in this factorization sursolids, distinguishing between them by use of ordinal numbers: that is, he defined 5 as the first sursolid, written as ʃz and 7 as the second sursolid, written as Bʃz. He also devised


id: word-processing-in-groups-20260505-0
file: data/en.wikipedia.org/wiki/Word_Processing_in_Groups-0.md
category: reference
title: Word Processing in Groups
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Word_Processing_in_Groups
date_saved: 2026-05-05T08:47:19.528199+00:00
instance: kb-cron
parent: word-processing-in-groups-20260505-0
summary:
Word Processing in Groups is a monograph in mathematics on the theory of automatic groups, a type of abstract algebra whose operations are defined by the behavior of finite automata. The book's authors are David B. A. Epstein, James W. Cannon, Derek F. Holt, Silvio V. F. Levy, Mike Paterson, and William Thurston. Widely circulated in preprint form, it formed the foundation of the study of automatic groups even before its 1992 publication by Jones and Bartlett Publishers (ISBN 0-86720-244-0). == Topics == The book is divided into two parts, one on the basic theory of these structures and another on recent research, connections to geometry and topology, and other related topics. The first part has eight chapters. They cover automata theory and regular languages, and the closure properties of regular languages under logical combinations; the definition of automatic groups and biautomatic groups; examples from topology and "combable" structure in the Cayley graphs of automatic groups; abelian groups and the automaticity of Euclidean groups; the theory of determining whether a group is automatic, and its practical implementation by Epstein, Holt, and Sarah Rees; extensions to asynchronous automata; and nilpotent groups. The second part has four chapters, on braid groups, isoperimetric


id: zahlbericht-20260505-0
file: data/en.wikipedia.org/wiki/Zahlbericht-0.md
category: reference
title: Zahlbericht
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Zahlbericht
date_saved: 2026-05-05T08:47:20.658964+00:00
instance: kb-cron
parent: zahlbericht-20260505-0
summary:
In mathematics, the Zahlbericht (number report) was a report on algebraic number theory by Hilbert (1897, 1998, (English translation)). == History == In 1893 the German Mathematical Society invited Hilbert and Minkowski to write reports on the theory of numbers. They agreed that Minkowski would cover the more elementary parts of number theory while Hilbert would cover algebraic number theory. Minkowski eventually abandoned his report, while Hilbert's report was published in 1897. It was reprinted in volume 1 of his collected works, and republished in an English translation in 1998. Corry (1996) and Schappacher (2005) and the English introduction to (Hilbert 1998) give detailed discussions of the history and influence of Hilbert's Zahlbericht. Some earlier reports on number theory include the report by H. J. S. Smith in 6 parts between 1859 and 1865, reprinted in Smith (1965), and the report by Brill & Noether (1894). Hasse (1926, 1927, 1930) wrote an update of Hilbert's Zahlbericht that covered class field theory (republished in 1 volume as (Hasse 1970)). == Contents == Part 1 covers the theory of general number fields, including ideals, discriminants, differents, units, and ideal classes. Part 2 covers Galois number fields, including in particular Hilbert's theorem 90.


id: aequanimitas-20260505-0
file: data/en.wikipedia.org/wiki/Aequanimitas-0.md
category: reference
title: Aequanimitas
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Aequanimitas
date_saved: 2026-05-05T08:47:22.189252+00:00
instance: kb-cron
parent: aequanimitas-20260505-0
summary:
Aequanimitas was one of Sir William Osler's most famous essays, delivered to new doctors in 1889 as his farewell address at the Pennsylvania School of Medicine, prior to his transfer to Johns Hopkins. It was published in the same year and in 1904 appeared in his collection of essays titled Aequanimitas with Other Addresses to Medical Students, Nurses and Practitioners of Medicine. A second edition was produced in 1906, and a third in 1932. In the essay, Osler advocates two qualities "imperturbability" and "equanimity", which he defined as "coolness and presence of mind under all circumstances". Between 1932 and 1953, Eli Lilly & Company distributed more than 150,000 copies of the third edition to medical graduates. Through the years Osler's ideal of "Aequanimitas" has been analysed by various academics. Daniel Sokol, medical ethics and law expert, reasons in the British Medical Journal in 2007, that whatever interpretation is made of Aequanimitas, it "tackles head-on a timeless question: what makes a good doctor?". == Publication == === The essay === Aequanimitas was an essay by Sir William Osler, delivered to new doctors on 1 May 1889 as his farewell address at the Pennsylvania School of Medicine. It was published in the


id: ahfs-drug-information-book-20260505-0
file: data/en.wikipedia.org/wiki/AHFS_Drug_Information_Book-0.md
category: reference
title: AHFS Drug Information Book
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/AHFS_Drug_Information_Book
date_saved: 2026-05-05T08:47:23.323678+00:00
instance: kb-cron
parent: ahfs-drug-information-book-20260505-0
summary:
The AHFS DI is one of several compendiums approved by the Social Security Act (Section 1861(t)(2)(B)(ii)(I)) as a source of off-label anti-cancer drug use. It was originally published in 1959 as the American Hospital Formulary Service (AHFS) by the American Society of Health-System Pharmacists. It is also the only one left of the originally authorized compendiums. == References == == Further reading == "Gain a solid understanding of compendia and its impact on patient access". Formulary Journal. 2012-07-01. Retrieved 2018-03-30. == External links == Official website


id: al-hawi-20260505-0
file: data/en.wikipedia.org/wiki/Al-Hawi-0.md
category: reference
title: Al-Hawi
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Al-Hawi
date_saved: 2026-05-05T08:47:24.437406+00:00
instance: kb-cron
parent: al-hawi-20260505-0
summary:
Kitab al-Hawi or Al-Hawi or Kitāb al-Ḥāwī fī al-ṭibb translated as The Comprehensive Book on Medicine is an extensive medical encyclopedia authored by the Persian polymath Abu Bakr Muhammad ibn Zakariya al-Razi (865–925), commonly known in the West as Rhazes in the 10th century. This monumental work is a compendium of Greek, Syrian, and early Arabic medical knowledge, as well as some Indian medical practices. It was first translated into Latin in 1279 under the title Continens by Faraj ben Salim, a physician of Sicilian-Jewish origin employed by Charles of Anjou. The oldest partial remaining copy of this work belongs to the National Library of Medicine in Bethesda, Maryland dated 1094 CE. == Historical context and composition == The Kitab al-Hawi was composed around the year 900 and spans 22 volumes. It was later published by the Dairat'l-Macarif-il-Osmania (Osmania Oriental Publications Bureau) in Hyderabad, India. == Contents and significance == The book covers a wide range of medical topics, including theoretical and practical medicine. Al-Razi's approach was notably comprehensive, as he not only included medical knowledge from Greek and Syrian sources but also incorporated insights from Indian medical traditions. Al-Razi frequently recommended various treatments, including those that might be considered


id: articella-20260505-0
file: data/en.wikipedia.org/wiki/Articella-0.md
category: reference
title: Articella
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Articella
date_saved: 2026-05-05T08:47:26.761166+00:00
instance: kb-cron
parent: articella-20260505-0
summary:
The Articella ('little art') or Ars medicinae ('art of medicine') is a Latin collection of medical treatises bound together in one volume that was used mainly as a textbook and reference manual between the 13th and the 16th centuries. In medieval times, several versions of this anthology circulated in manuscript form among medical students. Between 1476 and 1534, printed editions of the Articella were also published in several European cities. The earliest surviving manuscript of the collection was copied just after 1100. The original five texts, in their standard order, are the Isagoge Ioannitii ad Tegni Galieni by Hunayn ibn Ishaq; the Hippocratic Aphorisms and Prognostics; the De urinis of Theophilus Protospatharius; and the De pulsibus of Philaretus. The collection is usually supposed to have grown around Hunayn's Isagoge, an abridged introduction to Galen's classical Greek treatise Ars medica (Techne iatrike) translated from Arabic into Latin by Constantine the African in the 11th century. It circulated independently of the Articella. In the late 12th century, Galen's Ars was added to the Articella as a sixth text under the title Tegni. It was later moved into second place. In the mid-13th century, the emergence of formal medical education in several European


id: an-atlas-of-illustrations-of-clinical-medicine-surgery-and-pathology-20260505-0
category: reference
title: An Atlas of Illustrations of Clinical Medicine, Surgery and Pathology
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/An_Atlas_of_Illustrations_of_Clinical_Medicine,_Surgery_and_Pathology
date_saved: 2026-05-05T08:47:27.931520+00:00
instance: kb-cron
parent: an-atlas-of-illustrations-of-clinical-medicine-surgery-and-pathology-20260505-0
file:
data/en.wikipedia.org/wiki/An_Atlas_of_Illustrations_of_Clinical_Medicine,_Surgery_and_Pathology-0.md

summary:
An Atlas of Illustrations of Clinical Medicine, Surgery and Pathology is a medical book of images first published in 1901 by John Bale, Sons & Danielsson. It contains the widely cited photograph taken by Allan Warner of two 13-year-old boys from the same class, who after coming into contact with smallpox, the vaccinated boy remained well and the boy who did not receive the vaccine developed the disease. == References ==


id: autism-s-false-prophets-20260505-0
file: data/en.wikipedia.org/wiki/Autism's_False_Prophets-0.md
category: reference
title: Autism's False Prophets
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Autism's_False_Prophets
date_saved: 2026-05-05T08:47:30.278207+00:00
instance: kb-cron
parent: autism-s-false-prophets-20260505-0
summary:
Autism's False Prophets: Bad Science, Risky Medicine, and the Search for a Cure is a 2008 book by Paul Offit, a vaccine expert and chief of infectious diseases at Children's Hospital of Philadelphia. The book focuses on the controversy surrounding the now-discredited link between vaccines and autism. The scientific consensus is that no convincing scientific evidence supports these claims, and a 2011 pharmacotherapy journal article described the vaccine-autism connection as "the most damaging medical hoax of the last 100 years". == Summary == Offit describes the origins and development of claims regarding the MMR vaccine and the vaccine preservative thiomersal, as well as subsequent scientific evidence which has disproved a link with autism. The book discusses possible explanations for the persistence of these claims in the face of scientific evidence to the contrary, as well as the proliferation of potentially risky and unproven treatments for autism. The author takes a critical view of several advocates of a vaccine–autism link, including Andrew Wakefield, David Kirby, Mark Geier, and Boyd Haley, raising scientific and, in some cases, ethical and legal concerns. The book also explores divisions within the autism community on the topic of vaccines, as some parents consider the ongoing narrow


id: bad-pharma-20260505-0
file: data/en.wikipedia.org/wiki/Bad_Pharma-0.md
category: reference
title: Bad Pharma
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Bad_Pharma
date_saved: 2026-05-05T08:47:31.497683+00:00
instance: kb-cron
parent: bad-pharma-20260505-0
summary:
Bad Pharma: How Drug Companies Mislead Doctors and Harm Patients is a book by the British physician and academic Ben Goldacre about the pharmaceutical industry, its relationship with the medical profession, and the extent to which it controls academic research into its own products. It was published in the UK in September 2012 by the Fourth Estate imprint of HarperCollins, and in the United States in February 2013 by Faber and Faber. Goldacre argues in the book that "the whole edifice of medicine is broken", because the evidence on which it is based is systematically distorted by the pharmaceutical industry. He writes that the industry finances most of the clinical trials into its own products and much of doctors' continuing education, that clinical trials are often conducted on small groups of unrepresentative subjects and negative data is routinely withheld, and that apparently independent academic papers may be planned and even ghostwritten by pharmaceutical companies or their contractors, without disclosure. Describing the situation as a "murderous disaster", he makes suggestions for action by patients' groups, physicians, academics and the industry itself. Responding to the book's publication, the Association of the British Pharmaceutical Industry issued a statement in 2012 arguing that the


id: bad-pharma-20260505-1
file: data/en.wikipedia.org/wiki/Bad_Pharma-1.md
category: reference
title: Bad Pharma
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Bad_Pharma
date_saved: 2026-05-05T08:47:31.497683+00:00
instance: kb-cron
parent: bad-pharma-20260505-0
summary:
=== Chapter 2: "Where Do New Drugs Come From?" === In the second chapter, the book describes the process as new drugs move from animal testing through phase 1 (first-in-man study), phase 2, and phase 3 clinical trials. Phase 1 participants are referred to as volunteers, but in the US are paid $200–$400 per day, and because studies can last several weeks and subjects may volunteer several times a year, earning potential becomes the main reason for participation. Participants are usually taken from the poorest groups in society, and outsourcing increasingly means that trials may be conducted in countries with low wages by contract research organizations (CROs). The rate of growth for clinical trials in India is 20 percent a year, in Argentina 27 percent, and in China 47 percent, while trials in the UK have fallen by 10 percent a year and in the US by six percent. The shift to outsourcing raises issues about data integrity, regulatory oversight, language difficulties, the meaning of informed consent among a much poorer population, the standards of clinical care, the extent to which corruption may be regarded as routine in certain countries, and the ethical problem of raising a population's expectations for


id: bad-pharma-20260505-2
file: data/en.wikipedia.org/wiki/Bad_Pharma-2.md
category: reference
title: Bad Pharma
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Bad_Pharma
date_saved: 2026-05-05T08:47:31.497683+00:00
instance: kb-cron
parent: bad-pharma-20260505-0
summary:
=== Chapter 6: "Marketing" === In the final chapter, Goldacre looks at how doctors are persuaded to prescribe "me-too drugs," brand-name drugs that are no more effective than significantly cheaper off-patent ones. He cites as examples the statins atorvastatin (Lipitor, made by Pfizer) and simvastatin (Zocor), which he writes seem to be equally effective, or at least there is no evidence to suggest otherwise. Simvastatin came off patent several years ago, yet there are still three million prescriptions a year in the UK for atorvastatin, costing the National Health Service (NHS) an annual £165 million extra. He addresses the issue of medicalization of certain conditions (or, as he argues, of personhood), whereby pharmaceutical companies "widen the boundaries of diagnosis" before offering solutions. Female sexual dysfunction was highlighted in 1999 by a study published in the Journal of the American Medical Association, which alleged that 43 percent of women were suffering from it. After the article appeared, the New York Times wrote that two of its three authors had worked as consultants for Pfizer, which at the time was preparing to launch UK-414,495, known as female Viagra. The journal's editor said that the failure to disclose the relationship with Pfizer was


id: bad-pharma-20260505-3
file: data/en.wikipedia.org/wiki/Bad_Pharma-3.md
category: reference
title: Bad Pharma
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Bad_Pharma
date_saved: 2026-05-05T08:47:31.497683+00:00
instance: kb-cron
parent: bad-pharma-20260505-0
summary:
== Reception == The book was generally well received. The Economist described it as "slightly technical, eminently readable, consistently shocking, occasionally hectoring and unapologetically polemical". Helen Lewis in the New Statesman called it an important book, while Luisa Dillner, writing in the Guardian, described it as a "thorough piece of investigative medical journalism". Andrew Jack wrote in the Financial Times that Goldacre is "at his best in methodically dissecting poor clinical trials. ... He is less strong in explaining the complex background reality, such as the general constraints and individual slips of regulators and pharma companies' employees." Jack also argued that the book failed to reflect how many lives have been improved by the current system, for example with new treatments for HIV, rheumatoid arthritis and cancer. Max Pemberton, a psychiatrist, wrote in the Daily Telegraph that "this is a book to make you enraged ... because it's about how big business puts profits over patient welfare, allows people to die because they don't want to disclose damning research evidence, and the tricks they play to make sure doctors do not have all the evidence when it comes to appraising whether a drug really works or not." The Association of


id: big-pharma-book-20260505-0
file: data/en.wikipedia.org/wiki/Big_Pharma_(book)-0.md
category: reference
title: Big Pharma (book)
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Big_Pharma_(book)
date_saved: 2026-05-05T08:47:32.673802+00:00
instance: kb-cron
parent: big-pharma-book-20260505-0
summary:
Big Pharma: How the World's Biggest Drug Companies Control Illness is a 2006 book by British journalist Jacky Law. The book examines the history of the pharmaceutical industry. Before the book, Law was the associate editor of Scrip Magazine. == Reception == Ike Iheanacho writes about the book that "The author is clearly no great fan of the industry. But, refreshingly, she avoids the sort of lazy polemic that casts major pharmaceutical companies as an evil empire that continually foists its products on unwilling and unsuspecting healthcare professionals and patients." == See also == Bad Pharma (2012) by Ben Goldacre Side Effects (2008) by Alison Bass Lists about the pharmaceutical industry == References == == External links == Excerpt from the book


id: a-colour-atlas-of-urology-20260505-0
file: data/en.wikipedia.org/wiki/A_Colour_Atlas_of_Urology-0.md
category: reference
title: A Colour Atlas of Urology
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/A_Colour_Atlas_of_Urology
date_saved: 2026-05-05T08:47:33.835758+00:00
instance: kb-cron
parent: a-colour-atlas-of-urology-20260505-0
summary:
A Colour Atlas of Urology is a medical textbook of urology images first published by Wolfe Medical Publications in 1983. It is co-authored by Reginald Wyndham Lloyd-Davies, James G. Gow and D. R. Davies. 1,188 Images include those of pathological specimens, photographs at endoscopy of the bladder and diagrams that explain urological diagnostic procedures. 70 images relate to lesions of the penis and scrotum. A second edition was published in 1994. A review in the Postgraduate Medical Journal noted that the X-ray of lung metastases was back to front. Another review considered it a complete work covering everything a urologist could possibly see in their profession. The British Journal of Venereal Diseases noted that the book was aimed at urologists but suggested that genitourinary physicians might be interested in it. All three reviews reported that the book was expensive. == Publication == A Colour Atlas of Urology is co-authored by Reginald Wyndham Lloyd-Davies, James G. Gow and D. R. Davies, and was first published by Wolfe Medical Publications in 1983 at a cost of £48. A second edition, with co-author Helen Parkhouse, was published in 1994. == Content == 1,188 images include those of pathological specimens, photographs at endoscopy of


id: current-reviews-in-obstetrics-and-gynaecology-20260505-0
file: data/en.wikipedia.org/wiki/Current_Reviews_in_Obstetrics_and_Gynaecology-0.md
category: reference
title: Current Reviews in Obstetrics and Gynaecology
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Current_Reviews_in_Obstetrics_and_Gynaecology
date_saved: 2026-05-05T08:47:34.991149+00:00
instance: kb-cron
parent: current-reviews-in-obstetrics-and-gynaecology-20260505-0
summary:
Current Reviews in Obstetrics and Gynaecology, also spelled Current Reviews in Obstetrics and Gynecology, is a book series on obstetrics and gynecology which was edited by Tom Lind, Albert Singer, and Joseph A. Jordan and was published by Churchill Livingstone in the 1980s. Its International Standard Serial Number (ISSN) is 0264-5610. == Volumes == Volume 1: Obstetric Analgesia and Anaesthesia (Selwyn Crawford, 1982) Volume 2: Early Diagnosis of Fetal Defects (Brock, 1982) Volume 3: Early Teenage Pregnancy (Russell, 1982) Volume 4: Ovarian Malignancies: The Clinical Care of Adults and Adolescents (Piver & Scully, 1983) Volume 5: Cancer of the Cervix: Diagnosis and Treatment (Shingleton & Orr, 1983) Volume 6: Aspects of Care in Labour (Beazley & Lobb, 1983) Volume 7: Drug Prescribing in Pregnancy (Krauer, Krauer, & Hytten, 1984) Volume 8: Spontaneous Abortion (Huisjes, 1984) Volume 9: Female Puberty and Its Abnormalities (Dewhurst, 1984) Volume 10: Coagulation Problems During Pregnancy (Letsky, 1985) Volume 11: Infertility in the Male (Jequier, 1986) Volume 12: Endometriosis (O'Connor, 1987) Volume 13: Diabetic Pregnancy (Brudenell & Doddridge, 1989) == References == == External links == Current Reviews in Obstetrics & Gynaecology (0264-5610) - ISSN Portal Current Reviews in Obstetrics and Gynaecology - WorldCat Search


id: the-deadly-dinner-party-20260505-0
file: data/en.wikipedia.org/wiki/The_Deadly_Dinner_Party-0.md
category: reference
title: The Deadly Dinner Party
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/The_Deadly_Dinner_Party
date_saved: 2026-05-05T08:47:37.245785+00:00
instance: kb-cron
parent: the-deadly-dinner-party-20260505-0
summary:
The Deadly Dinner Party and Other Medical Detective Stories (2009, ISBN 978-0-300-12558-0) is a nonfiction book by Jonathan A. Edlow, MD about medical mysteries. The book contains fifteen real-life stories of everyday people caught up in medical crises that take deduction and detective work to solve, and to determine a correct diagnosis. The book has been compared to the "medical mystery" books of Berton Roueché. The book is published by Yale University Press. == Reception == In a review for New Scientist, Druin Burch wrote that the "collection of bite-sized essays about obscure infections, poisons and diseases […] make an enjoyable and interesting book. The stories don’t flow, but they do add up to more than a list of anecdotes […]." In The New York Review of Books, Jerome Groopman described how Edlow wrote in "clear and fluid prose" about unusual diagnoses and the ultimate need for a "discerning doctor". == See also == Diagnosis Medical ethics How Doctors Think Fatal Care: Survive in the U.S. Health System == References == == External links == Review of book in The New York Review of Books (November 5, 2009) Review in New Scientist (October 11, 2009)


id: the-desideratum-or-electricity-made-plain-and-useful-20260505-0
file: data/en.wikipedia.org/wiki/The_Desideratum-0.md
category: reference
title: The Desideratum; or, Electricity Made Plain and Useful
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/The_Desideratum;_or,_Electricity_Made_Plain_and_Useful
date_saved: 2026-05-05T08:47:38.416207+00:00
instance: kb-cron
parent: the-desideratum-or-electricity-made-plain-and-useful-20260505-0
summary:
The Desideratum; or, Electricity Made Plain and Useful - By a Lover of Mankind, and of Common Sense is a 1760 book by John Wesley advocating the use of electric shock therapy. Wesley collected the accounts of other researchers with "electrifying machines", and to them added observations from his own experiments in public clinics. == Legacy == The 72-page book has led Wesley to be mentioned alongside his contemporaries Richard Lovett and Jean Paul Marat as a pioneer advocate of the medical uses of electroconvulsive therapy, despite the fact that Wesley's tests and results are not considered scientific by modern standards. == References == == External links == Digital copy of an 1871 reprint at Archive.org


id: diagnosis-mercury-20260505-0
file: data/en.wikipedia.org/wiki/Diagnosis_Mercury-0.md
category: reference
title: Diagnosis Mercury
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Diagnosis_Mercury
date_saved: 2026-05-05T08:47:39.612590+00:00
instance: kb-cron
parent: diagnosis-mercury-20260505-0
summary:
Diagnosis Mercury: Money, Politics and Poison is a 2008 book by Jane Hightower. The book explains that mercury is a poison and that the majority of mercury in the environment comes from coal-fired power plants. But the book is mainly concerned with human exposure from the eating of large predatory fish such as swordfish, shark, king mackerel, large tuna, etc. The book also discusses industrial mercury poisonings, such as those in Minamata, Japan, in the 1950s and Ontario, Canada, in the 1970s. == See also == Mercury in fish Minamata Convention on Mercury == References == == External links == Diagnosis: Mercury Mercury poisoning symptoms and fish recommendations Mercury poisoning time line Mercury guidelines Author Bio at California Pacific Medical Center Mercury Facts


id: die-homosexualit-t-des-mannes-und-des-weibes-20260505-0
file: data/en.wikipedia.org/wiki/Die_Homosexualität_des_Mannes_und_des_Weibes-0.md
category: reference
title: Die Homosexualität des Mannes und des Weibes
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Die_Homosexualität_des_Mannes_und_des_Weibes
date_saved: 2026-05-05T08:47:40.768630+00:00
instance: kb-cron
parent: die-homosexualit-t-des-mannes-und-des-weibes-20260505-0
summary:
Die Homosexualität des Mannes und des Weibes is a classic 1914 book on homosexuality in men and women that was written by German sexologist Magnus Hirschfeld. A second edition was published in 1920. Hirschfeld was himself gay and an occasional crossdresser, known by other Berlin crossdressers as "Aunt Magnesia". The book was part of the series Handbuch der Gesamten Sexualwissenschaft in Einzeldarstellungen and was the third volume of this series. Die Homosexualität des Mannes und des Weibes was not translated until 2000, under the title The Homosexuality of Men and Women by Michael Lombardi-Nash. It has been said that the book was the most significant and authoritative text on homosexuality of its time. The book has often been overlooked in the English-speaking academia. == See also == Die Transvestiten: Eine Untersuchung über den Erotischen Verkleidungstrieb (Hirschfeld, 1910) == References ==


id: die-transvestiten-eine-untersuchung-ber-den-erotischen-verkleidungstrieb-20260505-0
category: reference
title: Die Transvestiten: Eine Untersuchung über den Erotischen Verkleidungstrieb
tags: science, encyclopedia
date_saved: 2026-05-05T08:47:41.916181+00:00
instance: kb-cron
parent: die-transvestiten-eine-untersuchung-ber-den-erotischen-verkleidungstrieb-20260505-0
file:
data/en.wikipedia.org/wiki/Die_Transvestiten:_Eine_Untersuchung_über_den_Erotischen_Verkleidungstrieb-0.md

summary:
Die Transvestiten: Eine Untersuchung über den Erotischen Verkleidungstrieb is a classic 1910 book on crossdressing and transvestism that was written by German sexologist Magnus Hirschfeld. An illustrated companion second volume to the book was published by Hirschfeld and Max Tilke in 1912. In addition, a second edition of Die Transvestiten was published by Hirschfeld in 1925. Subsequent to its publication, the book was translated into English with the title Transvestites: The Erotic Drive to Cross-Dress by Michael Lombardi-Nash in 1991. == Background == Hirschfeld was himself gay and an occasional crossdresser, known by other Berlin crossdressers as "Aunt Magnesia". It has been said that Die Transvestiten was the most significant and authoritative text on transvestism of its time. While the book is about crossdressing, it also clearly includes some people with cross-gender feelings who would likely be referred to as transgender today. The book has often been overlooked in the English-speaking academia. == Contents == Die Transvestiten includes first-person narratives of crossdressing, Hirschfeld's commentaries on these cases, and theorizing based on the observations. Of the narratives, there were 17 in total, with 16 of them natal male and one of them natal female. In the book, Hirschfeld wished to distinguish

source_url:
https://en.wikipedia.org/wiki/Die_Transvestiten:_Eine_Untersuchung_über_den_Erotischen_Verkleidungstrieb


id: the-doctor-in-war-20260505-0
file: data/en.wikipedia.org/wiki/The_Doctor_in_War-0.md
category: reference
title: The Doctor in War
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/The_Doctor_in_War
date_saved: 2026-05-05T08:47:43.085159+00:00
instance: kb-cron
parent: the-doctor-in-war-20260505-0
summary:
The Doctor in War is a book published in November 1918 by Woods Hutchinson, an American physician who travelled throughout Europe from 15 January to 24 December 1917 visiting hospitals, ambulance trains, and other locations to offer his services to the war effort during World War I. == Background == As Hutchinson believed that "the doctor and the sanitarian would play an important part" in the World War, he offered to help the British Army medical staff but was told in order to serve he would have to swear allegiance and in turn lose his American citizenship. With the help of Secretary of War Newton Diehl Baker and Colonel Roosevelt he was able to travel to Europe and see everything that had "any value or interest from a medical and public health point of view." == Summary == Hutchinson emphasizes the importance that doctors played in the war. One of the major things they have contributed is the decrease in deaths due to disease. In the American Civil War the ratio was five deaths to disease for every one in battle, however during 'The Great War' the ratio was changed to ten deaths in battle for every one to disease.


id: donguibogam-20260505-0
file: data/en.wikipedia.org/wiki/Donguibogam-0.md
category: reference
title: Donguibogam
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Donguibogam
date_saved: 2026-05-05T08:47:44.248506+00:00
instance: kb-cron
parent: donguibogam-20260505-0
summary:
The Dongui Bogam (Korean: 동의보감; translated as "Principles and Practice of Eastern Medicine") is a Korean book compiled by the royal physician, Heo Jun and was first published in 1613 during the Joseon period of Korea. The book is regarded as important in traditional Korean medicine, and is one of the classics of Oriental medicine today. In July 2009, it was added to UNESCO’s Memory of the World International Register. The original edition of Dongui Bogam is currently preserved by the Korean National Library. The original was written in Hanja and only part of it was transcribed in Korean for wide reading use, as only officials understood in Hanmun. It was translated to English in 2013. == Name == The title literally translates as "A Precious Mirror of Eastern Medicine". The phrase "Precious Mirror" (보감 寶鑑) is a metaphorical idiom meaning 'something which can be modeled after'. Meanwhile, the phrase "Eastern Medicine" (동의 東醫) is not the antonym to 'Western Medicine'; "Dongguk" (동국 東國), meaning "Eastern Country," was one of the names of Korea, which means the country to the east of China. Therefore, the title can be rendered as "An Exemplary Explanation of Korean Medicine" and is listed in


id: endemic-goiter-20260505-0
file: data/en.wikipedia.org/wiki/Endemic_Goiter-0.md
category: reference
title: Endemic Goiter
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Endemic_Goiter
date_saved: 2026-05-05T08:47:45.385720+00:00
instance: kb-cron
parent: endemic-goiter-20260505-0
summary:
Endemic Goiter: The Adaptation of Man to Iodine Deficiency is a monograph about a study of endemic goiters conducted in Mendoza Province, Argentina by the Massachusetts General Hospital and the University of Cuyo. Written by John B. Stanbury, Gordon L. Brownell, Douglas S. Riggs, Hector Perinetti, Juan Itoiz and Enrique B. Del Castillo, it was published in 1954 by Harvard University Press as part of their Harvard University Monographs in Medicine and Public Health series. The study itself was conducted just before the addition of iodine was made mandatory in Mendoza, and it suggested that a thyroid deprived of iodine absorbed iodide in blood more quickly than their iodine-satiated counterparts. Contemporaneous reviews in The Quarterly Review of Biology, Archives of Internal Medicine, Science, and the American Journal of Clinical Pathology all praised the book for what they felt was clear, well-articulated research on the part of the authors. The reviews also felt that the work had provided a great deal of knowledge on thyroids, and several recommended it to wider audience, or just endocrinologists. The Journal of the American Medical Association differed in its assessment, feeling that the book was "too complex and theoretical" for general practitioners, though recommended it


id: ending-aging-20260505-0
file: data/en.wikipedia.org/wiki/Ending_Aging-0.md
category: reference
title: Ending Aging
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Ending_Aging
date_saved: 2026-05-05T08:47:46.562153+00:00
instance: kb-cron
parent: ending-aging-20260505-0
summary:
Ending Aging: The Rejuvenation Breakthroughs that Could Reverse Human Aging in Our Lifetime is a 2007 book written by biogerontologist Aubrey de Grey, with his research assistant Michael Rae. Ending Aging describes de Grey's proposal for eliminating aging as a cause of debilitation and death in humans, and restoring the body to an indefinitely youthful state, a project that he calls the "strategies for engineered negligible senescence" ("SENS"). De Grey argues that defeating aging is feasible, possibly within a few decades, and he outlines steps that can be taken to hasten the development of regenerative medicine treatments for each side of aging. == Editions == St. Martin's Press, 1st edition (hardcover, 389 pages), released September 4, 2007: ISBN 0-312-36706-6 St. Martin's Griffin, 1st reprint edition with new afterword (paperback, 448 pages), released October 14, 2008: ISBN 0-312-36707-4 == Translations == German: Niemals alt!: So lässt sich das Altern umkehren. Fortschritte der Verjüngungsforschung, transcript Verlag, Bielefeld 2010 Spanish: El Fin del Envejecimiento. Los avances que podrían revertir el envejecimiento humano durante nuestra vida, Lola Books, Berlín 2013 Italian: La fine dell'invecchiamento: Come la scienza potrà esaudire il sogno dell'eterna giovinezza, D Editore, Roma 2016 Portuguese: O fim do envelhecimento: Os avanços


id: epidemiology-in-country-practice-20260505-0
file: data/en.wikipedia.org/wiki/Epidemiology_in_Country_Practice-0.md
category: reference
title: Epidemiology in Country Practice
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Epidemiology_in_Country_Practice
date_saved: 2026-05-05T08:47:47.739445+00:00
instance: kb-cron
parent: epidemiology-in-country-practice-20260505-0
summary:
Epidemiology in Country Practice is a book by William Pickles (1885–1969), a rural general practitioner (GP) physician in Wensleydale, North Yorkshire, England, first published in 1939. The book reports on how careful observations can lead to correlations between transmission of infective disease between families, farms and villages. It contains the detailed observational studies of a 1928 epidemic of catarrhal jaundice and a 1929 epidemic of Bornholm disease which were published in the British Medical Journal (BMJ) in 1930 and 1933 respectively. == Background == William Pickles first realised the possibilities for epidemiological studies for a GP after he read James Mackenzie's The Principles of Diagnosis and Treatment in Heart Affections in the 1920s. With the assistance of his wife Gertie, who kept the charts, Pickles recorded his observations on a 1928 epidemic of catarrhal jaundice and a 1929 epidemic of Bornholm Disease in his district. His findings were published in the British Medical Journal in 1930 and 1933 respectively and in 1935 he presented them at the Royal Society of Medicine. The work was praised by Major Greenwood who wrote that Pickles's work would mark a "new era in epidemiology". His observations led to new understandings of the transmission of


id: epidemiology-in-relation-to-air-travel-20260505-0
file: data/en.wikipedia.org/wiki/Epidemiology_in_Relation_to_Air_Travel-0.md
category: reference
title: Epidemiology in Relation to Air Travel
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Epidemiology_in_Relation_to_Air_Travel
date_saved: 2026-05-05T08:47:48.910523+00:00
instance: kb-cron
parent: epidemiology-in-relation-to-air-travel-20260505-0
summary:
Epidemiology in Relation to Air Travel is a book by Arthur Massey, the medical officer of health of Coventry, published by H. K. Lewis & Co. in 1933. By comparing the travel times of journeys by ship to those of travelling by air, he demonstrated how the quarantinable diseases plague, cholera, yellow fever and smallpox, could arrive in the UK in the early 1930s. Massey noted that travelling by aeroplane, from countries where major infectious diseases were common, to countries where those diseases were rare or non-existent, risked spreading those diseases during the incubation period. It was noted by Air Commodore H. E. Whittingham and in The Indian Medical Gazette to be one of the earliest works of its kind. == Publication == Epidemiology in Relation to Air Travel was written by the Coventry-based medical officer of health Arthur Massey, and published by H. K. Lewis and Co. Ltd. in 1933, when the topic was relatively new, and in the year after the International Sanitary Convention for Aerial Navigation was drawn up. It has 59 pages and five maps. == Synopsis == The book deals briefly with the danger of spreading infectious disease via aircraft as flight times in the


id: etiology-concept-and-prophylaxis-of-childbed-fever-20260505-0
file: data/en.wikipedia.org/wiki/Etiology,_Concept_and_Prophylaxis_of_Childbed_Fever-0.md
category: reference
title: Etiology, Concept and Prophylaxis of Childbed Fever
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Etiology,_Concept_and_Prophylaxis_of_Childbed_Fever
date_saved: 2026-05-05T08:47:50.066960+00:00
instance: kb-cron
parent: etiology-concept-and-prophylaxis-of-childbed-fever-20260505-0
summary:
Etiology, Concept and Prophylaxis of Childbed Fever (German: Die Ätiologie, der Begriff und die Prophylaxis des Kindbettfiebers) is a pioneering medical book written by Ignaz Semmelweis and published in 1861, which explains how hygiene in hospitals can drastically reduce unnecessary deaths. The book and concept saved millions of mothers from a preventable streptococcal infection. The book is 524 pages long and includes studies in hospitals conducted in Vienna in 1847. It is claimed to be one of the most comprehensive medical studies ever published. It was translated into English in 1983 by Dr. K. Codell Carter. Semmelweis's findings challenged conventional ideas about the incidence of puerperal fever (also known as postpartum infections or childbed fever), finding that it could be drastically reduced by requiring hand disinfection in obstetrical clinics. He also cites bed hygiene by washing linens after each patient. Puerperal fever was a deadly infection, common in mid-19th-century hospitals. Semmelweis proposed the practice of washing hands with chlorinated lime solutions in 1847 while working in Vienna General Hospital's First Obstetrical Clinic, where doctors' wards had three times the mortality of midwives' wards. Semmelweis had his life ruined at the time of publication because his ideas, though now proved and


id: fantastic-voyage-live-long-enough-to-live-forever-20260505-0
file: data/en.wikipedia.org/wiki/Fantastic_Voyage:_Live_Long_Enough_to_Live_Forever-0.md
category: reference
title: Fantastic Voyage: Live Long Enough to Live Forever
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Fantastic_Voyage:_Live_Long_Enough_to_Live_Forever
date_saved: 2026-05-05T08:47:51.226341+00:00
instance: kb-cron
parent: fantastic-voyage-live-long-enough-to-live-forever-20260505-0
summary:
Fantastic Voyage: Live Long Enough to Live Forever (Rodale Books, ISBN 1-57954-954-3) is a book authored by Ray Kurzweil and Terry Grossman published in 2004. The basic premise of the book is that if middle aged people can live long enough, until approximately 120 years, they will be able to live forever—as humanity overcomes all diseases and old age itself. This might also be considered a break-even scenario where developments made during a year increase life expectancy by more than one year. Biogerontologist Aubrey de Grey called this the "Longevity escape velocity" in a 2005 TED talk. The book focuses primarily on health topics such as heart disease, cancer, and type 2 diabetes. It promotes lifestyle changes such as a low glycemic index diet, calorie restriction, exercise, drinking green tea and alkalinized water, and other changes to daily living. They also promote aggressive supplementation to make up for nutrient deficiencies they believe are common in Western society. In contrast to his previous book The 10% Solution for a Healthy Life, in which he recommended a diet with 10% of calories from fat, in this book, Kurzweil recommends consuming less than one third of calories from carbohydrates (and less than one


id: feminine-forever-20260505-0
file: data/en.wikipedia.org/wiki/Feminine_Forever-0.md
category: reference
title: Feminine Forever
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Feminine_Forever
date_saved: 2026-05-05T08:47:52.361242+00:00
instance: kb-cron
parent: feminine-forever-20260505-0
summary:
Feminine Forever is a 1966 book written by American gynecologist Robert A. Wilson. The book characterized menopause and associated symptoms as a serious disease state and strongly advocated the use of estrogen-based menopausal hormone therapy to alleviate it, maintain femininity and well-being, and improve quality of life and health. Wilson's claims were criticized as not being based on adequate research and evidence. Nonetheless, Wilson's book was marketed directly to women and was a best-seller, with it having been implicated in causing a rapid and large rise in prescriptions of menopausal hormone therapy. Subsequently, trials such as the Women's Health Initiative (WHI) contradicted Wilson's claims and showed that menopausal hormone therapy could have significant medical risks, such as venous thromboembolism and breast cancer, and that its benefits were not as great as once believed. Decades after the book's publication, it was revealed that the manufacturer of the estrogen drug Premarin had secretly paid Wilson to promote its use by menopausal women. == References ==


id: fixing-sex-20260505-0
file: data/en.wikipedia.org/wiki/Fixing_Sex-0.md
category: reference
title: Fixing Sex
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Fixing_Sex
date_saved: 2026-05-05T08:47:53.573873+00:00
instance: kb-cron
parent: fixing-sex-20260505-0
summary:
Fixing Sex: Intersex, Medical Authority, and Lived Experience, a book by Stanford anthropologist and bioethicist Katrina Karkazis, was published in 2008. Described as "thoughtful", "meticulous", and an "authoritative treatise on intersex", the book examines the perspectives of intersex people, their families, and clinicians to offer compassionate look at the treatment of people born with atypical sex characteristics. == Synopsis == In a scholarly work, Karkazis draws heavily on interviews with intersex adults, parents, and physicians to explore how intersex is understood and treated. In part 1, she reviews the history of treatment for intersex traits, highlighting the work of John Money and the introduction of the, then new, terms "gender", "gender role" and "gender identity". She explores the events following publication of Milton Diamond's study of the David Reimer or "John/Joan" case, and the ways in which public opinion impacted on medical treatment. In part 2, Karkazis presents an analysis of current medical approaches to intersex, and the risks involved, in the wake of a 2006 "consensus statement on the management of intersex disorders". She also reviews the methods utilised to assign a sex of rearing to intersex infants, such as genitals and penis size, chromosomes, fertility, "sexing of the


id: flexner-report-20260505-0
file: data/en.wikipedia.org/wiki/Flexner_Report-0.md
category: reference
title: Flexner Report
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Flexner_Report
date_saved: 2026-05-05T08:47:54.714737+00:00
instance: kb-cron
parent: flexner-report-20260505-0
summary:
The Flexner Report is a book-length landmark report of medical education in the United States and Canada, written by Abraham Flexner and published in 1910 under the aegis of the Carnegie Foundation. Flexner not only described the state of medical education in North America, but he also gave detailed descriptions of the medical schools that were operating at the time. He provided both criticisms and recommendations for improvements of medical education in the United States. While it had many positive effects on American medical education, the Flexner report has been accused of introducing policies that encouraged systemic racism and sexism. The Report, also called Carnegie Foundation Bulletin Number Four, called on American medical schools to enact higher admission and graduation standards, and to adhere strictly to the protocols of mainstream science principles in their teaching and research. The report talked about the need for revamping and centralizing medical institutions. Many American medical schools fell short of the standard advocated in the Flexner Report and, subsequent to its publication, nearly half of such schools merged or were closed outright. Colleges for the education of the various forms of alternative medicine, such as electrotherapy, were closed. Homeopathy, traditional osteopathy, eclectic medicine, and


id: flexner-report-20260505-1
file: data/en.wikipedia.org/wiki/Flexner_Report-1.md
category: reference
title: Flexner Report
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Flexner_Report
date_saved: 2026-05-05T08:47:54.714737+00:00
instance: kb-cron
parent: flexner-report-20260505-0
summary:
== Recommended changes == To help with the transition and change the minds of other doctors and scientists, John D. Rockefeller gave many millions to colleges, hospitals and founded a philanthropic group called "General Education Board" (GEB). In the nineteenth century, it was relatively easy to not only receive a medical education, but also to start a medical school. When Flexner researched his report, many American medical schools were small "proprietary" trade schools owned by one or more doctors, unaffiliated with a college or university, and run to make a profit. A degree was typically awarded after only two years of study with laboratory work and dissection optional. Many of the instructors were local doctors teaching part-time. There were very few full-time professors, dedicated to medical education. Medical schools did not receive funding, and their only money came from the students' tuitions. Regulation of the medical profession by state governments was minimal or nonexistent. American doctors varied enormously in their scientific understanding of human physiology, and the word "quack" was in common use. Flexner carefully examined the situation. Using the Johns Hopkins School of Medicine as the ideal medical school, he issued the following recommendations: Reduce both the number of


id: flexner-report-20260505-2
file: data/en.wikipedia.org/wiki/Flexner_Report-2.md
category: reference
title: Flexner Report
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Flexner_Report
date_saved: 2026-05-05T08:47:54.714737+00:00
instance: kb-cron
parent: flexner-report-20260505-0
summary:
=== Strengthening state regulation of medical licensure === Chapter 11 of the Flexner Report, "The State Boards," offers a scathing critique of the medical regulatory landscape at the time, particularly focusing on the inefficacy and inconsistency of state medical boards. Flexner identifies the critical role these boards were intended to play in upholding medical education standards, both legally and ethically, but argues that they had largely failed in this responsibility."In 1906, the worst of the Chicago schools a school with no entrance requirement, no laboratory teaching, no hospital connections made before state boards the best record attained by any Chicago school in that year. This school, essentially the same now as then, has only recently been declared "not in good standing" with the state board of Illinois. Everywhere in Canada and the United States wretched institutions refute criticism by pointing to their successful state board records."Flexner's broader reform plan, which aimed to elevate medical education in the United States, was fundamentally dependent on state medical boards functioning as effective gatekeepers to the profession. He insisted that state boards must rigorously ensure that only those who completed proper, standardized training could enter medical practice. From a legal standpoint, state boards were


id: flexner-report-20260505-3
file: data/en.wikipedia.org/wiki/Flexner_Report-3.md
category: reference
title: Flexner Report
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Flexner_Report
date_saved: 2026-05-05T08:47:54.714737+00:00
instance: kb-cron
parent: flexner-report-20260505-0
summary:
"The practice of the Negro doctor will be limited to his own race, which in its turn will be cared for better by good Negro physicians than by poor white ones. But the physical well-being of the Negro is not only of moment to the Negro himself. Ten million of them live in close contact with sixty million whites. Not only does the Negro himself suffer from hookworm and tuberculosis; he communicates them to his white neighbors, precisely as the ignorant and unfortunate white contaminates him. Self-protection not less than humanity offers weighty counsel in this matter; self- interest seconds philanthropy. The Negro must be educated not only for his sake, but for ours. He is, as far as the human eye can see, a permanent factor in the nation." Flexner's findings also restricted opportunities for African-American physicians in the medical sphere. Even the Howard and Meharry schools struggled to stay open following the Flexner Report, having to meet the institutional requirements of white medical schools, reflecting a divide in access to health care between white and African-Americans. Following the Flexner Report, African-American students sued universities, challenging the precedent set by Plessy v. Ferguson. However, those students were met by


id: full-catastrophe-living-20260505-0
file: data/en.wikipedia.org/wiki/Full_Catastrophe_Living-0.md
category: reference
title: Full Catastrophe Living
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Full_Catastrophe_Living
date_saved: 2026-05-05T08:47:55.897257+00:00
instance: kb-cron
parent: full-catastrophe-living-20260505-0
summary:
Full Catastrophe Living: Using the Wisdom of Your Body and Mind to Face Stress, Pain, and Illness is a book by Jon Kabat-Zinn, first published in 1990, revised in 2013, which describes the mindfulness-based stress reduction (MBSR) program developed at the University of Massachusetts Medical Center's Stress Reduction Clinic. In addition to describing the content and background of MBSR, Kabat-Zinn describes scientific research showing the medical benefits of mindfulness-based interventions (MBIs), and lays out an approach to mind-body medicine emphasizing the depth of the interconnections between physical and mental health. The book has been called "one of the great classics of mind/body medicine", and has been seen as a landmark in the development of the secular mindfulness movement in the United States and internationally. == Background == Full Catastrophe Living grew out of the work of the University of Massachusetts Medical Center's Stress Reduction Clinic, founded in 1979 by Jon Kabat-Zinn. The purpose of the Clinic was to "serve as a referral service for physicians and other health providers, to which they could send medical patients with a wide range of diagnoses and conditions who were not responding completely to more traditional treatments, or who were 'falling through the cracks'


id: full-catastrophe-living-20260505-1
file: data/en.wikipedia.org/wiki/Full_Catastrophe_Living-1.md
category: reference
title: Full Catastrophe Living
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Full_Catastrophe_Living
date_saved: 2026-05-05T08:47:55.897257+00:00
instance: kb-cron
parent: full-catastrophe-living-20260505-0
summary:
=== Introduction === In the introduction to the revised edition of 2013, Kabat-Zinn defines mindfulness, reflects on the massive growth of MBSR and other mindfulness-based practices since the publication of the first edition in 1990, and lays out the findings of relevant scientific studies. He defines mindfulness operationally as "the awareness that arises by paying attention on purpose, in the present moment, and non-judgmentally", while noting that "when we speak of mindfulness, it is important to keep in mind that we equally mean heartfulness ... It is a more-than-conceptual knowing. It is more akin to wisdom, and to the freedom a wisdom perspective provides." He emphasizes that mindfulness involves accessing within ourselves capacities that we in fact already possess, "finding, recognizing, and making use of that in us which is already okay, already beautiful, already whole by virtue of our being human—and drawing upon it to live our lives as if it really mattered how we stand in relationship to what arises, whatever it is." While stressing that "mindfulness has its own internal logic and poetry", he suggests that scientific research showing its beneficial effects for health and well-being may provide extra incentive to follow the MBSR curriculum. He highlights,


id: full-catastrophe-living-20260505-2
file: data/en.wikipedia.org/wiki/Full_Catastrophe_Living-2.md
category: reference
title: Full Catastrophe Living
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Full_Catastrophe_Living
date_saved: 2026-05-05T08:47:55.897257+00:00
instance: kb-cron
parent: full-catastrophe-living-20260505-0
summary:
Health can be undermined by a lifetime of ingrained behavior patterns that compound and exacerbate the pressures of living we continually face. Ultimately, our habitual and automatic reactions to the stressors we encounter, particularly when we get in the habit of reacting maladaptively, determine in large measure how much stress we experience. Automatic reactions triggered out of unawareness—especially when the circumstances are not life-threatening but we take them that way all the same—can compound and exacerbate stress, making what might have remained basically simple problems into worse ones over time. They can prevent us from seeing clearly, from solving problems creatively, and from expressing our emotions effectively when we need to communicate with other people or even understand what is going on within ourselves. ... A lifetime of unconscious and unexamined habitual reactivity to challenges and perceived threats is likely to increase our risk of eventual breakdown and illness significantly. Habitual maladaptive reactions to stressors can include physical tensions, workaholism, addiction to various chemicals, drugs, or foods, and depressive rumination. Kabat-Zinn describes how mindfulness practice can help people to overcome such maladaptive reactions by bringing them into awareness, "allowing you to engage in and influence the flow of events and


id: galileo-s-middle-finger-20260505-0
file: data/en.wikipedia.org/wiki/Galileo's_Middle_Finger-0.md
category: reference
title: Galileo's Middle Finger
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Galileo's_Middle_Finger
date_saved: 2026-05-05T08:47:57.079400+00:00
instance: kb-cron
parent: galileo-s-middle-finger-20260505-0
summary:
Galileo's Middle Finger is a 2015 book about the ethics of medical research by Alice Dreger, an American bioethicist and author. Dreger explores the relationship between science and social justice by discussing a number of scientific controversies. These include the debates surrounding intersex genital surgery, autogynephilia, and anthropologist Napoleon Chagnon's work. == Synopsis == The first part of Galileo's Middle Finger recounts Dreger's activism against surgical "correction" of intersex individuals' genitalia. Some surgeons called this "total urogenital mobilization" which is "...ripping out everything that didn't seem right to the doctor and rebuilding a girl's genitals from scratch using Frankenstein stitches..." Based on her interactions with the intersex community as well as her own research, she advocated that genital surgery for intersex children be postponed until the individual is old enough to make an informed decision, in the absence of any evidence that the benefits of such surgery outweighed its already reported risks. The second section provides her analysis of the controversy surrounding The Man Who Would Be Queen (2003), by sex researcher and psychologist J. Michael Bailey. In that book, Bailey summarized research on Blanchard's transsexualism typology in a way that Dreger says is scientifically accurate, well-intended, and sympathetic, but


id: the-green-book-immunisation-guide-20260505-0
file: data/en.wikipedia.org/wiki/The_Green_Book_(immunisation_guide)-0.md
category: reference
title: The Green Book (immunisation guide)
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/The_Green_Book_(immunisation_guide)
date_saved: 2026-05-05T08:47:58.214179+00:00
instance: kb-cron
parent: the-green-book-immunisation-guide-20260505-0
summary:
Immunisation against infectious disease, popularly known as The Green Book, provides information on vaccines for vaccine-preventable diseases. It acts as a guide to the UK's vaccination schedule for health professionals and health departments that give vaccines in the United Kingdom. The first two editions were published in 1992 and 1996. A third edition in 2006, was the last to appear in print. Updates have since been added by its clinical editors through advice and recommendations from the Joint Committee on Vaccination and Immunisation (JCVI) and appear only online as individual chapters via the immunisation section of the GOV.UK website. As of 2021 it includes updates on COVID-19. == Purpose == Immunisation against infectious disease is popularly known as The Green Book, to provide information on the UK's vaccination schedule and vaccines for vaccine preventable infectious diseases. It is a guide for health professionals and health departments that give vaccines in the UK. Updates are added by its clinical editors through advice and recommendations from the Joint Committee on Vaccination and Immunisation (JCVI), as accepted by the Secretaries of State. Larger updates may also need consultations with UK health departments and public health bodies, MHRA, vaccine manufacturers, NHS England, National Travel


id: homeopathy-and-its-kindred-delusions-20260505-0
file: data/en.wikipedia.org/wiki/Homeopathy_and_Its_Kindred_Delusions-0.md
category: reference
title: Homeopathy and Its Kindred Delusions
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Homeopathy_and_Its_Kindred_Delusions
date_saved: 2026-05-05T08:47:59.420677+00:00
instance: kb-cron
parent: homeopathy-and-its-kindred-delusions-20260505-0
summary:
Homœopathy and Its Kindred Delusions is a work by Oliver Wendell Holmes Sr., based upon two lectures he gave in 1842, Medical Delusions and Homœopathy. The work criticizes homeopathy, which he considered to be akin to "astrology, palmistry and other methods of getting a living out of the weakness and credulity of mankind and womankind". It is considered to be a classic text, one of Holmes' most important works, as well as one of the earliest criticisms of homeopathy. == Synopsis == Homeopathy and Its Kindred Delusions is composed of two parts. In the first, Holmes explains how the placebo effect can produce false positives, and describes numerous forms of popular but ineffective quackery (including the royal touch, the tractors of Elisha Perkins, and the powder of sympathy), to demonstrate that positive anecdotal evidence is not necessarily indicative of an effective medical therapy. He also describes how Perkins claimed the healing powers of the tractors were due to their being made of a special alloy, but how they declined in popularity after it was discovered that the tractors had the same effect no matter what they were made of. In the second, he criticizes the basis of homeopathy itself, such


id: the-human-embryo-20260505-0
file: data/en.wikipedia.org/wiki/The_Human_Embryo-0.md
category: reference
title: The Human Embryo
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/The_Human_Embryo
date_saved: 2026-05-05T08:48:01.741856+00:00
instance: kb-cron
parent: the-human-embryo-20260505-0
summary:
The Human Embryo: Aristotle and the Arabic and European Traditions is a book looking at the philosophy and religious viewpoints of human reproduction over the ages by the Reverend Canon G. R. Dunstan and published by University of Exeter Press in 1990. It specialises in the study of the human embryo both historically and from different cultural viewpoints. The largest section is devoted to the understanding of the embryo in the Middle Ages, with seven articles alone reinterpreting Dante's passages on the animation of the embryo. == References ==


id: in-training-stories-from-tomorrow-s-physicians-20260505-0
file: data/en.wikipedia.org/wiki/In-Training:_Stories_from_Tomorrow's_Physicians-0.md
category: reference
title: In-Training: Stories from Tomorrow's Physicians
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/In-Training:_Stories_from_Tomorrow's_Physicians
date_saved: 2026-05-05T08:48:02.942655+00:00
instance: kb-cron
parent: in-training-stories-from-tomorrow-s-physicians-20260505-0
summary:
in-Training: Stories from Tomorrow’s Physicians is a print collection of 102 manuscripts originally published on in-Training, the online magazine for medical students, since its founding in July 2012. The collection was written, curated, and edited entirely by medical students. The book is “a compendium of peer-edited narratives written by medical students on humanism, our real-life patients, and the challenges of being a physician-in-training.” The book was published by Pager Publications, Inc., a 501c3 nonprofit literary corporation founded by Ajay Major and Aleena Paul, the founders of in-Training. == Authors == The 80 authors of the manuscripts in the collection are medical students across the United States and Canada, all of whom were writers for in-Training. The book was curated and edited by Ajay Major and Aleena Paul, the founders of in-Training. == Contents == The 102 manuscripts in the collection were selected from over 800 articles originally published on in-Training since its founding in July 2012. Each manuscript is accompanied by reflective discussion questions written by the medical student editors of in-Training. The book was designed as a resource guide for medical students and educators interested in the medical humanities, so the collection includes first-person accounts of experiences in dissection


id: kaitai-shinsho-20260505-0
file: data/en.wikipedia.org/wiki/Kaitai_Shinsho-0.md
category: reference
title: Kaitai Shinsho
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Kaitai_Shinsho
date_saved: 2026-05-05T08:48:04.089453+00:00
instance: kb-cron
parent: kaitai-shinsho-20260505-0
summary:
Kaitai Shinsho (解体新書; Kyūjitai: 解體新書, roughly meaning "New Text on Anatomy") is a medical text translated into Japanese during the Edo period. It was written by Sugita Genpaku, and was published by Suharaya Ichibee (須原屋市兵衛) in 1774, the third year of An'ei. The body comprises four volumes, the illustrations, one. The contents are written kanbun-style. It is based on a translation of the Dutch Ontleedkundige Tafelen, often known in Japan as Tafel Anatomie (ターヘル・アナトミア, Tāheru Anatomia), of Johann Adam Kulmus’ Latin Tabulae Anatomicae, published before 1722 (exact year is unknown) in Gdańsk, Polish–Lithuanian Commonwealth. As a full-blown translation from a Western language, it was the first of its kind in Japan. == Background == On 4 March 1771, the eighth year of Meiwa, the students of Rangaku medicine Sugita Genpaku, Maeno Ryōtaku, Nakagawa Jun'an, et al., by studying performing autopsies on criminals executed at the Kozukappara execution grounds (now, there is a possibility that Katsuragawa Hoshū was at this facility as well, but from the description in Rangaku Koto Hajime (蘭学事始), it seems more likely that he was not). Both Sugita and Maeno had the book Ontleedkundige Tafelen, imported from Holland. Sugita, marveling at the accuracy of the work while


id: kaitai-shinsho-20260505-1
file: data/en.wikipedia.org/wiki/Kaitai_Shinsho-1.md
category: reference
title: Kaitai Shinsho
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Kaitai_Shinsho
date_saved: 2026-05-05T08:48:04.089453+00:00
instance: kb-cron
parent: kaitai-shinsho-20260505-0
summary:
Kaitai Shinsho is generally said to be a translation of Ontleedkundige Tafelen. However, other than the work itself, Bartholini's, Blankaart's, Schamberger’s, Koyter’s, Veslingius', Palfijn's, and others' works were also consulted; the cover is based on Valuerda's. Of course, Asian sources and opinions also had an influence. The book is not a mere translation; the translation was done mostly by Maeno Ryōtaku and then transponed into classical Chinese by Sugita. There are notes in various places left by Sugita, as leftovers from the work. All those lengthy footnotes that cover more than 50% of Kulmus' book were left out. The contents are split into four volumes: Volume I General remarks; forms and names; parts of the body; skeletal structure: general remarks about joints; skeletal structure: detailed exposition about joints. Volume II The head; the mouth; the brain and nerves; the eyes; the ears; the nose; the tongue. Volume III The chest and the diaphragm; the lungs; the heart; arteries; veins; the portal vein; the abdomen; the bowels and stomach; the mesentery and lacteals; the pancreas. Volume IV The spleen; the liver and gall bladder; the kidneys and the bladder; the genitalia; pregnancy; the muscles. The illustrations only comprise one volume. ==


