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+---
+title: "A Man of Misconceptions"
+chunk: 1/1
+source: "https://en.wikipedia.org/wiki/A_Man_of_Misconceptions"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T03:59:55.116751+00:00"
+instance: "kb-cron"
+---
+
+A Man of Misconceptions: The Life of an Eccentric in an Age of Change is a biography written by John Glassie about Athanasius Kircher, a 17th-century German Jesuit scholar, scientist, author, and inventor. Published by Riverhead Books in 2012, it is regarded by The New York Times as the first general-interest biography of Kircher, who has experienced a resurgence of academic attention in recent decades.
+The book traces Kircher's life from his birth in 1602 in Germany through his rise as a scholar at the Jesuit Collegio Romano to the decline of his reputation and his death in Rome in 1680. After Kircher arrived in Rome in 1633, a few months after the Galileo trial, he pursued myriad interests, authoring more than thirty books on such subjects as optics, magnetism, music, medicine, and mathematics, and developing a collection of natural specimens and curiosities into a well known Cabinet of Curiosities or early modern museum. He also worked with Gianlorenzo Bernini on his Fountain of the Four Rivers in the Piazza Navona and labored for many years on the decipherment of Egyptian hieroglyphs. The book places Kircher's work and his interest in natural magic and mysticism within the context of the Scientific Revolution. Glassie draws connections between Kircher and 17th-century figures such as René Descartes, Gottfried Leibniz, and Isaac Newton. He also illustrates later influences on Edgar Allan Poe, Jules Verne, Madame Blavatsky, and Marcel Duchamp.
+Reviews have appeared in The New York Times, The New York Times Book Review, The New Yorker, The Wall Street Journal, The Nation, The Daily Beast and a number of other media outlets. Glassie has appeared on the NPR shows All Things Considered and Science Friday as well as on C-SPAN2's BookTV to discuss the biography. A Man of Misconceptions was selected as a New York Times Book Review "Editor's Choice." It was named one of the best science books of 2012 by Jennifer Ouellette, a writer for Scientific American, and included in an Atlantic Wire article "The Books We Loved in 2012."
+
+
+== References ==
+John Glassie: A Man of Misconceptions: The Life of an Eccentric in an Age of Change. New York, Riverhead, 2012. ISBN 978-1594488719.
+
+
+== External links ==
+Boing Boing: "Athanasius Kircher, A Man of Misconceptions — Exclusive excerpts"
+Believer Magazine excerpt: "A Stony Mass of Not Small Size"
+Public Domain Review excerpt: "Athanasius, Underground"
+Paris Review Daily essay: "Making Monuments"
+Baltimore City Paper
+The Leonard Lopate Show
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+---
+title: "History of forensic photography"
+chunk: 1/2
+source: "https://en.wikipedia.org/wiki/History_of_forensic_photography"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T03:59:44.476607+00:00"
+instance: "kb-cron"
+---
+
+Forensic science holds the branch of forensic photography which encompasses documenting both suspected and convicted criminals, and also the crime scenes, victims, and other evidence needed to make a conviction. Although photography was widely acknowledged as the most accurate way to depict and document people and objects, it was not until key developments in the late 19th century that it came to be widely accepted as a forensic means of identification.
+
+== Overview ==
+Forensic photography resulted from the modernization of criminal justice systems and the power of photographic realism. During the nineteenth and twentieth centuries, these two developments were significant to both forensic photography and police work in general. They can be attributed to a desire for accuracy. First, government bureaucracies became more professionalized and thus collected much more data about their citizens. Then, criminal justice systems began incorporating science into the procedures of police and judiciaries. The main reason, however, for the acceptance of police photography, is a conventional one. Other than its growing popularity, the widespread notion of photography was the prominent belief in the realism of the medium.
+
+== History ==
+The earliest evidence of photographic documentation of prison inmates dates back to 1843–44 in Belgium and 1851 in Denmark. This, however, was solely experimental and was yet to be ruled by technical or legal regulations. The shots ranged from mug shot resemblances, to prisoners in their cells; and the purpose of them also varied from documentation to experimentation. There was no training required and pictures were often taken by amateurs, commercial photographers, and even policemen or prison officials.
+By the 1870s, the practice had spread to many countries, though limited to larger cities. Professional photographers would then be employed to take posed portraits of the criminals. This was early evidence that led to the standard mug shot known today and was unlike any previously known portraiture. Though there was no set standard yet, there was rarely creativity employed with lighting or angle. This was not like photographing portraits of families or children. These were documenting criminals. It was one of the first times people saw portraiture being used for something other than art. Though these were slowly adapted to police regulations, photographing criminals and suspects was widespread until the latter part of the 19th century, when the process of having one's picture taken and archived was limited to individuals convicted of serious offenses. This was, of course, by discretion of the police.
+As the number of criminals climbed, so too did the number of photographs. Organizing and storing the archives became a problem. Collections called, "Rogues Galleries" classified criminals according to types of offenses. The earliest evidence of these galleries was found in Birmingham, England in the 1850s. Shortly after this were initial attempts at standardizing the photographs.
+
+== Alphonse Bertillon ==
+French photographer, Alphonse Bertillon was the first to realize that photographs were futile for identification if they were not standardized by using the same lighting, scale and angles.   He wanted to replace traditional photographic documentation of criminals with a system that would guarantee reliable identification. He suggested anthropological studies of profiles and full-face shots to identify criminals. He published La Photographie Judiciaire (1890), which contained rules for a scientifically exact form of identification photography. He stated that the subjects should be well lit, photographed full face and also in profile, with the ear visible. Bertillon maintained that the precepts of commercial portraits should be forgotten in this type of photography. By the turn of the century, both his measurement system and photographic rules had been accepted and introduced in almost all states. Thus, Bertillon is credited with the invention of the mug shot. 
+Some people believe that Bertillon's methods were influenced by crude Darwinian ideas and attempted to confirm assumptions that criminals were physically distinguishable from law-abiding citizens. It is speculated in the article, "Most Wanted Photography," that it is from this system that many of the stereotype looks (skin color, eye color, hair color, body type and more) of criminals in movies, books and comics were founded.   Although the measurement system was soon replaced by fingerprinting, the method of standardized photographs survived.
+
+== Historical aspects ==
+Photographic processes have been used since the emergence of Forensic Sciences, however, photography, whether analogue or digital, has occasionally been the subject of questioning. Despite being a research resource in certain cases questionable, photography when used according to scientific criteria, is an advantageous documentary resource. It allows immediate recognition of individuals and diverse subjects with better cost-benefit. 
+Learn more about the genesis of Forensic Photography by accessing the article "Forensic Photography - historical aspects. Urgency for a new focus in Brazil". Article published in Revista Brasileira de Criminalística has almost 12,000 accesses. 
+Available at: Doi:https://doi.org/10.15260/rbc.v6i1.144 and https://www.researchgate.net/publication/316052381_Forensic_Photography_-_Historical_Aspects_Urgency_of_a_new_focus_in_Brazil_-_English_version
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+---
+title: "History of forensic photography"
+chunk: 2/2
+source: "https://en.wikipedia.org/wiki/History_of_forensic_photography"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T03:59:44.476607+00:00"
+instance: "kb-cron"
+---
+
+== Crime photography ==
+On the other side of the spectrum of forensic photography, is the crime photography that involves documenting the scene of the crime, rather than the criminal. Though this type of forensic photography was also created for the purpose of documenting, identifying and convicting, it allows more room for creative interpretation and variance of style. It includes taking pictures of the victim (scars, wounds, birthmarks, etc.) for the purpose of identification or conviction; and pictures of the scene (placement of objects, position of body, photos of evidence and fingerprints). The development of this type of forensic photography is responsible for radical changes in the field, including public involvement (crime photos appearing in the newspaper) and new interpretations and purposes of the field. Weiner.
+Bertillon was also the first to methodically photograph and document crime scenes. He did this both at ground level and overhead, which he called "God's-eye-view." While his mug shots encourage people to find differences (from themselves) in physical characteristics of criminals, his crime scene photographs revealed similarities to the public. This made people question, when looking in a newspaper at pictures of a murder that took place in a home that resembles their own, "could this happen to me?"  For the first time, people other than criminologists, police or forensic photographers were seeing the effects of crime through forensic photography.
+
+== Weegee ==
+Among the more famous, and arguably the most famous crime photographer, is Arthur Fellig, better known as "Weegee". He was known for routinely arriving at crime scenes before other reporters, or often even before the police, The nickname is speculated to come from an alternate spelling of the word "Ouija", implying that Fellig had a supernatural force telling where the action was going to occur. His first exhibition was a solo exhibition, entitled, "Weegee: Murder is My Business" and showed in 1941 at the Photo League in New York. The Museum of Modern Art purchased five of his photos and showed them in an exhibit called "Action Photography." Forensic photography had now transcended mere documentation. It was considered an art. Weegee did not consider his photos art, but many perceived them that way. He is a prime example of the different purposes of forensic photography. His photographs were intended as documentation and were viewed that way in the paper by many people, but were shown in museums and seen as art by many others. His first book was published in 1945 and was titled, Naked City.
+
+== Future ==
+With technology like digital photography becoming more common, forensic photography continues to advance and now includes many categories where specialists are required to perform more sophisticated tasks. The use of infrared and ultraviolet light is used for trace evidence photography of fingerprints, tiny blood samples and many other things. Necropsy photographs, or photographs taken both before and after the victim's clothing is removed. These photos include close-ups of scars, tattoos, wounds, teeth marks and anything else that would help in identifying the victim, or determining his or her time and cause of death.
+
+== References ==
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+---
+title: "History of genetics"
+chunk: 1/3
+source: "https://en.wikipedia.org/wiki/History_of_genetics"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T03:59:45.663532+00:00"
+instance: "kb-cron"
+---
+
+The history of genetics dates from the classical era with contributions by Pythagoras, Hippocrates, Aristotle, Epicurus, and others. Modern genetics began with the work of the Augustinian friar Gregor Johann Mendel. His works on pea plants, published in 1866, provided the initial evidence that, on its rediscovery in the 1900s, helped to establish the theory of Mendelian inheritance.
+In ancient Greece, Hippocrates suggested that all organs of the body of a parent gave off invisible "seeds", miniaturised components that were transmitted during sexual intercourse and combined in the mother's womb to form a baby. In the early modern period, William Harvey's
+book On Animal Generation contradicted Aristotle's theories of genetics and embryology.
+The 1900 rediscovery of Mendel's work by Hugo de Vries, Carl Correns and Erich von Tschermak led to rapid advances in genetics. By 1915 the basic principles of Mendelian genetics had been studied in a wide variety of organisms – most notably the fruit fly Drosophila melanogaster. Led by Thomas Hunt Morgan and his fellow "drosophilists", geneticists developed the Mendelian model, which was widely accepted by 1925. Alongside experimental work, mathematicians developed the statistical framework of population genetics, bringing genetic explanations into the study of evolution.
+With the basic patterns of genetic inheritance established, many biologists turned to investigations of the physical nature of the gene. In the 1940s and early 1950s, experiments pointed to DNA as the portion of chromosomes (and perhaps other nucleoproteins) that held genes. A focus on new model organisms such as viruses and bacteria, along with the discovery of the double helical structure of DNA in 1953, marked the transition to the era of molecular genetics.
+In the following years, chemists developed techniques for sequencing both nucleic acids and proteins, while many others worked out the relationship between these two forms of biological molecules and discovered the genetic code. The regulation of gene expression became a central issue in the 1960s; by the 1970s gene expression could be controlled and manipulated through genetic engineering. In the last decades of the 20th century, many biologists focused on large-scale genetics projects, such as sequencing entire genomes.
+
+== Pre-Mendel ideas on heredity ==
+
+=== Ancient theories ===
+
+The most influential early theories of heredity were that of Hippocrates and Aristotle. Hippocrates' theory (possibly based on the teachings of Anaxagoras) was similar to Darwin's later ideas on pangenesis, involving heredity material that collects from throughout the body. Aristotle suggested instead that the (nonphysical) form-giving principle of an organism was transmitted through semen (which he considered to be a purified form of blood) and the mother's menstrual blood, which interacted in the womb to direct an organism's early development. For both Hippocrates and Aristotle—and nearly all Western scholars through to the late 19th century—the inheritance of acquired characters was a supposedly well-established fact that any adequate theory of heredity had to explain. At the same time, individual species were taken to have a fixed essence; such inherited changes were merely superficial. The Athenian philosopher Epicurus observed families and proposed the contribution of both males and females of hereditary characters ("sperm atoms"), noticed dominant and recessive types of inheritance and described segregation and independent assortment of "sperm atoms".
+The Roman poet and philosopher Lucretius describes heredity in his work "De rerum natura".
+
+ From this semen, Venus produces a varied variety of characteristics and reproduces ancestral traits of expression, voice or hair; These features, as well as our faces, bodies, and limbs, are also determined by the specific semen of our relatives.
+Similarly, Marcus Terentius Varro in "Rerum rusticarum libri tres" and Publius Vergilius Maro propose that wasps and bees originate from animals like horses, calves, and donkeys, with wasps coming from horses and bees from calves or donkeys.
+In 1000 CE, the Arab physician, Abu al-Qasim al-Zahrawi (known as Albucasis in the West) was the first physician to describe clearly the hereditary nature of haemophilia in his Al-Tasrif. In 1140 CE, Judah HaLevi described dominant and recessive genetic traits in The Kuzari.
+
+=== Preformation theory ===
+
+The preformation theory is a developmental biological theory, which was represented in antiquity by the Greek philosopher Anaxagoras. It reappeared in modern times in the 17th century and then prevailed until the 19th century. Another common term at that time was the theory of evolution, although "evolution" (in the sense of development as a pure growth process) had a completely different meaning than today. The preformists assumed that the entire organism was preformed in the sperm (animalkulism) or in the egg (ovism or ovulism) and only had to unfold and grow. This was contrasted by the theory of epigenesis, according to which the structures and organs of an organism only develop in the course of individual development (Ontogeny). Epigenesis had been the dominant opinion since antiquity and into the 17th century, but was then replaced by preformist ideas. Since the 19th century epigenesis was again able to establish itself as a view valid to this day.
+
+=== Plant systematics and hybridisation ===
+
+In the 18th century, with increased knowledge of plant and animal diversity and the accompanying increased focus on taxonomy, new ideas about heredity began to appear. Linnaeus and others (among them Joseph Gottlieb Kölreuter, Carl Friedrich von Gärtner, and Charles Naudin) conducted extensive experiments with hybridisation, especially hybrids between species. Species hybridisers described a wide variety of inheritance phenomena, include hybrid sterility and the high variability of back-crosses.
+Plant breeders were also developing an array of stable varieties in many important plant species. In the early 19th century, Augustin Sageret established the concept of dominance, recognising that when some plant varieties are crossed, certain characteristics (present in one parent) usually appear in the offspring; he also found that some ancestral characteristics found in neither parent may appear in offspring. However, plant breeders made little attempt to establish a theoretical foundation for their work or to share their knowledge with current work of physiology, although Gartons Agricultural Plant Breeders in England explained their system.
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+---
+title: "History of genetics"
+chunk: 2/3
+source: "https://en.wikipedia.org/wiki/History_of_genetics"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T03:59:45.663532+00:00"
+instance: "kb-cron"
+---
+
+== Mendel ==
+ Between 1856 and 1865, Gregor Mendel conducted breeding experiments using the pea plant Pisum sativum and traced the inheritance patterns of certain traits. Through these experiments, Mendel saw that the genotypes and phenotypes of the progeny were predictable and that some traits were dominant over others. These patterns of Mendelian inheritance demonstrated the usefulness of applying statistics to inheritance. They also contradicted 19th-century theories of blending inheritance, showing, rather, that genes remain discrete through multiple generations of hybridisation.
+From his statistical analysis, Mendel defined a concept that he described as a character (which in his mind holds also for "determinant of that character"). In only one sentence of his historical paper, he used the term "factors" to designate the "material creating" the character: " So far as experience goes, we find it in every case confirmed that constant progeny can only be formed when the egg cells and the fertilising pollen are off like the character so that both are provided with the material for creating quite similar individuals, as is the case with the normal fertilisation of pure species. We must, therefore, regard it as certain that exactly similar factors must be at work also in the production of the constant forms in the hybrid plants."(Mendel, 1866).
+
+Mendel's work was published in 1866 as "Versuche über Pflanzen-Hybriden" (Experiments on Plant Hybridisation) in the Verhandlungen des Naturforschenden Vereins zu Brünn (Proceedings of the Natural History Society of Brünn), following two lectures he gave on the work in early 1865.
+
+== Post-Mendel, pre-rediscovery ==
+
+=== Pangenesis ===
+
+Mendel's work was published in a relatively obscure scientific journal, and it was not given any attention in the scientific community. Instead, discussions about modes of heredity were galvanised by Darwin's theory of evolution by natural selection, in which mechanisms of non-Lamarckian heredity seemed to be required. Darwin's own theory of heredity, pangenesis, did not meet with any large degree of acceptance. A more mathematical version of pangenesis, one which dropped much of Darwin's Lamarckian holdovers, was developed as the "biometrical" school of heredity by Darwin's cousin, Francis Galton.
+
+=== Germ plasm ===
+
+In 1883 August Weismann conducted experiments involving breeding mice whose tails had been surgically removed. His results — that surgically removing a mouse's tail had no effect on the tail of its offspring — challenged the theories of pangenesis and Lamarckism, which held that changes to an organism during its lifetime could be inherited by its descendants. Weismann proposed the germ plasm theory of inheritance, which held that hereditary information was carried only in sperm and egg cells.
+
+== Rediscovery of Mendel ==
+Hugo de Vries wondered what the nature of germ plasm might be, and in particular he wondered whether or not germ plasm was mixed like paint or whether the information was carried in discrete packets that remained unbroken. In the 1890s he was conducting breeding experiments with a variety of plant species and in 1897 he published a paper on his results that stated that each inherited trait was governed by two discrete particles of information, one from each parent, and that these particles were passed along intact to the next generation. In 1900 he was preparing another paper on his further results when he was shown a copy of Mendel's 1866 paper by a friend who thought it might be relevant to de Vries's work. He went ahead and published his 1900 paper without mentioning Mendel's priority. Later that same year another botanist, Carl Correns, who had been conducting hybridisation experiments with maize and peas, was searching the literature for related experiments prior to publishing his own results when he came across Mendel's paper, which had results similar to his own. Correns accused de Vries of appropriating terminology from Mendel's paper without crediting him or recognising his priority. At the same time another botanist, Erich von Tschermak was experimenting with pea breeding and producing results like Mendel's. He too discovered Mendel's paper while searching the literature for relevant work. In a subsequent paper de Vries praised Mendel and acknowledged that he had only extended his earlier work.
+
+== Emergence of molecular genetics ==
+After the rediscovery of Mendel's work there was a feud between William Bateson and Pearson over the hereditary mechanism, solved by Ronald Fisher in his work "The Correlation Between Relatives on the Supposition of Mendelian Inheritance".
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+---
+title: "History of genetics"
+chunk: 3/3
+source: "https://en.wikipedia.org/wiki/History_of_genetics"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T03:59:45.663532+00:00"
+instance: "kb-cron"
+---
+
+In 1910, Thomas Hunt Morgan showed that genes reside on specific chromosomes. He later showed that genes occupy specific locations on the chromosome. With this knowledge, Alfred Sturtevant, a member of Morgan's famous fly room, using Drosophila melanogaster, provided the first chromosomal map of any biological organism. In 1928, Frederick Griffith showed that genes could be transferred. In what is now known as Griffith's experiment, injections into a mouse of a deadly strain of bacteria that had been heat-killed transferred genetic information to a safe strain of the same bacteria, killing the mouse.
+A series of subsequent discoveries (e.g.) led to the realization decades later that the genetic material is made of DNA (deoxyribonucleic acid) and not, as was widely believed until then, of proteins. In 1941, George Wells Beadle and Edward Lawrie Tatum showed that mutations in genes caused errors in specific steps of metabolic pathways. This showed that specific genes code for specific proteins, leading to the "one gene, one enzyme" hypothesis. Oswald Avery, Colin Munro MacLeod, and Maclyn McCarty showed in 1944 that DNA holds the gene's information. In 1952, Rosalind Franklin and Raymond Gosling produced a strikingly clear x-ray diffraction pattern indicating a helical form. Using these x-rays and information already known about the chemistry of DNA, James D. Watson and Francis Crick demonstrated the molecular structure of DNA in 1953. Together, these discoveries established the central dogma of molecular biology, which states that proteins are translated from RNA which is transcribed by DNA. This dogma has since been shown to have exceptions, such as reverse transcription in retroviruses.
+In 1947, Salvador Luria discovered the reactivation of irradiated phage leading to many further studies on the fundamental processes of repair of DNA damage (for review of early studies, see ). In 1958, Meselson and Stahl demonstrated that DNA replicates semiconservatively, leading to the understanding that each of the individual strands in double-stranded DNA serves as a template for new strand synthesis. In 1960, Jacob and collaborators discovered the operon which consists of a sequence of genes whose expression is coordinated by operator DNA.  In the period 1961 – 1967, through work in several different labs, the nature of the genetic code was determined (e.g.).
+In 1972, Walter Fiers and his team at the University of Ghent were the first to determine the sequence of a gene: the gene for bacteriophage MS2 coat protein. Richard J. Roberts and Phillip Sharp discovered in 1977 that genes can be split into segments. This led to the idea that one gene can make several proteins. The successful sequencing of many organisms' genomes has complicated the molecular definition of the gene. In particular, genes do not always sit side by side on DNA like discrete beads. Instead, regions of the DNA producing distinct proteins may overlap, so that the idea emerges that "genes are one long continuum". It was first hypothesised in 1986 by Walter Gilbert that neither DNA nor protein would be required in such a primitive system as that of a very early stage of the earth if RNA could serve both as a catalyst and as genetic information storage processor.
+The modern study of genetics at the level of DNA is known as molecular genetics, and the synthesis of molecular genetics with traditional Darwinian evolution is known as the modern evolutionary synthesis.
+
+== See also ==
+List of sequenced eukaryotic genomes
+History of molecular biology
+History of RNA Biology
+History of evolutionary thought
+One gene-one enzyme hypothesis
+Phage group
+
+== References ==
+
+== Further reading ==
+
+Elof Axel Carlson, Mendel's Legacy: The Origin of Classical Genetics (Cold Spring Harbor Laboratory Press, 2004.) ISBN 0-87969-675-3
+
+== External links ==
+
+Olby's "Mendel, Mendelism, and Genetics," at MendelWeb
+Andrei, A. (2013). ""Experiments in Plant Hybridization" (1866), by Johann Gregor Mendel". Embryo Project Encyclopedia. Arizona State University.
+http://www.accessexcellence.org/AE/AEPC/WWC/1994/geneticstln.html
+http://www.sysbioeng.com/index/cta94-11s.jpg
+http://www.esp.org/books/sturt/history/
+http://cogweb.ucla.edu/ep/DNA_history.html
+"The history of genetics". BBC. 2000.
+https://web.archive.org/web/20120323085256/http://www.hchs.hunter.cuny.edu/wiki/index.php?title=Modern_Science&printable=yes
+Avery, Oswald T.; MacLeod, Colin M.; McCarty, Maclyn (February 1944). "Studies on the chemical nature of the substance inducing transformation of Pneumococcal types: Induction of transformation by a DEsoxyribonucleic acid fraction isolated from Pneumococcus Type III ". J Exp Med. 79 (2): 137–158. doi:10.1084/jem.79.2.137. PMC 2135445. PMID 19871359.
+http://www.nature.com/physics/looking-back/crick/Crick_Watson.pdf
+Todd, AR (1954). "Chemical Structure of the Nucleic Acids". Proc. Natl. Acad. Sci. U.S.A. 40 (8): 748–55. Bibcode:1954PNAS...40..748T. doi:10.1073/pnas.40.8.748. PMC 534157. PMID 16589553.
+http://www.genomenewsnetwork.org/resources/timeline/1960_mRNA.php
+https://web.archive.org/web/20120403041525/http://www.molecularstation.com/molecular-biology-images/data/503/MRNA-structure.png
+http://www.genomenewsnetwork.org/resources/timeline/1973_Boyer.php
+Struhl, Kevin (1 October 2008). "The hisB463 Mutation and Expression of a Eukaryotic Protein in Escherichia coli". Genetics. 180 (2): 709–714. doi:10.1534/genetics.104.96693. PMC 2567374. PMID 18927256.
+Sanger, F; Nicklen, S; Coulson, AR (December 1977). "DNA sequencing with chain-terminating inhibitors". Proc. Natl. Acad. Sci. U.S.A. 74 (12): 5463–7. Bibcode:1977PNAS...74.5463S. doi:10.1073/pnas.74.12.5463. PMC 431765. PMID 271968.
+Jeffreys, AJ; Wilson, V; Thein, SL (1985). "Individual-specific 'fingerprints' of human DNA". Nature. 316 (6023): 76–79. Bibcode:1985Natur.316...76J. doi:10.1038/316076a0. PMID 2989708. S2CID 4229883.
+Cech, T. R.; Bass, B. L. (1986). "Biological Catalysis by RNA". Annual Review of Biochemistry. 55 (1): 599–629. Bibcode:1986ARBio..55..599C. doi:10.1146/annurev.bi.55.070186.003123. PMID 2427016.
+"A sheep cloning how-to, more or less". CNN. February 1997.
+"Human Genome Project" (Fact Sheet). National Human Genome Research Institute.
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+---
+title: "History of geography"
+chunk: 1/11
+source: "https://en.wikipedia.org/wiki/History_of_geography"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T03:59:47.409771+00:00"
+instance: "kb-cron"
+---
+
+The history of geography includes many histories of geography which have differed over time and between different cultural and political groups. In more recent developments, geography has become a distinct academic discipline. 'Geography' derives from the Greek γεωγραφία – geographia, literally "Earth-writing", that is, description or writing about the Earth. The first person to use the word geography was Eratosthenes (276–194 BC). However, there is evidence for recognizable practices of geography, such as cartography, prior to the use of the term.
+
+== Egypt ==
+The known world of Ancient Egypt saw the Nile as the center, and the world as based upon "the" river.  Various oasis were known to the east and west, and were considered locations of various gods (e.g. Siwa, for Amon).  To the South lay the Kushitic region, known as far as the 4th cataract.  Punt was a region south along the shores of the Red Sea.  Various Asiatic peoples were known as Retenu, Kanaan, Que, Harranu, or Khatti (Hittites).  At various times especially in the Late Bronze Age Egyptians had diplomatic and trade relationships with Babylonia and Elam.  The Mediterranean was called "the Great Green" and was believed to be part of a world encircling ocean.  Europe was unknown although may have become part of the Egyptian world view in Phoenician times.  To the west of Asia lay the realms of Keftiu, possibly Crete, and Mycenae (thought to be part of a chain of islands, that joined Cyprus, Crete, Sicily and later perhaps Sardinia, Corsica and the Balearics to Africa).
+
+== Babylon ==
+The oldest known world maps date back to ancient Babylon from the 9th century BC. The best known Babylonian world map, however, is the Imago Mundi of 600 BC. The map as reconstructed by Eckhard Unger shows Babylon on the Euphrates, surrounded by a circular landmass showing Assyria, Urartu and several cities, in turn surrounded by a "bitter river" (Oceanus), with seven islands arranged around it so as to form a seven-pointed star. The accompanying text mentions seven outer regions beyond the encircling ocean. The descriptions of five of them have survived.
+In contrast to the Imago Mundi, an earlier Babylonian world map dating back to the 9th century BC depicted Babylon as being further north from the center of the world, though it is not certain what that center was supposed to represent.
+
+== Greco-Roman world ==
+
+The ancient Greeks viewed Homer as the founder of geography. His works the Iliad and the Odyssey are works of literature, but both contain a great deal of geographical information. Homer describes a circular world ringed by a single massive ocean. The works show that the Greeks by the 8th century BC had considerable knowledge of the geography of the eastern Mediterranean. The poems contain a large number of place names and descriptions, but for many of these it is uncertain what real location, if any, is actually being referred to.
+Thales of Miletus is one of the first known philosophers known to have wondered about the shape of the world. He proposed that the world was based on water, and that all things grew out of it. He also laid down many of the astronomical and mathematical rules that would allow geography to be studied scientifically. His successor Anaximander is the first person known to have attempted to create a scale map of the known world and to have introduced the gnomon to Ancient Greece.
+
+Hecataeus of Miletus initiated a different form of geography, avoiding the mathematical calculations of Thales and Anaximander he learnt about the world by gathering previous works and speaking to the sailors who came through the busy port of Miletus. From these accounts he wrote a detailed prose account of what was known of the world. A similar work, and one that mostly survives today, is Herodotus' Histories. While primarily a work of history, the book contains a wealth of geographic descriptions covering much of the known world. Egypt, Scythia, Persia, and Asia Minor are all described, including a mention of India. The description of Africa as a whole are contentious, with Herodotus describing the land surrounded by a sea. Though he described the Phoenicians as having circumnavigated Africa in the 6th century BC, through much of later European history the Indian Ocean was thought to be an inland sea, the southern part of Africa wrapping around in the south to connect with the eastern part of Asia. This was not completely abandoned by Western cartographers until the circumnavigation of Africa by Vasco da Gama. Some, though, hold that the descriptions of areas such as India are mostly imaginary. Regardless, Herodotus made important observations about geography. He is the first to have noted the process by which large rivers, such as the Nile, build up deltas, and is also the first recorded as observing that winds tend to blow from colder regions to warmer ones.
+Pythagoras was perhaps the first to propose a spherical world, arguing that the sphere was the most perfect form. This idea was embraced by Plato, and Aristotle presented empirical evidence to verify this. He noted that the Earth's shadow during a lunar eclipse is curved from any angle (near the horizon or high in the sky), and also that stars increase in height as one moves north. Eudoxus of Cnidus used the idea of a sphere to explain how the sun created differing climatic zones based on latitude. This led the Greeks to believe in a division of the world into five regions. At each of the poles was an uncharitably cold region. While extrapolating from the heat of the Sahara it was deduced that the area around the equator was unbearably hot. Between these extreme regions both the northern and southern hemispheres had a temperate belt suitable for human habitation.
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+title: "History of geography"
+chunk: 2/11
+source: "https://en.wikipedia.org/wiki/History_of_geography"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T03:59:47.409771+00:00"
+instance: "kb-cron"
+---
+
+=== Hellenistic period ===
+These theories clashed with the evidence of explorers, however, Hanno the Navigator had traveled as far south as Sierra Leone, and Egyptian Pharaoh Necho II of Africa is related by Herodotus and others as having commissioned a successful circumnavigation of Africa by Phoenician sailors. While they were sailing west around the Southern tip of Africa, it was found that the Sun was to their right (the north). This is thought to have been a key trigger in the realization that the Earth is spherical, in the classical world.
+In the 4th century BC the Greek explorer Pytheas traveled through northeast Europe, and circled the British Isles. He found that the region was considerably more habitable than theory expected, but his discoveries were largely dismissed by his contemporaries because of this. Conquerors also carried out exploration, for example, Caesar's invasions of Britain and Germany, expeditions/invasions sent by Augustus to Arabia Felix and Ethiopia (Res Gestae 26), and perhaps the greatest Ancient Greek explorer of all, Alexander the Great, who deliberately set out to learn more about the east through his military expeditions and so took a large number of geographers and writers with his army who recorded their observations as they moved east.
+The ancient Greeks divided the world into three continents, Europe, Asia, and Libya (Africa). The Hellespont formed the border between Europe and Asia. The border between Asia and Libya was generally considered to be the Nile river, but some geographers, such as Herodotus objected to this. Herodotus argued that there was no difference between the people on the east and west sides of the Nile, and that the Red Sea was a better border. The relatively narrow habitable band was considered to run from the Atlantic Ocean in the west to an unknown sea somewhere east of India in the east. The southern portion of Africa was unknown, as was the northern portion of Europe and Asia, so it was believed that they were circled by a sea. These areas were generally considered uninhabitable.
+The size of the Earth was an important question to the Ancient Greeks. Eratosthenes calculated the Earth's circumference with great precision. Since the distance from the Atlantic to India was roughly known, this raised the important question of what was in the vast region east of Asia and to the west of Europe. Crates of Mallus proposed that there were in fact four inhabitable land masses, two in each hemisphere. In Rome a large globe was created depicting this world. Posidonius set out to get a measurement, but his number actually was considerably smaller than the real one, yet it became accepted that the eastern part of Asia was not a huge distance from Europe.
+
+=== Roman period ===
+
+While the works of almost all earlier geographers have been lost, many of them are partially known through quotations found in Strabo (64/63 BC – ca. AD 24). Strabo's seventeen volume work of geography is almost completely extant, and is one of the most important sources of information on classical geography. Strabo accepted the narrow band of habitation theory, and rejected the accounts of Hanno and Pytheas as fables. None of Strabo's maps survive, but his detailed descriptions give a clear picture of the status of geographical knowledge of the time. Pliny the Elder's (AD 23 – 79) Natural History also has sections on geography. A century after Strabo Ptolemy (AD 90 – 168) launched a similar undertaking. By this time the Roman Empire had expanded through much of Europe, and previously unknown areas such as the British Isles had been explored. The Silk Road was also in operation, and for the first time knowledge of the far east began to be known. Ptolemy's Geographia opens with a theoretical discussion about the nature and techniques of geographical inquiry, and then moves to detailed descriptions of much the known world. Ptolemy lists a huge number of cities, tribes, and sites and places them in the world. It is uncertain what Ptolemy's names correspond to in the modern world, and a vast amount of scholarship has gone into trying to link Ptolemaic descriptions to known locations.
+It was the Romans who made far more extensive practical use of geography and maps. The Roman transportation system, consisting of 55,000 miles (89,000 km) of roads, could not have been designed without the use of geographical systems of measurement and triangulation. The cursus publicus, a department of the Roman government devoted to transportation, employed full-time gromatici (surveyors). The surveyors' job was to gather topographical information and then to determine the straightest possible route where a road might be built. Instruments and principles used included sun dials for determining direction, theodolites for measuring horizontal angles, and triangulation without which the creation of perfectly straight stretches, some as long as 35 miles (56 km), would have been impossible. During the Greco-Roman era, those who performed geographical work could be divided into four categories:
+
+Land surveyors determined the exact dimensions of a particular area such as a field, dividing the land into plots for distribution, or laying out the streets in a town.
+Cartographical surveyors made maps, involving finding latitudes, longitudes and elevations.
+Military surveyors were called upon to determine such information as the width of a river an army would need to cross.
+Engineering surveyors investigated terrain in order to prepare the way for roads, canals, aqueducts, tunnels and mines.
+Around AD 400 a scroll map called the Peutinger Table was made of the known world, featuring the Roman road network. Besides the Roman Empire which at that time spanned from Britain to the Middle East and Africa, the map includes India, Sri Lanka and China. Cities are demarcated using hundreds of symbols. It measures 1.12 ft (0.34 m) high and 22.15 ft (6.75 m) long.
+The tools and principles of geography used by the Romans would be closely followed with little practical improvement for the next 700 years.
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+---
+title: "History of geography"
+chunk: 11/11
+source: "https://en.wikipedia.org/wiki/History_of_geography"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T03:59:47.409771+00:00"
+instance: "kb-cron"
+---
+
+The term critical geography has been in use since at least 1749, when the book  Geography reformed: a new system of general geography, according to an Accurate Analysis of the science in four parts dedicated a chapter to the topic titled "of Critical Geography." This chapter described critical geography as an approach geographers take to build upon the work of others, and make corrections to their maps based on new information. In the 1970s, the term saw a resurgence as so called "radical geographers" took on the framework of critical theory and Marxist philosophy, using critical geography as an umbrella uniting various theoretical frameworks in geography, including Marxist geography and feminist geography.
+Critical geography re-emerged within the discipline in part as a radical critique of positivist approaches that gained popularity during the quantitative revolution. The first strain of critical geography to emerge was humanistic geography. Drawing on the philosophies of existentialism and phenomenology, humanistic geographers (such as Yi-Fu Tuan) focused on people's sense of, and relationship with, places. More influential was Marxist geography, which applied the social theories of Karl Marx and his followers to geographic phenomena. David Harvey, Milton Santos and Richard Peet are well-known Marxist geographers. Feminist geography is, as the name suggests, the use of ideas from feminism in geographic contexts. The most recent strain of critical geography is postmodernist geography, which employs the ideas of postmodernist and poststructuralist theorists to explore the social construction of spatial relations.
+Critical geography is often viewed as directly opposed to the positive approaches during the 20th century, and quantitative geographers have levied counter criticisms. Some argue the rise in critical geography was in response to the difficulty in understanding the new techniques and technology, and that the early criticisms of these technologies critical geographers put forth in the 20th century have been addressed by advances in computers. Critical geography has been called "anti-science."
+
+== 21st century ==
+
+=== Social theory/spatial analysis split ===
+After an initial debate on the merits of positivism, where critical geographers attempted "to excise everything that went before in quantitative geography" and "overthrow the dominant quantitative approach" during the 1960s and 1970s, by 1995, GIS practitioners and quantitative geographers began to "decline comment" to critical geography in an academic context. While quantitative geographers and critical geographers continued to work together in some context, a lack of "common vocabulary," and rounds of "polarizing debates," lead to a situation of "mutual indifference and absence of dialog between the two groups" during the 2000s. The result of this split led to the creation of two camps within human geography that many view as irreconcilable, described by geographer Mei-Po Kwan as the "social-cultural geographies" and the "spatial-analytical geographies."
+
+== See also ==
+Chorography
+Economic geography
+Geographers on Film
+Human geography
+List of explorers
+List of geographers
+List of maritime explorers
+Physical geography
+Royal Geographical Society
+Royal Scottish Geographical Society
+
+== Notes ==
+
+== References ==
+Bowen, M. (1981). Empiricism and Geographical Thought from Francis Bacon to Alexander von Humboldt. Cambridge University Press.
+Casey, E. (2013). The Fate of Place: A Philosophical History. University of California Press.
+Earle, C., Kenzer, M. S., & Mathewson, K. (Eds.). (1995). Concepts in Human Geography. Rowman & Littlefield Publishers.
+Harley, J.B. and David Woodward. (eds.) The History of Cartography series Chicago: University of Chicago Press, 1987
+Hsu, Mei-ling. "The Qin Maps: A Clue to Later Chinese Cartographic Development," Imago Mundi (Volume 45, 1993): 90–100.
+Livingstone, D. (1993). The Geographical Tradition: Episodes in the history of a contested enterprise. Wiley-Blackwell.
+Martin, Geoffrey J. All Possible Worlds: A History of Geographical Ideas. New York: Oxford University Press, 2005.
+Needham, Joseph (1986). Science and Civilization in China: Volume 3. Taipei: Caves Books, Ltd.
+Needham, Joseph (1986). Science and Civilization in China: Volume 4, Part 3. Taipei: Caves Books, Ltd.
+
+== External links ==
+The Encyclopædia of Geography: comprising a complete description of the earth, physical, statistical, civil, and political, 1852, Hugh Murray, 1779–1846, et al. (Philadelphia: Blanchard and Lea) at the University of Michigan Making of America site.
+Allen, Nellie Burnham (1916). Geographical and industrial studies; Asia. Ginn and company. Retrieved 24 April 2014.
+Smith, Joseph Russell (1921). Peoples and countries. Vol. 1 of Human Geography. John C. Winston Company. Retrieved 24 April 2014.
+The Story of Maps, a history of cartography; why North is at the "top" of a map, how they surveyed all of Europe and other interesting facts.
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+title: "History of geography"
+chunk: 3/11
+source: "https://en.wikipedia.org/wiki/History_of_geography"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T03:59:47.409771+00:00"
+instance: "kb-cron"
+---
+
+== India ==
+A vast corpus of Indian texts embraced the study of geography. The Vedas and Puranas contain elaborate descriptions of rivers and mountains and treat the relationship between physical and human elements. According to religious scholar Diana Eck, a notable feature of geography in India is its interweaving with Hindu mythology,
+
+No matter where one goes in India, one will find a landscape in which mountains, rivers, forests, and villages are elaborately linked to the stories and gods of Indian culture. Every place in this vast country has its story; and conversely, every story of Hindu myth and legend has its place.
+
+=== Ancient period ===
+The geographers of ancient India put forward theories regarding the origin of the Earth. They theorized that the Earth was formed by the solidification of gaseous matter and that the Earth's crust is composed of hard rocks (sila), clay (bhumih) and sand (asma). Theories were also propounded to explain earthquakes (bhukamp) and it was assumed that earth, air and water combined to cause earthquakes. The Arthashastra, a compendium by Kautilya (also known as Chanakya) contains a range of geographical and statistical information about the various regions of India. The composers of the Puranas divided the known world into seven continents of dwipas, Jambu Dwipa, Krauncha Dwipa, Kusha Dwipa, Plaksha Dwipa, Pushkara Dwipa, Shaka Dwipa and Shalmali Dwipa. Descriptions were provided for the climate and geography of each of the dwipas.
+
+=== Early Medieval period ===
+The Vishnudharmottara Purana (compiled between 300 and 350 AD) contains six chapters on physical and human geography. The locational attributes of peoples and places, and various seasons are the topics of these chapters. Varāhamihira's Brihat-Samhita gave a thorough treatment of planetary movements, rainfall, clouds and the formation of water.  The mathematician-astronomer Aryabhatiya gave a precise estimate of the Earth's circumference in his treatise Āryabhaṭīya. Aryabhata accurately calculated the Earth's circumference as 24,835 miles (39,968 km), which was only 0.2% smaller than the actual value of 24,902 miles (40,076 km).
+
+=== Late Medieval period ===
+The Mughal chronicles Tuzuk-i-Jehangiri, Ain-i-Akbari and Dastur-ul-aml contain detailed geographical narratives. These were based on the earlier geographical works of India and the advances made by medieval Muslim geographers, particularly the work of Alberuni.
+
+== China ==
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+---
+title: "History of geography"
+chunk: 4/11
+source: "https://en.wikipedia.org/wiki/History_of_geography"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T03:59:47.409771+00:00"
+instance: "kb-cron"
+---
+
+In China, the earliest known geographical Chinese writing dates back to the 5th century BC, during the beginning of the Warring States period (481 BC – 221 BC). This work was the Yu Gong ('Tribute of Yu') chapter of the Shu Jing or Book of Documents, which describes the traditional nine provinces of ancient China, their kinds of soil, their characteristic products and economic goods, their tributary goods, their trades and vocations, their state revenues and agricultural systems, and the various rivers and lakes listed and placed accordingly. The nine provinces at the time of this geographical work were relatively small in size compared to those of modern China with the book's descriptions pertaining to areas of the Yellow River, the lower valleys of the Yangtze and the plain between them as well as the Shandong peninsula and to the west the most northern parts of the Wei and Han Rivers along with the southern parts of modern-day Shanxi province.
+In this ancient geographical treatise, which would greatly influence later Chinese geographers and cartographers, the Chinese used the mythological figure of Yu the Great to describe the known earth (of the Chinese). Apart from the appearance of Yu, however, the work was devoid of magic, fantasy, Chinese folklore, or legend. Although Chinese geographical writings in the time of Herodotus and Strabo were of lesser quality and contained less systematic approaches, this would change from the 3rd century onwards, as Chinese methods of documenting geography became more complex than those found in Europe, a state of affairs that would persist until the 13th century.
+The earliest extant maps found in archeological sites of China date to the 4th century BC and were made in the ancient State of Qin. The earliest known reference to the application of a geometric grid and mathematically graduated scale to a map was contained in the writings of the cartographer Pei Xiu (224–271). From the 1st century AD onwards, official Chinese historical texts contained a geographical section, which was often an enormous compilation of changes in place-names and local administrative divisions controlled by the ruling dynasty, descriptions of mountain ranges, river systems, taxable products, etc. The ancient Chinese historian Ban Gu (32–92) most likely started the trend of the gazetteer in China, which became prominent in the Northern and Southern dynasties period and Sui dynasty. Local gazetteers would feature a wealth of geographic information, although its cartographic aspects were not as highly professional as the maps created by professional cartographers.
+From the time of the 5th century BC Shu Jing forward, Chinese geographical writing provided more concrete information and less legendary element. This example can be seen in the 4th chapter of the Huainanzi (Book of the Master of Huainan), compiled under the editorship of Prince Liu An in 139 BC during the Han dynasty (202 BC – 202 AD). The chapter gave general descriptions of topography in a systematic fashion, given visual aids by the use of maps (di tu) due to the efforts of Liu An and his associate Zuo Wu. In Chang Chu's Hua Yang Guo Chi (Historical Geography of Sichuan) of 347, not only rivers, trade routes, and various tribes were described, but it also wrote of a 'Ba Jun Tu Jing' ('Map of Sichuan'), which had been made much earlier in 150. The Shui Jing (Waterways Classic) was written anonymously in the 3rd century during the Three Kingdoms era (attributed often to Guo Pu), and gave a description of some 137 rivers found throughout China. In the 6th century, the book was expanded to forty times its original size by the geographers Li Daoyuan, given the new title of Shui Jing Zhu (The Waterways Classic Commented).
+In later periods of the Song dynasty (960–1279) and Ming dynasty (1368–1644), there were much more systematic and professional approaches to geographic literature. The Song dynasty poet, scholar, and government official Fan Chengda (1126–1193) wrote the geographical treatise known as the Gui Hai Yu Heng Chi. It focused primarily on the topography of the land, along with the agricultural, economic and commercial products of each region in China's southern provinces. The polymath Chinese scientist Shen Kuo (1031–1095) devoted a significant amount of his written work to geography, as well as a hypothesis of land formation (geomorphology) due to the evidence of marine fossils found far inland, along with bamboo fossils found underground in a region far from where bamboo was suitable to grow. The 14th-century Yuan dynasty geographer Na-xin wrote a treatise of archeological topography of all the regions north of the Yellow River, in his book He Shuo Fang Gu Ji. The Ming dynasty geographer Xu Xiake (1587–1641) traveled throughout the provinces of China (often on foot) to write his enormous geographical and topographical treatise, documenting various details of his travels, such as the locations of small gorges, or mineral beds such as mica schists. Xu's work was largely systematic, providing accurate details of measurement, and his work (translated later by Ding Wenjiang) read more like a 20th-century field surveyor than an early 17th-century scholar.
+The Chinese were also concerned with documenting geographical information of foreign regions far outside of China. Although Chinese had been writing of civilizations of the Middle East, India, and Central Asia since the traveler Zhang Qian (2nd century BC), later Chinese would provide more concrete and valid information on the topography and geographical aspects of foreign regions. The Tang dynasty (618–907) Chinese diplomat Wang Xuance traveled to Magadha (modern northeastern India) during the 7th century. Afterwards he wrote the book Zhang Tian-zhu Guo Tu (Illustrated Accounts of Central India), which included a wealth of geographical information. Chinese geographers such as Jia Dan (730–805) wrote accurate descriptions of places far abroad. In his work written between 785 and 805, he described the sea route going into the mouth of the Persian Gulf, and that the medieval Iranians (whom he called the people of the Luo-He-Yi country, i.e. Persia) had erected 'ornamental pillars' in the sea that acted as lighthouse beacons for ships that might go astray. Confirming Jia's reports about lighthouses in the Persian Gulf, Arabic writers a century after Jia wrote of the same structures, writers such as al-Mas'udi and al-Muqaddasi. The later Song dynasty ambassador Xu Jing wrote his accounts of voyage and travel throughout Korea in his work of 1124, the Xuan-He Feng Shi Gao Li Tu Jing (Illustrated Record of an Embassy to Korea in the Xuan-He Reign Period). The geography of medieval Cambodia (the Khmer Empire) was documented in the book Zhen-La Feng Tu Ji of 1297, written by Zhou Daguan.
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+title: "History of geography"
+chunk: 5/11
+source: "https://en.wikipedia.org/wiki/History_of_geography"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T03:59:47.409771+00:00"
+instance: "kb-cron"
+---
+
+== Middle Ages ==
+
+=== Byzantine Empire and Syria ===
+After the fall of the western Roman Empire, the Eastern Roman Empire, ruled from Constantinople and known as the Byzantine Empire, continued to thrive and produced several noteworthy geographers. Stephanus of Byzantium (6th century) was a grammarian at Constantinople and authored the important geographical dictionary Ethnica.  This work is of enormous value, providing well-referenced geographical and other information about ancient Greece.
+The geographer Hierocles (6th century) authored the Synecdemus  (prior to AD 535) in which he provides a table of administrative divisions of the Byzantine Empire and lists the cities in each. The Synecdemus and the Ethnica were the principal sources of Constantine VII's work on the Themes or divisions of Byzantium, and are the primary sources we have today on political geography of the sixth-century East.
+George of Cyprus is known for his Descriptio orbis Romani (Description of the Roman world), written in the decade 600–610. Beginning with Italy and progressing counterclockwise including Africa, Egypt and the western Middle East, George lists cities, towns, fortresses and administrative divisions of the Byzantine or Eastern Roman Empire.
+Cosmas Indicopleustes, (6th century) also known as "Cosmas the Monk", was an Alexandrian merchant.  By the records of his travels, he seems to have visited India, Sri Lanka, the Kingdom of Axum in modern Ethiopia, and Eritrea. Included in his work Christian Topography were some of the earliest world maps. Though Cosmas believed the earth to be flat, most Christian geographers of his time disagreed with him.
+Syrian bishop Jacob of Edessa (633–708) adapted scientific material sourced from Aristotle, Theophrastus, Ptolemy and Basil to develop a carefully structured picture of the cosmos. He corrects his sources and writes more scientifically, whereas Basil's Hexaemeron is theological in style.
+Karl Müller has collected and printed several anonymous works of geography from this era, including the Expositio totius mundi.
+
+=== Islamic world ===
+
+In the latter 7th century, adherents of the new religion of Islam surged northward out of Arabia taking over lands in which Jews, Byzantine Christians and Persian Zoroastrians had been established for centuries. There, carefully preserved in the monasteries and libraries, they discovered the Greek classics which included great works of geography by Egyptian Ptolemy's Almagest and Geography, along with the geographical wisdom of the Chinese and the great accomplishments of the Roman Empire. The Arabs, who spoke only Arabic, employed Christians and Jews to translate these and many other manuscripts into Arabic.
+The primary geographical scholarship of this era occurred throughout the Islamic Realms: in West Asia's newly intellectually dynamic regions like Persia, today's Iran, but also in the great learning center the House of Wisdom at Baghdad, in today's Iraq as well as in Syria, both being centers of knowledge from the earliest times. Early caliphs encouraged scholarship. Under their rule, native West Asians served as mawali or dhimmi,  and most geographers in this period were Syrian or Persian, i.e. of either Zoroastrian or Christian background, like much of the region's population.
+Persians who wrote on geography or created maps during the Middle Ages included:
+
+Al-Khwārizmī (780–850) wrote The Image of the Earth (Kitab surat al-ard), in which he used the Geography (Ptolemy) of Ptolemy but improved upon his values for the Mediterranean Sea, Asia, and Africa.
+Ibn Khurdadhbih (820–912) authored a book of administrative geography Book of the Routes and Provinces (Kitab al-masalik wa’l-mamalik), which is the earliest surviving Arabic work of its kind. He made the first quadratic scheme map of four sectors.
+Sohrab or Sorkhab (died 930) wrote Marvels of the Seven Climes to the End of Habitation describing and illustrating a rectangular grid of latitude and longitude to produce a world map.
+Al-Balkhi (850–934)  founded the "Balkhī school" of terrestrial mapping in Baghdad.
+Al-Istakhri (died 957) compiled the Book of the Routes of States, (Kitab Masalik al-Mamalik) from personal observations and literary sources
+Al-Biruni (973–1052) described polar equi-azimuthal equidistant projection of the celestial sphere.
+Abu Nasr Mansur (960–1036) known for his work with the spherical sine law. His Book of Azimuths is no longer extant.
+Avicenna (980–1037) wrote on earth sciences in his Book of Healing.
+Ibn al-Faqih (10th century) wrote Concise Book of Lands (Mukhtasar Kitab al-Buldan).
+Ibn Rustah (10th century) wrote a geographical compendium known as Book of Precious Records.
+Arabs who contributed to this tradition included:
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+---
+title: "History of geography"
+chunk: 6/11
+source: "https://en.wikipedia.org/wiki/History_of_geography"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T03:59:47.409771+00:00"
+instance: "kb-cron"
+---
+
+Al-Jahiz (776-869) who described the impact of the physical environment of man upon his appearance, which led him to compare the peoples of various regions of the world and the peoples inhabiting them.
+Ya'qubi (d. 897) whose Kitab al-Buldan describes numerous places across Africa and Asia, while also giving pride of place to the description of the peoples inhabiting the lands mentioned, as well as their beliefs and practices.
+Abu Muhammad al-Hasan al-Hamdani (893-947) whose Sifat Jazirat al-Arab remains one of the most valuable sources on the geography, flaura, fauna, and peoples of the Arabian Peninsula.
+al-Masudi (896-956) who wrote The Meadows of Gold, combining universal history with scientific geography.
+Ibn Hawqal (d. 978) who wrote Surat Al-Ard, adding further detail on the Islamic West as well as more accurate maps to the currents of Western Asian scholarship to which he belonged.
+al-Maqdisi (945-991) whose description and cultural division of the world in his work Aḥsan al-taqāsīm make it a landmark in geographical studies. His work also highlighted a tendency to give greater attention and depth of analysis to the lands of the Islamic world.
+Al-Bakri (1040-1094) whose Book of Roads and Kingdoms (al-Bakri) contains important descriptions of the Atlantic world, the Sahara and Central Africa.
+Muhammad al-Idrisi (1100-1165) whose Tabula Rogeriana is one of the most advanced works of geography of the whole Middle Ages. Here, a reversal of the trend that had started a few centuries earlier can be noted, with a tentative return to universal geography, transcending the boundaries of the religious spheres.
+Ibn Jubayr (1145-1217) who left behind an account of his pilgrimage across the Mediterranean towards the Hijaz, providing precious descriptions of the interactions between the Norman, Byzantine and Arab cultural spheres in the region.
+Ibn Khaldun (1332-1406) whose Muqaddimah, an introduction to his world history, extensively discusses the influence of different geographic settings, not only on the physical appearance of men, but also on the forms of social organization they develop.
+Further details about some of the authors are given below:
+In the early 10th century, Abū Zayd al-Balkhī, a Persian originally from Balkh, founded the "Balkhī school" of terrestrial mapping in Baghdad. The geographers of this school also wrote extensively of the peoples, products, and customs of areas in the Muslim world, with little interest in the non-Muslim realms. Suhrāb, a late 10th-century Persian geographer, accompanied a book of geographical coordinates with instructions for making a rectangular world map, with equirectangular projection or cylindrical equidistant projection. In the early 11th century, Avicenna hypothesized on the geological causes of mountains in The Book of Healing (1027).
+
+In mathematical geography, Persian Abū Rayhān al-Bīrūnī, around 1025, was the first to describe a polar equi-azimuthal equidistant projection of the celestial sphere. He was also regarded as the most skilled when it came to mapping cities and measuring the distances between them, which he did for many cities in the Middle East and western Indian subcontinent. He combined astronomical readings and mathematical equations to record degrees of latitude and longitude and to measure the heights of mountains and depths of valleys, recorded in The Chronology of the Ancient Nations. He discussed human geography and the planetary habitability of the Earth, suggesting that roughly a quarter of the Earth's surface is habitable by humans.
+By the early 12th century the Normans had overthrown the Arabs in Sicily. Palermo had become a crossroads for travelers and traders from many nations and the Norman King Roger II, having great interest in geography,  commissioned the creation of a book and map that would compile all this wealth of geographical information. Researchers were sent out and the collection of data took 15 years.  Al-Idrisi, one of few Arabs who had ever been to France and England as well as Spain, Central Asia and Constantinople, was employed to create the book from this mass of data. Utilizing the information inherited from the classical geographers, he created one of the most accurate maps of the world to date, the Tabula Rogeriana (1154). The map, written in Arabic, shows the Eurasian continent in its entirety and the northern part of Africa.
+An adherent of environmental determinism was the medieval Afro-Arab writer al-Jahiz (776–869), who explained how the environment can determine the physical characteristics of the inhabitants of a certain community. He used his early theory of evolution to explain the origins of different human skin colors, particularly black skin, which he believed to be the result of the environment. He cited a stony region of black basalt in the northern Najd as evidence for his theory.
+
+=== Medieval Europe ===
+
+During the Early Middle Ages, geographical knowledge in Europe regressed (though it is a popular misconception that they thought the world was flat), and the simple T and O map became the standard depiction of the world.
+The trips of Venetian explorer Marco Polo throughout Mongol Empire in the 13th century, the Christian Crusades of the 12th and 13th centuries, and the Portuguese and Spanish voyages of exploration during the 15th and 16th centuries opened up new horizons and stimulated geographic writings.
+The Mongols also had wide-ranging knowledge of the geography of Europe and Asia, based in their governance and ruling of much of this area and used this information for the undertaking of large military expeditions. The evidence for this is found in historical resources such as The Secret History of Mongols and other Persian chronicles written in 13th and 14th centuries. For example, during the rule of the Great Yuan Dynasty a world map was created and is currently kept in South Korea. See also: Maps of the Yuan Dynasty
+During the 15th century, Henry the Navigator of Portugal supported explorations of the African coast and became a leader in the promotion of geographic studies. Among the most notable accounts of voyages and discoveries published during the 16th century were those by Giambattista Ramusio in Venice, by Richard Hakluyt in England, and by Theodore de Bry in what is now Belgium.
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+title: "History of geography"
+chunk: 7/11
+source: "https://en.wikipedia.org/wiki/History_of_geography"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T03:59:47.409771+00:00"
+instance: "kb-cron"
+---
+
+== Early modern period ==
+
+Following the journeys of Marco Polo, interest in geography spread throughout Europe. From around c. 1400, the writings of Ptolemy and his successors provided a systematic framework to tie together and portray geographical information. This framework was used by academics for centuries to come, the positives being the lead-up to the geographical enlightenment, however, women and indigenous writings were largely excluded from the discourse.
+The European global conquests started in the early 15th century with the first Portuguese expeditions to Africa and India, as well as the conquest of America by Spain in 1492 and continued with a series of European naval expeditions across the Atlantic and later the Pacific and Russian expeditions to Siberia  until the 18th century.
+European overseas expansion led to the rise of colonial empires, with the contact between the "Old" and "New World"s producing the Columbian Exchange: a wide transfer of plants, animals, foods, human populations (including slaves), communicable diseases and culture between the continents.
+These  colonialist endeavours in 16th and 17th centuries revived a desire for both "accurate" geographic detail, and more solid theoretical foundations. The Geographia Generalis by Bernhardus Varenius, which was used in Newton's teaching of geography at Cambridge, and Gerardus Mercator's world map are prime examples of the new breed of scientific geography.
+The Waldseemüller map Universalis Cosmographia, created by German cartographer Martin Waldseemüller in April 1507, is the first map of the Americas in which the name "America" is mentioned.
+The Eurocentric map was patterned after a modification of Ptolemy's second projection but expanded to include the Americas. The Waldseemuller Map has been called "America's birth certificate" Waldseemüller also created printed maps called globe gores, that could be cut out and glued to spheres resulting in a globe.
+This has been debated widely as being dismissive of the extensive Native American history that predated the 16th-century invasion, in the sense that the implication of a "birth certificate" implies a blank history prior.
+
+=== 16th–18th centuries in the West ===
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+title: "History of geography"
+chunk: 8/11
+source: "https://en.wikipedia.org/wiki/History_of_geography"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T03:59:47.409771+00:00"
+instance: "kb-cron"
+---
+
+Geography as a science experiences excitement and exerts influence during the Scientific Revolution and Reformation. In the Victorian period, the oversea exploration gave it institutional identity and geography was "the science of imperialism par excellence."Imperialism is a crucial concept for the Europeans, as the institution become involved in geographical exploration and colonial project. Authority was questioned, and utility gained its importance. In the era of Enlightenment, geography generated knowledge and made it intellectually and practically possible as a university discipline. The natural theology required geography to investigate the world as a grand machine from the Divine. Scientific voyages and travels constructed geopolitical power from geographical knowledge, partly sponsored by Royal Society. The discourse of geographical history gave way to many new thoughts and theories, but the hegemony of the European male academia led to the exclusion of non-western theories, observations and knowledges. One such example is the interaction between humans and nature, with Marxist thought critiquing nature as a commodity within Capitalism, European thought seeing nature as either a romanticised or objective concept differing to human society, and Native American discourse, which saw nature and humans as within one category. The implied hierarchy of knowledge that perpetuated throughout these institutions has only been recently challenged, with the Royal Geographical Society enabling women to join as members in the 20th century. After English Civil War, Samuel Hartlib and his Baconian community promoted scientific application, which showed the popularity of utility. For William Petty, the administrators should be "skilled in the best rules of judicial astrology" to "calculate the events of diseases and prognosticate the weather." Institutionally, Gresham College propagated scientific advancement to a larger audience like tradesmen, and later this institute grew into Royal Society. William Cuningham illustrated the utilitarian function of cosmography by the military implement of maps. John Dee used mathematics to study location—his primary interest in geography and encouraged exploiting resource with findings collected during voyages. Religion Reformation stimulated geographical exploration and investigation. Philipp Melanchthon shifted geographical knowledge production from "pages of scripture" to "experience in the world." Bartholomäus Keckermann separated geography from theology because the "general workings of providence" required empirical investigation; Varenius was among his followers. Science develops along with empiricism. Empiricism gains its central place while reflection on it also grew. Practitioners of magic and astrology first embraced and expanded geographical knowledge. Reformation Theology focused more on the providence than the creation as previously. Realistic experience, instead of translated from scripture, emerged as a scientific procedure. Geographical knowledge and method play roles in economic education and administrative application, as part of the Puritan social program. Foreign travels provided content for geographic research and formed theories, such as environmentalism. Cartography showed its practical, theoretical, and artistic value. The concepts of "Space" and "Place" attract attention in geography. Why things are there and not elsewhere is an important topic in Geography, together with debates on space and place. Such insights could date back in 16th and 17th centuries, identified by M. Curry as "Natural Space", "Absolute Space", "Relational Space" (On Space and Spatial Practice). After Descartes's Principles of Philosophy, Locke and Leibniz considered space as relative, which has long-term influence on the modern view of space. For Descartes, Grassendi and Newton, place is a portion of "absolution space", which are neural and given. However, according to John Locke, "Our Idea of Place is nothing else, but such a relative Position of any thing" (in An Essay Concerning Human Understanding). "Distance" is the pivot modification of space, because "Space considered barely in length between any two Beings, without considering any thing else between them". Also, the place is "made by Men, for their common use, that by it they might be able to design the particular Position of Things". In the Fifth Paper in Reply to Clarke, Leibniz stated: "Men fancy places, traces, and space, though these things consist only in the truth of relations and not at all in any absolute reality". Space, as an "order of coexistence", "can only be an ideal thing, containing a certain order, wherein the mind conceives the application of relation". Leibniz moved further for the term "distance" as he discussed it together with "interval" and "situation", not just a measurable character. Leibniz bridged place and space to quality and quantity, by saying "Quantity or magnitude is that in things which can be known only through their simultaneous compresence—or by their simultaneous perception... Quality, on the other hand, is what can be known in things when they are observed singly, without requiring any compresence." In Modern Space as Relative, place and what is in place are integrated. "The Supremacy of Space" is observed by E. Casey when the place is resolved as "position and even point" by Leibniz's rationalism and Locke's empiricism. During the Age of Enlightenment, advancements in science mean widening human knowledge and enable further exploiting nature, along with industrialization and empire expansion in Europe. David Hume, "the real father of positivist philosophy" according to Leszek Kolakowski, implied the "doctrine of facts", emphasizing the importance of scientific observations. The "fact" is related with sensationalism that object cannot be isolated from its "sense-perceptions", an opinion of Berkeley. Galileo, Descartes, later Hobbes and Newton advocated scientific materialism, viewing the universe—the entire world and even human mind—as a machine. The mechanist world view is also found in the work of Adam Smith based on historical and statistics methods. In chemistry, Antoine Lavoisier proposed the "exact science model" and stressed quantitative methods from experiment and mathematics. Carl Linnaeus classified plants and organisms based on an assumption of fixed species. Later, the idea of evolution emerged not only for species but also for society and human intellect. In General Natural History and Theory of the Heavens, Kant laid out his hypothesis of cosmic evolution, and made him "the great founder of the modern scientific conception of Evolution" according to Hastie. Francis Bacon and his followers believed progress of science and technology drive betterment of man. This belief was attached by Jean-Jacques Rousseau who defended human emotions and morals. His discussion on geography education piloted local regional studies. Leibniz and Kant formed the major challenge to the mechanical materialism. Leibniz conceptualized the world as a changing whole, rather than "sum of its parts" as a machine. Nevertheless, he acknowledged experience requires rational interpretation—the power of human reason. Kant tried to reconcile the division of sense and reason by stressing moral rationalism grounded on aesthetic experience of nature as "order, harmony, and unity". For knowledge, Kant distinguished phenomena (sensible world) and noumena (intelligible world), and he asserted "all phenomena are perceived in the relations of space and time." Drawing a line between "rational science" and "empirical science", Kant regarded Physical geography—associating with space—as natural science. During his tenure in Königsberg, Kant offered lectures on physical geography since 1756 and published the lecture notes Physische Geographie in 1801. Kant's involvement in travel and geographical research is fairly limited, although Manfred Büttner asserted that is "Kantian emancipation of geography from theology." Kant's work on empirical and rational science influence Alexander von Humboldt and at smaller extent Carl Ritter.
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+title: "History of geography"
+chunk: 9/11
+source: "https://en.wikipedia.org/wiki/History_of_geography"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T03:59:47.409771+00:00"
+instance: "kb-cron"
+---
+
+Humboldt and Ritter are both regarded as the founders of modern geography as they later established it as an independent scientific discipline. Humboldt is admired as a great geographer, according to D. Livingstone that "modern geography was first and last a synthesizing science and as such, if Goetzmann is to be believed, 'it became the key scientific activity of the age'." In 1789, Humboldt met the geographer George Forster in Mainz, before travelling with him through parts of Western Europe the following year. Forster's travel accounts and writings influenced Humboldt. His Geognosia including the geography of rocks, animals, and plants is "an important model for modern geography". As a Prussian mining officer, Humboldt founded the Free Royal Mining School at Steben for miners, later regarded the prototype of such institutes. German Naturphilosophie, especially the work of Goethe and Herder, stimulated Humboldt's idea and research of a universal science. In his letter, he made observations while his "attention will never lose sight of the harmony of concurrent forces, the influence of the inanimate world on the animal and vegetable kingdom." His American travel stressed the geography of plants as his focus of science. Meanwhile, Humboldt used empirical method to study the indigenous people in the New World, regarded as a most important work in human geography. In Relation historique du Voyage, Humboldt called these research a new science Physique du monde, Theorie de la Terre, or Geographie physique. During 1825 to 1859, Humboldt devoted in Kosmos, which is about the knowledge of nature. There are growing works about the New World since then. In the Jeffersonian era, "American geography was born of the geography of America", meaning the knowledge discovery helped form the discipline. Practical knowledge and national pride are main components of the Teleological tradition. Institutions such as the Royal Geographical Society indicate geography as an independent discipline. Mary Somerville's Physical Geography was the "conceptual culmination of ... Baconian ideal of universal integration". According to Francis Bacon, "No natural phenomenon can be adequately studied by itself alone – but, to be understood, it must be considered as it stands connected with all nature."
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+---
+title: "History of geography"
+chunk: 10/11
+source: "https://en.wikipedia.org/wiki/History_of_geography"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T03:59:47.409771+00:00"
+instance: "kb-cron"
+---
+
+== 19th century ==
+
+By the 18th century, geography had become recognized as a discrete discipline and became part of a typical university curriculum in Europe (especially Paris and Berlin), although not in the United Kingdom where geography was generally taught as a sub-discipline of other subjects.
+A holistic view of geography and nature can be seen in the work by the 19th-century polymath Alexander von Humboldt. One of the great works of this time was Humboldt's Kosmos: a sketch of a physical description of the Universe, the first volume of which was published in German in 1845. Such was the power of this work that Dr Mary Somerville, of Cambridge University intended to scrap publication of her own Physical Geography on reading Kosmos. Von Humboldt himself persuaded her to publish (after the publisher sent him a copy).
+In 1877, Thomas Henry Huxley published his Physiography with the philosophy of universality presented as an integrated approach in the study of the natural environment. The philosophy of universality in geography was not a new one but can be seen as evolving from the works of Alexander von Humboldt and Immanuel Kant. The publication of Huxley physiography presented a new form of geography that analysed and classified cause and effect at the micro-level and then applied these to the macro-scale (due to the view that the micro was part of the macro and thus an understanding of all the micro-scales was need to understand the macro level). This approach emphasized the empirical collection of data over the theoretical. The same approach was also used by Halford John Mackinder in 1887. However, the integration of the Geosphere, Atmosphere and Biosphere under physiography was soon over taken by Davisian geomorphology.
+Over the past two centuries the quantity of knowledge and the number of tools has exploded. There are strong links between geography and the sciences of geology and botany, as well as economics, sociology and demographics.
+The Royal Geographical Society was founded in England in 1830, although the United Kingdom did not get its first full chair of geography until 1917. The first real geographical intellect to emerge in United Kingdom geography was Halford John Mackinder, appointed reader at Oxford University in 1887.
+The National Geographic Society was founded in the United States in 1888 and began publication of the National Geographic magazine which became and continues to be a great popularizer of geographic information. The society has long supported geographic research and education.
+
+== 20th century ==
+
+In the West during the second half of the 19th and the 20th century, the discipline of geography at various time engaged with four broad themes: environmental determinism, regional geography, the quantitative revolution, and critical geography.
+
+=== Environmental determinism ===
+
+Environmental determinism is the theory that a people's physical, mental and moral habits are directly due to the influence of their natural environment. Prominent environmental determinists included Carl Ritter, Ellen Churchill Semple, and Ellsworth Huntington. Environmentally deterministic hypotheses included stereotypes such as "heat makes inhabitants of the tropics lazy" and "frequent changes in barometric pressure make inhabitants of temperate latitudes more intellectually agile." Environmental determinist geographers attempted to make the study of such influences scientific. Around the 1930s, this school of thought was widely repudiated as lacking any basis and being prone to (often bigoted) generalizations. Environmental determinism remains an embarrassment to many contemporary geographers, and leads to skepticism among many of them of claims of environmental influence on culture (such as the theories of Jared Diamond). 
+
+=== Regional geography ===
+
+Regional geography was coined by a group of geographers known as possibilists and represented a reaffirmation that the proper topic of geography was study of places (regions). Regional geographers focused on the collection of descriptive information about places, as well as the proper methods for dividing the Earth up into regions. Well-known names from these period are Alfred Hettner in Germany and Paul Vidal de la Blache in France. The philosophical basis of this field in United States was laid out by Richard Hartshorne, who defined geography as a study of areal differentiation, which later led to criticism of this approach as overly descriptive and unscientific.
+However, the concept of a Regional geography model focused on Area Studies has remained incredibly popular amongst students of geography, while less so amongst scholars who are proponents of Critical Geography and reject a Regional geography paradigm. During its heyday in the 1970s through the early 1990s, regional geography made substantive contributions to students' and readers' understanding of foreign cultures and the real world effects of the delineation of borders.
+
+=== The quantitative revolution ===
+
+The quantitative revolution in geography began in the 1950s. Geographers formulated geographical theories and subjected the theories to empirical tests, usually using statistical methods (especially hypothesis testing). This quantitative revolution laid the groundwork for the development of geographic information systems. Well-known geographers from this period are Fred K. Schaefer, Waldo Tobler, William Garrison, Peter Haggett, Richard J. Chorley, William Bunge, Edward Augustus Ackerman and Torsten Hägerstrand. An important concept that emerged from this is the first law of geography, proposed by Waldo Tobler, which states that "everything is related to everything else, but near things are more related than distant things."
+
+=== Critical geography ===
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+---
+title: "History of glass"
+chunk: 1/5
+source: "https://en.wikipedia.org/wiki/History_of_glass"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T03:59:48.666461+00:00"
+instance: "kb-cron"
+---
+
+The history of glass-making dates back to at least 3,600 years ago in Mesopotamia. However, most writers claim that they may have been producing copies of glass objects from Egypt. Other archaeological evidence suggests that the first true glass was made in coastal east Syria, Mesopotamia or Egypt. The earliest known glass objects, of the mid 2,000 BCE, were beads, perhaps initially created as the accidental by-products of metal-working (slags) or during the production of faience, a pre-glass vitreous material made by a process similar to glazing. Glass products remained a luxury until the disasters that overtook the late Bronze Age civilizations seemingly brought glass-making to a halt.
+Development of glass technology in India may have begun in 1,730 BCE.
+From across the former Roman Empire, archaeologists have recovered glass objects that were used in domestic, industrial and funerary contexts. Anglo-Saxon glass has been found across England during archaeological excavations of both settlement and cemetery sites. Glass in the Anglo-Saxon period was used in the manufacture of a range of objects, including vessels, beads, windows, and was even used in jewellery.
+
+== Origins ==
+
+Naturally occurring glass, especially the volcanic glass obsidian, has been used by many Stone Age societies across the globe for the production of sharp cutting tools and, due to its limited source areas, was extensively traded. But in general, archaeological evidence suggests that the first true glass was made in coastal north Syria, Mesopotamia or ancient Egypt.
+A lump of glass was found at Eridu in Iraq that can be dated to the twenty-first century BCE or even earlier; it was produced during the Akkadian Empire or the early Ur III period. The glass is of blue colour, which was achieved with cobalt. Such glass is generally known as Egyptian blue, but the technique was attested in Eridu long before it emerged in Egypt.
+Because of Egypt's favorable environment for preservation, the majority of well-studied early glass is found there, although some of this is likely to have been imported. The earliest known glass objects, of the mid-third millennium BCE, were beads, perhaps initially created as accidental by-products of metal-working (slags) or during the production of faience, a pre-glass vitreous material made by a process similar to glazing.
+During the Late Bronze Age in Egypt (e.g., the Ahhotep "Treasure") and Western Asia (e.g., Megiddo), there was a rapid growth in glassmaking technology. Archaeological finds from this period include colored glass ingots, vessels (often colored and shaped in imitation of highly prized hardstone carvings in semi-precious stones) and the ubiquitous beads. The alkali of Syrian and Egyptian glass was soda ash (sodium carbonate), which can be extracted from the ashes of many plants, notably halophile seashore plants like saltwort. The latest vessels were 'core-formed', produced by winding a ductile rope of glass around a shaped core of sand and clay over a metal rod, then fusing it by reheating it several times.
+Threads of thin glass of different colors made with admixtures of oxides were subsequently wound around these to create patterns, which could be drawn into festoons by using metal raking tools. The vessel would then be rolled smooth (marvered) on a slab in order to press the decorative threads into its body. Handles and feet were applied separately. The rod was subsequently allowed to cool as the glass slowly annealed and was eventually removed from the center of the vessel, after which the core material was scraped out. Glass shapes for inlays were also often created in moulds. Much of early glass production, however, relied on grinding techniques borrowed from stone working. This meant that the glass was ground and carved in a cold state.
+By the 15th century BCE, extensive glass production was occurring in Western Asia, Crete, and Egypt; and the Mycenaean Greek term 𐀓𐀷𐀜𐀺𐀒𐀂, ku-wa-no-wo-ko-i, meaning "workers of lapis lazuli and glass" (written in Linear b syllabic script) is attested. 
+It is thought that the techniques and recipes required for the initial fusing of glass from raw materials were a closely guarded technological secret reserved for the large palace industries of powerful states. Glass workers in other areas therefore relied on imports of preformed glass, often in the form of cast ingots such as those found on the Ulu Burun shipwreck off the coast of modern Turkey.
+
+Glass remained a luxury material, and the disasters that overtook Late Bronze Age civilizations seemed to have brought glass-making to a halt. It picked up again in its former sites, Syria and Cyprus, in the 9th century BCE, when the techniques for making colorless glass were discovered.
+The first glassmaking "manual" dates back to ca. 650 BCE. Instructions on how to make glass are contained in cuneiform tablets discovered in the library of the Assyrian king Ashurbanipal.
+In Egypt, glass-making did not revive until it was reintroduced in Ptolemaic Alexandria. Core-formed vessels and beads were still widely produced, but other techniques came to the fore with experimentation and technological advancements.
+During the Hellenistic period many new techniques of glass production were introduced and glass began to be used to make larger pieces, notably table wares. Techniques developed during this period include 'slumping' viscous (but not fully molten) glass over a mould in order to form a dish and 'millefiori' (meaning 'thousand flowers') technique, where canes of multicolored glass were sliced and the slices arranged together and fused in a mould to create a mosaic-like effect. It was also during this period that colorless or decolored glass began to be prized and methods for achieving this effect were investigated more fully.
+According to Pliny the Elder, Phoenician traders were the first to stumble upon glass manufacturing techniques at the site of the Belus River. Georgius Agricola, in De re metallica, reported a traditional serendipitous "discovery" tale of familiar type:
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+---
+title: "History of glass"
+chunk: 2/5
+source: "https://en.wikipedia.org/wiki/History_of_glass"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T03:59:48.666461+00:00"
+instance: "kb-cron"
+---
+
+The tradition is that a merchant ship laden with nitrum being moored at this place, the merchants were preparing their meal on the beach, and not having stones to prop up their pots, they used lumps of nitrum from the ship, which fused and mixed with the sands of the shore, and there flowed streams of a new translucent liquid, and thus was the origin of glass.
+This account is more a reflection of Roman experience of glass production, however, as white silica sand from this area was used in the production of glass within the Roman Empire due to its high purity levels. During the 1st century BCE, glass blowing was discovered on the Syro-Judean coast, revolutionizing the industry.  The first evidence of the invention of glassblowing was found in the Jewish Quarter of Jerusalem, in a layer of fill inside a ritual bath that was overlain with the paving stones of the Herodian street. Several other site of producing "Judean Glass" were found in Galilee. Glass vessels were now inexpensive compared to pottery vessels. Growth of the use of glass products occurred throughout the Roman world. Glass became the Roman plastic, and glass containers produced in Alexandria spread throughout the Roman Empire. With the discovery of clear glass (through the introduction of manganese dioxide), by glass blowers in Alexandria circa 100 CE, the Romans began to use glass for architectural purposes. Cast glass windows, albeit with poor optical qualities, began to appear in the most important buildings in Rome and the most luxurious villas of Herculaneum and Pompeii. Over the next 1,000 years, glass making and working continued and spread through southern Europe and beyond.
+
+== History by culture ==
+
+=== Iran ===
+The first Persian glass comes in the form of beads dating to the late Bronze Age (1600 BCE), and was discovered during the explorations of Dinkhah Tepe in Iranian  by Charles Burney. Glass tubes were discovered by French archaeologists at Chogha Zanbil, belonging to the middle Elamite period. Mosaic glass cups have also been found at Teppe Hasanlu and Marlik Tepe in northern Iran, dating to the Iron Age. These cups resemble ones from Mesopotamia, as do cups found in Susa during the late Elamite period.
+Glass tubes containing kohl have also been found in Iranian, belonging to the Achaemenid period. During this time, glass vessels were usually plain and colorless. By the Seleucid and late Parthian era, Greek and Roman techniques were prevalent. During the Sasanian period, glass vessels were decorated with local motifs.
+
+=== Levant and Anatolia ===
+A glassmaking crucible was discovered at Alalakh in the Amuq Valley of Turkey during the excavation seasons 2011–2014. This is the earliest evidence for glassmaking in the Syro-Levantine zone – the area which became famous for glassmaking later on. This material is "contemporary with, or even slightly earlier" than the fourteenth-century BC dates from Egypt.
+The discovery provides the earliest evidence for Late Bronze Age glassmaking outside of Egypt and the central Mesopotamia.
+This production area may be associated with the Kingdom of Mitanni. According to the authors, this geographical area can be linked to the descriptions of glassmaking in cuneiform tablets, which provides some additional historical context.
+A glass bottle fragment from Büklükale, in central Turkey, is estimated to be around 1600 BC old. This may represent the oldest glass work in Anatolia. The fragment is from the Hittite Empire period. It is unusually large compared to other glass bottles from Mesopotamia at the time. A production centre of glass may have existed in this area of Anatolia.
+
+=== India ===
+Evidence of glass during the Chalcolithic has been found in Hastinapur, India. The earliest glass item from the Indus Valley civilization is a brown glass bead found at Harappa, dating to 1700 BCE. This makes it the earliest evidence of glass in South Asia. Glass discovered from later sites dating from 600 to 300 BCE displays common colors.
+Texts such as the Shatapatha Brahmana and Vinaya Pitaka mention glass, implying they could have been known in India during the early first millennium BCE. Glass objects have also been found at Beed, Sirkap and Sirsukh, all dating to around the 5th century BCE. However, the first unmistakable evidence for widespread glass usage comes from the ruins of Taxila (3rd century BCE), where bangles, beads, small vessels, and tiles were discovered in large quantities. These glassmaking techniques may have been transmitted from cultures in Western Asia.
+The site of Kopia, in Uttar Pradesh, is the first site in India to locally manufacture glass, with items dating between the 7th century BCE to the 2nd century CE. Early Indian glass of this period was likely made locally, as they differ significantly in chemical composition when compared to Babylonian, Roman and Chinese glass.
+By the 1st century AD, glass was being used for ornaments and casing in South Asia. Contact with the Greco-Roman world added newer techniques, and Indians artisans mastered several techniques of glass molding, decorating and coloring by the succeeding centuries. The Satavahana period of India also produced short cylinders of composite glass, including those displaying a lemon yellow matrix covered with green glass.
+
+=== China ===
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+---
+title: "History of glass"
+chunk: 3/5
+source: "https://en.wikipedia.org/wiki/History_of_glass"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T03:59:48.666461+00:00"
+instance: "kb-cron"
+---
+
+In China, glass played a peripheral role in arts and crafts when compared to ceramics and metal work. The earliest glass items in China come from the Warring States period (475–221 BCE), although they are rare in number and limited in archaeological distribution.
+Glassmaking developed later in China compared to cultures in Mesopotamia, Egypt and India. Imported glass objects first reached China during the late Spring and Autumn period (early 5th century BCE), in the form of polychrome eye beads. These imports created the impetus for the production of indigenous glass beads.
+During the Han Dynasty (206 BCE–220 CE), the use of glass diversified. The introduction of glass casting in this period encouraged the production of moulded objects, such as bi disks and other ritual objects. Chinese glass objects from the Warring States and Han period vary greatly in chemical composition from the imported glass objects. The glasses from this period contain high levels of barium oxide and lead, distinguishing them from the soda–lime–silica glasses of Western Asia and Mesopotamia. At the end of the Han Dynasty (AD 220), the lead-barium glass tradition declined, with glass production only resuming during the 4th and 5th centuries AD. Literary sources also mention the manufacture of glass during the 5th century AD.
+
+=== Roman World ===
+
+Roman glass production developed from Hellenistic technical traditions, initially concentrating on the production of intensely colored, cast glass vessels. Glass objects have been recovered across the Roman Empire in domestic, funerary and industrial contexts. Glass was used primarily for the production of vessels, although mosaic tiles and window glass were also produced.
+However, during the 1st century CE, the industry underwent rapid technical growth that saw the introduction of glass-blowing and the dominance of colorless or ‘aqua’ glasses. Raw glass was produced in geographically separate locations to the working of glass into finished vessels, and, by the end of the 1st century CE, large scale manufacturing, primarily in  Alexandria, resulted in the establishment of glass as a commonly available material in the Roman world.
+
+=== Islamic world ===
+
+Islamic glass continued the achievements of pre-Islamic cultures, especially the Sasanian glass of Persia. The Arab poet al-Buhturi (820–897) described the clarity of such glass: "Its color hides the glass as if it is standing in it without a container." In the 8th century, the Persian-Arab chemist Jābir ibn Hayyān (Geber) described 46 recipes for producing colored glass in Kitab al-Durra al-Maknuna (The Book of the Hidden Pearl), in addition to 12 recipes inserted by al-Marrakishi in a later edition of the book. By the 11th century, clear glass mirrors were being produced in Islamic Spain.
+
+=== Africa ===
+
+Evidence suggests that indigenous glass production existed in West Africa well before extensive contact with other glassmaking regions. The most significant and well-documented example is the Ife Empire of Southwestern Nigeria. Archaeological excavations at Igbo Olokun, a site in northern Ife, have yielded a substantial quantity of glass beads, crucibles, and production debris dating from the 11th to 15th centuries CE. Chemical analysis revealed a unique chemical signature significantly different from known imported glass types. 
+The Igbo Olokun glass is characterized by a high-lime, high-alumina (HLHA) composition, reflecting the use of locally sourced raw materials, likely including granitic sands and possibly calcium carbonate from sources such as snail shells. At least two distinct glass types, HLHA and low-lime, high-alumina (LLHA), were produced at Igbo Olokun. Colorants including manganese, iron, cobalt, and copper were intentionally added to produce a range of colors, most notably various shades of dichroic blue and green. Analysis also revealed the presence of glass production waste, including fragments of crucibles bearing vitrified glass residues, confirming the onsite nature of the manufacturing.
+
+=== Medieval Europe ===
+
+After the collapse of the Western Roman Empire, independent glass making technologies emerged in Northern Europe, with artisan forest glass produced by several cultures. Byzantine Glass evolved the Roman tradition, in the Eastern Empire. The claw beaker was popular as a relatively easy to make but an impressive vessel that exploited the unique potential of glass.
+Glass objects from the 7th and 8th centuries have been found on the island of Torcello near Venice. These form an important link between Roman times and the later importance of that city in the production of the material. Around 1000 AD, an important technical breakthrough was made in Northern Europe when soda glass, produced from white pebbles and burnt vegetation was replaced by glass made from a much more readily available material: potash obtained from wood ashes. From this point on, northern glass differed significantly from that made in the Mediterranean area, where soda remained in common use.
+Until the 12th century, stained glass – glass to which metallic or other impurities had been added for coloring – was not widely used, but it rapidly became an important medium for Romanesque art and especially Gothic art.  Almost all survivals are in church buildings, but it was also used in grand secular buildings.  The 11th century saw the emergence in Germany of new ways of making sheet glass by blowing spheres. The spheres were swung out to form cylinders and then cut while still hot, after which the sheets were flattened. This technique was perfected in 13th century Venice. The crown glass process was used up to the mid-19th century. In this process, the glassblower would spin approximately 9 pounds (4 kg) of molten glass at the end of a rod until it flattened into a disk approximately 5 feet (1.5 m) in diameter. The disk would then be cut into panes. Domestic glass vessels in late medieval Northern Europe are known as forest glass.
+
+==== Anglo-Saxon world ====
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+---
+title: "History of glass"
+chunk: 4/5
+source: "https://en.wikipedia.org/wiki/History_of_glass"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T03:59:48.666461+00:00"
+instance: "kb-cron"
+---
+
+Anglo-Saxon glass has been found across England during archaeological excavations of both settlement and cemetery sites. Glass in the Anglo-Saxon period was used in the manufacture of a range of objects including vessels, beads, windows and was even used in jewelry. In the 5th century AD with the Roman departure from Britain, there were also considerable changes in the usage of glass. Excavation of Romano-British sites has revealed plentiful amounts of glass but, in contrast, the amount recovered from the 5th century and later Anglo-Saxon sites is minuscule.
+The majority of complete vessels and assemblages of beads come from the excavations of early Anglo-Saxon cemeteries, but a change in burial rites in the late 7th century affected the recovery of glass, as Christian Anglo-Saxons were buried with fewer grave goods, and glass is rarely found. From the late 7th century onwards, window glass is found more frequently. This is directly related to the introduction of Christianity and the construction of churches and monasteries. There are a few Anglo-Saxon ecclesiastical literary sources that mention the production and use of glass, although these relate to window glass used in ecclesiastical buildings. Glass was also used by the Anglo-Saxons in their jewelry, both as enamel or as cut glass insets.
+
+==== Murano ====
+
+The center for luxury Italian glassmaking from the 14th century was the island of Murano, which developed many new techniques and became the center of a lucrative export trade in dinnerware, mirrors, and other items. What made Venetian Murano glass significantly different was that the local quartz pebbles were almost pure silica, and were ground into a fine clear sand that was combined with soda ash obtained from the Levant, for which the Venetians held the sole monopoly. The clearest and finest glass is tinted in two ways: firstly, a natural coloring agent is ground and melted with the glass. Many of these coloring agents still exist today; for a list of coloring agents, see below. Black glass was called obsidianus after obsidian stone. A second method is apparently to produce a black glass which, when held to the light, will show the true color that this glass will give to another glass when used as a dye.
+The Venetian ability to produce this superior form of glass resulted in a trade advantage over other glass producing lands. Murano’s reputation as a center for glassmaking was born when the Venetian Republic, fearing fire might burn down the city’s mostly wood buildings, ordered glassmakers to move their foundries to Murano in 1291. Murano's glassmakers were soon the island’s most prominent citizens. Glassmakers were not allowed to leave the Republic. Many took a risk and set up glass furnaces in surrounding cities and as far afield as England and the Netherlands.
+
+==== Bohemia ====
+
+Bohemian glass, or Bohemia crystal, is a decorative glass produced in regions of Bohemia and Silesia, now in the current state of the Czech Republic, since the 13th century. Oldest archaeology excavations of glass-making sites date to around 1250 and are located in the Lusatian Mountains of Northern Bohemia. Most notable sites of glass-making throughout the ages are Skalice (German: Langenau), Kamenický Šenov (German: Steinschönau) and Nový Bor (German: Haida). Both Nový Bor and Kamenický Šenov have their own Glass Museums with many items dating since around 1600. It was especially outstanding in its manufacture of glass in high Baroque style from 1685 to 1750. In the 17th century, Caspar Lehmann, gem cutter to Emperor Rudolf II in Prague, adapted to glass the technique of gem engraving with copper and bronze wheels.
+
+== Modern glass production ==
+
+=== New processes ===
+
+A very important advance in glass manufacture was the technique of adding lead oxide to the molten glass; this improved the appearance of the glass and made it easier to melt using sea-coal as a furnace fuel. This technique also increased the "working period" of the glass, making it easier to manipulate. The process was first discovered by George Ravenscroft in 1674, who was the first to produce clear lead crystal glassware on an industrial scale. Ravenscroft had the cultural and financial resources necessary to revolutionise the glass trade, allowing England to overtake Venice as the centre of the glass industry in the eighteenth and nineteenth centuries. Seeking to find an alternative to Venetian cristallo, he used flint as a silica source, but his glasses tended to crizzle, developing a network of small cracks destroying its transparency. This was eventually overcome by replacing some of the potash flux with lead oxide to the melt.
+He was granted a protective patent in where production and refinement moved from his glasshouse on the Savoy to the seclusion of Henley-on-Thames.
+By 1696, after the patent expired, twenty-seven glasshouses in England were producing flint glass and were exporting all over Europe with such success that, in 1746, the British Government imposed a lucrative tax on it. Rather than drastically reduce the lead content of their glass, manufacturers responded by creating highly decorated, smaller, more delicate forms, often with hollow stems, known to collectors today as Excise glasses. The British glass making industry was able to take off with the repeal of the tax in 1845.
+Evidence of the use of the blown plate glass method dates back to 1620 in London and was used for mirrors and coach plates. Louis Lucas de Nehou and A. Thevart perfected the process of casting polished plate glass in 1688 in France. Prior to this invention, mirror plates, made from blown "sheet" glass, had been limited in size. De Nehou's process of rolling molten glass poured on an iron table rendered the manufacture of very large plates possible. This method of production was adopted by the English in 1773 at Ravenhead. The polishing process was industrialized around 1800 with the adoption of a steam engine to carry out the grinding and polishing of the cast glass.
+
+=== Industrial production ===
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+---
+title: "History of glass"
+chunk: 5/5
+source: "https://en.wikipedia.org/wiki/History_of_glass"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T03:59:48.666461+00:00"
+instance: "kb-cron"
+---
+
+The use of glass as a building material was heralded by The Crystal Palace of 1851, built by Joseph Paxton to house the Great Exhibition. Paxton's revolutionary new building inspired the public use of glass as a material for domestic and horticultural architecture. In 1832, the British Crown Glass Company (later Chance Brothers) became the first company to adopt the cylinder method to produce sheet glass with the expertise of Georges Bontemps, a famous French glassmaker. This glass was produced by blowing long cylinders of glass, which were then cut along the length and then flattened onto a cast-iron table, before being annealed. Plate glass involves the glass being ladled onto a cast-iron bed, where it is rolled into a sheet with an iron roller. The sheet, still soft, is pushed into the open mouth of an annealing tunnel or temperature-controlled oven called a lehr, down which it was carried by a system of rollers. James Hartley introduced the Rolled Plate method in 1847. This allowed a ribbed finish and was often used for extensive glass roofs such as within railway stations.
+An early advance in automating glass manufacturing was patented in 1821 by Henry Ricketts and in 1848 by the engineer Henry Bessemer, both of Britain. Ricketts patented a glass moulding machine while Bessemer's system produced a continuous ribbon of flat glass by forming the ribbon between rollers. This was an expensive process, as the surfaces of the glass needed polishing and was later abandoned by its sponsor, Robert Lucas Chance of Chance Brothers, as unviable. Bessemer also introduced an early form of "Float Glass" in 1843, which involved pouring glass onto liquid tin.
+In 1887, the mass production of glass was developed by the firm Ashley in Castleford, Yorkshire. This semi-automatic process used machines that were capable of producing 200 standardized bottles per hour, many times quicker than the traditional methods of manufacture. Chance Brothers also introduced the machine rolled patterned glass method in 1888.
+In 1898, Pilkington invented Wired Cast glass, where the glass incorporates a strong steel-wire mesh for safety and security. This was commonly given the misnomer "Georgian Wired Glass" but it greatly post-dates the Georgian era. The machine drawn cylinder technique was invented in the US and was the first mechanical method for the drawing of window glass. It was manufactured under licence in the UK by Pilkington from 1910 onwards.
+In 1938, the polished plate process was improved by Pilkington which incorporated a double grinding process to give an improved quality to the finish. Between 1953 and 1957, Sir Alastair Pilkington and Kenneth Bickerstaff of the UK's Pilkington Brothers developed the revolutionary float glass process, the first successful commercial application for forming a continuous ribbon of glass using a molten tin bath on which the molten glass flows unhindered under the influence of gravity. This method gave the sheet uniform thickness and very flat surfaces. Modern windows are made from float glass. Most float glass is soda–lime glass, but relatively minor quantities of specialty borosilicate and flat panel display glass are also produced using the float glass process. The success of this process lay in the careful balance of the volume of glass fed onto the bath, where it was flattened by its own weight. Full scale profitable sales of float glass were first achieved in 1960.
+
+== Gallery ==
+
+== See also ==
+Early glassmaking in the United States
+18th century glassmaking in the United States
+
+== Notes ==
+
+== References ==
+
+== Further reading ==
+Carboni, Stefano; Whitehouse, David (2001). Glass of the sultans. New York: The Metropolitan Museum of Art. ISBN 0870999869.
+
+== External links ==
+ Media related to History of Glassmaking at Wikimedia Commons
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+---
+title: "History of information theory"
+chunk: 1/2
+source: "https://en.wikipedia.org/wiki/History_of_information_theory"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T03:59:49.990118+00:00"
+instance: "kb-cron"
+---
+
+The study of information theory began with the publication of Claude E. Shannon's classic paper "A Mathematical Theory of Communication" in the Bell System Technical Journal in July and October 1948, although Shannon had substantially completed the paper at Bell Labs by the end of 1944, 
+Shannon introduced the qualitative and quantitative model of communication as a statistical process, opening with the assertion that 
+
+"The fundamental problem of communication is that of reproducing at one point, either exactly or approximately, a message selected at another point."
+With it came the ideas of 
+
+the information entropy and redundancy of a source, and its relevance through the source coding theorem;
+the mutual information, and the channel capacity of a noisy channel, including the promise of perfect loss-free communication given by the noisy-channel coding theorem;
+the practical result of the Shannon–Hartley law for the channel capacity of a Gaussian channel; and of course
+the bit - a new way of seeing the most fundamental unit of information.
+
+== Before 1948 ==
+
+=== Early telecommunications ===
+Some of the oldest methods of telecommunications implicitly used some of the ideas that were later formalized by Shannon in the development of information theory. In telegraphy, starting in the 1830s, Morse code considered the frequency of more common letters. Thus the letter "E", which is expressed as one "dot", is transmitted more quickly than less common letters like "J", which is expressed by one "dot" followed by three "dashes". The idea of encoding information in this manner is the cornerstone of lossless data compression. A hundred years later, frequency modulation illustrated that bandwidth can be considered merely another degree of freedom. The vocoder, now largely looked at as an audio engineering curiosity, was originally designed in 1939 to use less bandwidth than that of an original message, in much the same way that mobile phones now trade off voice quality with bandwidth.
+
+=== Quantitative ideas of information ===
+The most direct antecedents of Shannon's work were two papers published in the 1920s by Harry Nyquist and Ralph Hartley, who were both still research leaders at Bell Labs when Shannon arrived in the early 1940s.
+Nyquist's 1924 paper, "Certain Factors Affecting Telegraph Speed", is mostly concerned with some detailed engineering aspects of telegraph signals. But a more theoretical section discusses quantifying "intelligence" and the "line speed" at which it can be transmitted by a communication system, giving the relation
+
+  
+    
+      
+        W
+        =
+        K
+        log
+        ⁡
+        m
+        
+      
+    
+    {\displaystyle W=K\log m\,}
+  
+
+where W is the speed of transmission of intelligence, m is the number of different voltage levels to choose from at each time step, and K is a constant.
+Hartley's 1928 paper, called simply "Transmission of Information", went further by using the word information (in a technical sense), and making explicitly clear that information in this context was a measurable quantity, reflecting only the receiver's ability to distinguish that one sequence of symbols had been intended by the sender rather than any other—quite regardless of any associated meaning or other psychological or semantic aspect the symbols might represent. This amount of information he quantified as
+
+  
+    
+      
+        H
+        =
+        log
+        ⁡
+        
+          S
+          
+            n
+          
+        
+        
+      
+    
+    {\displaystyle H=\log S^{n}\,}
+  
+
+where S was the number of possible symbols, and n the number of symbols in a transmission. The natural unit of information was therefore the decimal digit, much later renamed the hartley in his honour as a unit or scale or measure of information. The Hartley information, H0, is still used as a quantity for the logarithm of the total number of possibilities.
+A similar unit of log10 probability, the ban, and its derived unit the deciban (one tenth of a ban), were introduced by Alan Turing in 1940 as part of the statistical analysis of the breaking of the German second world war Enigma cyphers. The decibannage represented the reduction in (the logarithm of) the total number of possibilities (similar to the change in the Hartley information); and also the log-likelihood ratio (or change in the weight of evidence) that could be inferred for one hypothesis over another from a set of observations. The expected change in the weight of evidence is equivalent to what was later called the Kullback discrimination information.
+But underlying this notion was still the idea of equal a-priori probabilities, rather than the information content of events of unequal probability; nor yet any underlying picture of questions regarding the communication of such varied outcomes.
+In a 1939 letter to Vannevar Bush, Shannon had already outlined some of his initial ideas of information theory.
+
+=== Entropy in statistical mechanics ===
+One area where unequal probabilities were indeed well known was statistical mechanics, where Ludwig Boltzmann had, in the context of his H-theorem of 1872, first introduced the quantity
+
+  
+    
+      
+        H
+        =
+        −
+        ∑
+        
+          f
+          
+            i
+          
+        
+        log
+        ⁡
+        
+          f
+          
+            i
+          
+        
+      
+    
+    {\displaystyle H=-\sum f_{i}\log f_{i}}
+  
+
+as a measure of the breadth of the spread of states available to a single particle in a gas of like particles, where f represented the relative frequency distribution of each possible state. Boltzmann argued mathematically that the effect of collisions between the particles would cause the H-function to inevitably increase from any initial configuration until equilibrium was reached; and further identified it as an underlying microscopic rationale for the macroscopic thermodynamic entropy of Clausius.
+Boltzmann's definition was soon reworked by the American mathematical physicist J. Willard Gibbs into a general formula for statistical-mechanical entropy, no longer requiring identical and non-interacting particles, but instead based on the probability distribution pi for the complete microstate i of the total system:
+
+  
+    
+      
+        S
+        =
+        −
+        
+          k
+          
+            B
+          
+        
+        ∑
+        
+          p
+          
+            i
+          
+        
+        ln
+        ⁡
+        
+          p
+          
+            i
+          
+        
+        
+      
+    
+    {\displaystyle S=-k_{\text{B}}\sum p_{i}\ln p_{i}\,}
+  
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+---
+title: "History of information theory"
+chunk: 2/2
+source: "https://en.wikipedia.org/wiki/History_of_information_theory"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T03:59:49.990118+00:00"
+instance: "kb-cron"
+---
+
+This (Gibbs) entropy, from statistical mechanics, can be found to directly correspond to the Clausius's classical thermodynamic definition.
+Shannon himself was apparently not particularly aware of the close similarity between his new measure and earlier work in thermodynamics, but John von Neumann was. It is said that, when Shannon was deciding what to call his new measure and fearing the term 'information' was already over-used, von Neumann told him firmly: "You should call it entropy, for two reasons. In the first place your uncertainty function has been used in statistical mechanics under that name, so it already has a name. In the second place, and more important, no one really knows what entropy really is, so in a debate you will always have the advantage."
+(Connections between information-theoretic entropy and thermodynamic entropy, including the important contributions by Rolf Landauer in the 1960s, are explored further in the article Entropy in thermodynamics and information theory).
+
+== Development since 1948 ==
+The publication of Shannon's 1948 paper, "A Mathematical Theory of Communication", in the Bell System Technical Journal was the founding of information theory as we know it today. Many developments and applications of the theory have taken place since then, which have made many modern devices for data communication and storage such as CD-ROMs and mobile phones possible.
+Notable later developments are listed in a timeline of information theory, including:
+
+The 1951, invention of Huffman encoding, a method of finding optimal prefix codes for lossless data compression.
+Irving S. Reed and David E. Muller proposing Reed–Muller codes in 1954.
+The 1960 proposal of Reed–Solomon codes.
+In 1966, Fumitada Itakura (Nagoya University) and Shuzo Saito (Nippon Telegraph and Telephone) develop linear predictive coding (LPC), a form of speech coding.
+In 1968, Elwyn Berlekamp invents the Berlekamp–Massey algorithm; its application to decoding BCH and Reed–Solomon codes is pointed out by James L. Massey the following year.
+In 1972, Nasir Ahmed proposes the discrete cosine transform (DCT). It later becomes the most widely used lossy compression algorithm, and the basis for digital media compression standards from 1988 onwards, including H.26x (since H.261) and MPEG video coding standards, JPEG image compression, MP3 audio compression, and Advanced Audio Coding (AAC).
+In 1976, Gottfried Ungerboeck gives the first paper on trellis modulation; a more detailed exposition in 1982 leads to a raising of analogue modem POTS speeds from 9.6 kbit/s to 33.6 kbit/s
+In 1977, Abraham Lempel and Jacob Ziv develop Lempel–Ziv compression (LZ77)
+In the early 1980s, Renuka P. Jindal at Bell Labs improves the noise performance of metal–oxide–semiconductor (MOS) devices, resolving issues that limited their receiver sensitivity and data rates. This leads to the wide adoption of MOS technology in laser lightwave systems and wireless terminal applications, enabling Edholm's law.
+In 1989, Phil Katz publishes the .zip format including DEFLATE (LZ77 + Huffman coding); later to become the most widely used archive container.
+In 1995, Benjamin Schumacher coins the term qubit and proves the quantum noiseless coding theorem.
+
+== See also ==
+Timeline of information theory
+Claude Shannon
+Ralph Hartley
+H-theorem
+
+== References ==
+
+== Further reading ==
+Gleick, James (2011). The Information: A History, a Theory, a Flood (1st ed.). New York: Pantheon Books. ISBN 978-1-4000-9623-7. OCLC 607975727.
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+title: "History of linguistics"
+chunk: 1/6
+source: "https://en.wikipedia.org/wiki/History_of_linguistics"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T03:59:52.500696+00:00"
+instance: "kb-cron"
+---
+
+Linguistics is the scientific study of language, involving analysis of language form, language meaning, and language in context.
+Language use was first systematically documented in Mesopotamia, with extant lexical lists of the 3rd to the 2nd Millennia BCE, offering glossaries on Sumerian cuneiform usage and meaning, and phonetical vocabularies of foreign languages. Later, Sanskrit would be systematically analysed, and its rules described, by Pāṇini (fl. 6-4th century BCE), in the Indus Valley. Beginning around the 4th century BCE, Warring States period China also developed its own grammatical traditions. Aristotle laid the foundation of Western linguistics as part of the study of rhetoric in his Poetics c. 335 BC. Traditions of Arabic grammar and Hebrew grammar developed during the Middle Ages in a religious context like Pānini's Sanskrit grammar.
+Modern approaches began to develop in the 18th century, eventually being regarded in the 19th century as belonging to the disciplines of psychology or biology, with such views establishing the foundation of mainstream Anglo-American linguistics, although in England philological approaches such as that of Henry Sweet tended to predominate.
+This was contested in the early 20th century by Ferdinand de Saussure, who established linguistics as an autonomous discipline within social sciences. Following Saussure's concept, general linguistics consists of the study of language as a semiotic system, which includes the subfields of phonology, morphology, syntax, and semantics. Each of these subfields can be approached either synchronically or diachronicially.
+Today, linguistics encompasses a large number of scientific approaches and has developed still more subfields, including applied linguistics, psycholinguistics, neurolinguistics, sociolinguistics, and computational linguistics.
+
+== Antiquity ==
+Across cultures, the early history of linguistics is associated with a need to disambiguate discourse, especially for ritual texts or arguments.  This often led to explorations of sound-meaning mappings, and the debate over conventional versus naturalistic origins for these symbols. Finally, this led to the processes by which larger structures are formed from units.
+
+=== Babylonia ===
+The earliest linguistic texts – written in cuneiform on clay tablets – date almost four thousand years before the present. In the early centuries of the second millennium BCE, in southern Mesopotamia, there arose a grammatical tradition that lasted more than 2,500 years. The linguistic texts from the earliest parts of the tradition were lists of nouns in Sumerian (a language isolate, that is, a language with no known genetic relatives), the language of religious and legal texts at the time. Sumerian was being replaced in everyday speech by a very different (and unrelated) language, Akkadian; it remained however as a language of prestige and continued to be used in religious and legal contexts. It therefore had to be taught as a foreign language, and to facilitate this, information about Sumerian was recorded in writing by Akkadian-speaking scribes.
+Over the centuries, the lists became standardised, and the Sumerian words were provided with Akkadian translations. Ultimately texts emerged that gave Akkadian equivalents for not just single words, but for entire paradigms of varying forms for words: one text, for instance, has 227 different forms of the verb ĝar "to place".
+
+=== India ===
+
+Linguistics in ancient India derives its impetus from the need to correctly recite and interpret the Vedic texts. Already in the oldest Indian text, the Rigveda, vāk ("speech") is deified.  By 1200 BCE, the oral performance of these texts becomes standardized, and treatises on ritual recitation suggest splitting up the Sanskrit compounds into words, stems, and phonetic units, providing an impetus for morphology and phonetics.
+Some of the earliest activities in the description of language have been attributed to the Indian grammarian Pāṇini (6th century BCE), who wrote a rule-based description of the Sanskrit language in his Aṣṭādhyāyī.
+Over the next few centuries, clarity was reached in the organization of sound units, and the stop consonants were organized in a 5x5 square (c. 800 BCE, Pratisakhyas), eventually leading to a systematic alphabet, Brāhmī, by the 3rd century BCE.
+In semantics, the early Sanskrit grammarian Śākaṭāyana (before c. 500 BCE) proposes that verbs represent ontologically prior categories, and that all nouns are etymologically derived from actions.  The etymologist Yāska (c. 5th century BCE) posits that meaning inheres in the sentence, and that word meanings are derived based on sentential usage.  He also provides four categories of words—nouns, verbs, pre-verbs, and particles/invariants—and a test for nouns both concrete and abstract: words which can be indicated by the pronoun that.
+Pāṇini (c. 6th century BCE) opposes the Yāska view that sentences are primary, and proposes a grammar for composing semantics from morphemic roots. Transcending the ritual text to consider living language, Pāṇini specifies a comprehensive set of about 4,000 aphoristic rules (sutras) that:
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+title: "History of linguistics"
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+source: "https://en.wikipedia.org/wiki/History_of_linguistics"
+category: "reference"
+tags: "science, encyclopedia"
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+---
+
+Map the semantics of verb argument structures into thematic roles
+Provide morphosyntactic rules for creating verb forms and nominal forms whose seven cases  are called karaka (similar to case) that generate the morphology
+Take these morphological structures and consider phonological processes (e.g., root or stem modification) by which the final phonological form is obtained
+In addition, the Pāṇinian school also provides a list of 2000 verb roots which form the objects on which these rules are applied, a list of sounds (the so-called Shiva-sutras), and a list of 260 words not derivable by the rules.
+The extremely succinct specification of these rules and their complex interactions led to considerable commentary and extrapolation over the following centuries.  The phonological structure includes defining a notion of sound universals similar to the modern phoneme, the systematization of consonants based on oral cavity constriction, and vowels based on height and duration.  However, it is the ambition of mapping these from morpheme to semantics that is truly remarkable in modern terms.
+Grammarians following Pāṇini include Kātyāyana (c. 3rd century BCE), who wrote aphorisms on Pāṇini (the Varttika) and advanced mathematics; Patañjali (2nd century BCE), known for his commentary on selected topics in Pāṇini's grammar (the Mahabhasya) and on Kātyāyana's aphorisms, as well as, according to some, the author of the Yoga Sutras, and Pingala,  with his mathematical approach to prosody. Several debates ranged over centuries, for example, on whether word-meaning mappings were conventional (Vaisheshika-Nyaya) or eternal (Kātyāyana-Patañjali-Mīmāṃsā).
+The Nyaya Sutras specified three types of meaning: the individual (this cow), the type universal (cowhood), and the image (draw the cow).
+That the sound of a word also forms a class (sound-universal) was observed  by Bhartṛhari (c. 500 CE), who also posits that language-universals are the units of thought, close to the nominalist or even the linguistic determinism position. Bhartṛhari also considers the sentence to be ontologically primary (word meanings are learned given their sentential use).
+Of the six canonical texts or Vedangas that formed the core syllabus in Brahminic education from the 1st century CE until the 18th century, four dealt with language:
+
+Shiksha (śikṣā): phonetics and phonology (sandhi), Gārgeya and commentators
+Chandas (chandas): prosody or meter, Pingala and commentators
+Vyakarana (vyākaraṇa): grammar, Pāṇini and commentators
+Nirukta (nirukta): etymology, Yāska and commentators
+Bhartrihari around 500 CE introduced a philosophy of meaning with his sphoṭa doctrine.
+Pāṇini's rule-based method of linguistic analysis and description has remained relatively unknown to Western linguistics until more recently. Franz Bopp used Pāṇini's work as a linguistic source for his 1807 Sanskrit grammar but disregarded his methodology. Pāṇini's system also differs from modern formal linguistics in that, since Sanskrit is a free word-order language, it did not provide syntactic rules. Formal linguistics, as first proposed by Louis Hjelmslev in 1943, is nonetheless based on the same concept that the expression of meaning is organised on different layers of linguistic form (including phonology and morphology).
+The Pali Grammar of Kacchayana, dated to the early centuries CE, describes the language of the Buddhist canon.
+
+=== Greece ===
+The Greeks developed an alphabet using symbols from the Phoenicians, adding signs for vowels and for extra consonants appropriate to their idiom (see Robins, 1997). In the Phoenicians and in earlier Greek writing systems, such as Linear B, graphemes indicated syllables, that is sound combinations of a consonant and a vowel. The addition of vowels by the Greeks was a major breakthrough as it facilitated the writing of Greek by representing both vowels and consonants with distinct graphemes. As a result of the introduction of writing, poetry such as the Homeric poems became written and several editions were created and commented on, forming the basis of philology and criticism.
+Along with written speech, the Greeks commenced studying grammatical and philosophical issues. A philosophical discussion about the nature and origins of language can be found as early as the works of Plato. A subject of concern was whether language was man-made, a social artifact, or supernatural in origin. Plato in his Cratylus presents the naturalistic view, that word meanings emerge from a natural process, independent of the language user.  His arguments are partly based on examples of compounding, where the meaning of the whole is usually related to the constituents, although by the end he admits a small role for convention. The sophists and Socrates introduced dialectics as a new text genre. The Platonic dialogs contain definitions of the meters of the poems and tragedy, the form and the structure of those texts (see the Republic and Phaidros, Ion, etc.).
+Aristotle supports the conventional origins of meaning. He defined the logic of speech and of the argument. Furthermore, Aristotle's works on rhetoric and poetics became of the utmost importance for the understanding of tragedy, poetry, public discussions etc. as text genres. Aristotle's work on logic interrelates with his special interest in language, and his work on this area was fundamentally important for the development of the study of language (logos in Greek means both "language" and "logic reasoning"). In Categories, Aristotle defines what is meant by "synonymous" or univocal words, what is meant by "homonymous" or equivocal words, and what is meant by "paronymous" or denominative words. He  divides forms of speech as being:
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+instance: "kb-cron"
+---
+
+Either simple, without composition or structure, such as "man," "horse," "fights," etc.
+Or having composition and structure, such as "a man fights," "the horse runs," etc.
+Next, he distinguishes between a subject of predication, namely that of which anything is affirmed or denied, and a subject of inhesion. A thing is said to be inherent in a subject, when, though it is not a part of the subject, it cannot possibly exist without the subject, e.g., shape in a thing having a shape. The categories are not abstract platonic entities but are found in speech, these are substance, quantity, quality, relation, place, time, position, state, action and affection. In de Interpretatione, Aristotle analyzes categoric propositions, and draws a series of basic conclusions on the routine issues of classifying and defining basic linguistic forms, such as simple terms and propositions, nouns and verbs, negation, the quantity of simple propositions (primitive roots of the quantifiers in modern symbolic logic), investigations on the excluded middle (which to Aristotle isn't applicable to future tense propositions — the Problem of future contingents), and on modal propositions.
+The Stoics made linguistics an important part of their system of the cosmos and the human. They played an important role in defining the linguistic sign-terms adopted later on by Ferdinand de Saussure like "significant" and "signifié".  The Stoics studied phonetics, grammar and etymology as separate levels of study. In phonetics and phonology the articulators were defined. The syllable became an important  structure for the understanding of speech organization. One of the most important contributions of the Stoics in language study was the gradual definition of the terminology and theory echoed in modern linguistics.
+Alexandrian grammarians also studied speech sounds and prosody; they defined parts of speech with notions such as "noun", "verb", etc. There was also a discussion about the role of analogy in language, in this discussion the grammatici in Alexandria supported the view that language and especially morphology is based on analogy or paradigm, whereas the grammatic in schools in Asia Minor consider that language is not based on analogical bases but rather on exceptions.
+Alexandrians, like their predecessors, were very interested in meter and its role in poetry. The metrical "feet" in the Greek was based on the length of time taken to pronounce each syllable, with syllables categorized according to their weight as either "long" syllables or "short" syllables (also known as "heavy" and "light" syllables, respectively, to distinguish them from long and short vowels). The foot is often compared to a musical measure and the long and short syllables to whole notes and half notes. The basic unit in Greek and Latin prosody is a mora, which is defined as a single short syllable. A long syllable is equivalent to two moras. A long syllable contains either a long vowel, a diphthong, or a short vowel followed by two or more consonants.
+Various rules of elision sometimes prevent a grammatical syllable from making a full syllable, and certain other lengthening and shortening rules (such as correption) can create long or short syllables in contexts where one would expect the opposite. The most important Classical meter as defined by the Alexandrian grammarians was the dactylic hexameter, the meter of Homeric poetry. This form uses verses of six feet. The first four feet are normally dactyls, but can be spondees. The fifth foot is almost always a dactyl. The sixth foot is either a spondee or a trochee. The initial syllable of either foot is called the ictus, the basic "beat" of the verse. There is usually a caesura after the ictus of the third foot.
+The text Tékhnē grammatiké (c. 100 BCE, Gk. gramma meant letter, and this title means "Art of letters"), possibly written by Dionysius Thrax (170 – 90 BCE), is considered the earliest grammar book in the Greek tradition. It lists eight parts of speech and lays out the broad details of Greek morphology including the case structures.  This text was intended as a pedagogic guide (as was Panini), and also covers punctuation and some aspects of prosody.  Other grammars by Charisius (mainly a compilation of Thrax, as well as lost texts by Remmius Palaemon and others) and Diomedes (focusing more on prosody) were popular in Rome as pedagogic material for teaching Greek to native Latin-speakers.
+One of the most prominent scholars of Alexandria and of the antiquity was Apollonius Dyscolus. Apollonius wrote more than thirty treatises on questions of syntax, semantics, morphology, prosody, orthography, dialectology, and more. Happily, four of these are preserved—we still have a Syntax in four books, and three one-book monographs on pronouns, adverbs, and connectives, respectively.
+Lexicography become an important domain of study as many grammarians compiled dictionaries, thesauri and lists of special words "λέξεις" that were old, or dialectical or special (such as medical words or botanic words) at that period. In the early medieval times we find more categories of dictionaries like the dictionary of Suida (considered the first encyclopedic dictionary), etymological dictionaries etc.
+At that period, the Greek language functioned as a lingua franca, a language spoken throughout the known world (for the Greeks and Romans) of that time and, as a result, modern linguistics struggles to overcome this. With the Greeks a tradition commenced in the study of language. The terminology invented by Greek and Latin grammarians in the ancient world and medieval period continue as a part of our everyday language. Think, for example, of notions such as the word, the syllable, the verb, the subject etc.
+
+=== Rome ===
+
+In the 4th century, Aelius Donatus compiled the Latin grammar Ars Grammatica that was to be the defining school text through the Middle Ages.  A smaller version, Ars Minor, covered only the eight parts of speech; eventually when books came to be printed in the 15th century, this was one of the first books to be printed. Schoolboys subjected to all this education gave us the current meaning of "grammar" (attested in English since 1176).
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+title: "History of linguistics"
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+tags: "science, encyclopedia"
+date_saved: "2026-05-05T03:59:52.500696+00:00"
+instance: "kb-cron"
+---
+
+=== China ===
+Similar to the Indian tradition, Chinese philology (小學; xiǎoxué; 'elementary studies') emerged as an aid to understanding the Chinese classics c. the 3rd century BCE, during the Western Han dynasty. Philology came to be divided into three branches: exegesis (訓詁; xùngǔ), grammatology (文字; wénzì) and phonology (音韻; yīnyùn). The field reached its golden age in the 17th century, during the Qing dynasty. The Erya (c. 3rd century BCE), comparable to the Indian Nighantu, is regarded as the first linguistic work in China. Shuowen Jiezi (c. 100 CE), the first Chinese dictionary, classifies Chinese characters by radicals, a practice that would be followed by most subsequent lexicographers. Two more pioneering works produced during the Han dynasty are Fangyan, the first Chinese work concerning dialects, and Shiming, devoted to etymology.
+As in ancient Greece, early Chinese thinkers were concerned with the relationship between names and reality. Confucius (c. 551 – c. 479 BCE) famously emphasized the moral commitment implicit in a name, (zhengming) stating that the moral collapse of the pre-Qin was a result of the failure to rectify behaviour to meet the moral commitment inherent in names: "Good government consists in the ruler being a ruler, the minister being a minister, the father being a father, and the son being a son... If names be not correct, language is not in accordance with the truth of things." (Analects 12.11, 13.3).
+However, what is the reality implied by a name? The later Mohists or the group known as School of Names,
+consider that a name (名; míng may refer to three kinds of actuality (實; shí): type universals (horse), individual (John), and unrestricted (thing). They adopt a realist position on the name-reality connection – universals arise because "the world itself fixes the patterns of similarity and difference by which things should be divided into kinds".  The philosophical tradition features a well known conundrum "a white horse is not a horse" by Gongsun Longzi (4th century  BCE), which resembles those of the sophists; Gongsun questions if in copula statements (X is Y), are X and Y identical or is X a subclass of Y.
+Xunzi (c. 310 – c. after 238 BCE) revisits the principle of zhengming, but instead of rectifying behaviour to suit the names, his emphasis is on rectifying language to correctly reflect reality. This is consistent with a more "conventional" view of word origins.
+The study of phonology in China began late, and was influenced by the Indian tradition, after Buddhism had become popular in China. The rime dictionary is a type of dictionary arranged by tone and rime, in which the pronunciations of  characters are indicated by fanqie spellings. Rime tables were later produced to aid the understanding of fanqie.
+Philological studies flourished during the Qing dynasty, with Duan Yucai and Wang Niansun as the towering figures. The last great philologist of the era was Zhang Binglin, who also helped lay the foundation of modern Chinese linguistics. The Western comparative method was brought into China by Bernard Karlgren, the first scholar to reconstruct Middle Chinese and Old Chinese with Latin alphabet (not IPA). Important modern Chinese linguists include Yuen Ren Chao, Luo Changpei, Li Fanggui and Wang Li.
+Ancient commentators on the classics focused their attention on  lexical content and the function of linking words rather than syntax; the first modern Chinese grammar was produced by Ma Jianzhong (late 19th century), based on a Western model.
+
+== Middle Ages ==
+
+=== Arabic grammar ===
+
+Owing to the rapid expansion of Islam in the 8th century, many people learned Arabic as a lingua franca. For this reason, the earliest grammatical treatises on Arabic are often written by non-native speakers.
+The earliest grammarian who is known to us is ʿAbd Allāh ibn Abī Isḥāq al-Ḥaḍramī (died 735-736 CE, 117 AH). The efforts of three generations of grammarians culminated in the book of  the Persian linguist Sibāwayhi (c. 760–793).
+Sibawayh made a detailed and professional description of Arabic in 760 in his monumental work, Al-kitab fi al-nahw (الكتاب في النحو, The Book on Grammar). In his book he distinguished phonetics from phonology.
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+title: "History of linguistics"
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+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T03:59:52.500696+00:00"
+instance: "kb-cron"
+---
+
+=== European vernaculars ===
+The Irish Sanas Cormaic 'Cormac's Glossary' (10th century) is Europe's first etymological and encyclopedic dictionary in any non-Classical language. The Auraicept na n-Éces, compiled over the course of several centuries — possibly starting as early as in the 8th century — is a treatise on that same language and the first instance of a philosophical defence of a spoken European vernacular over Latin.
+A milestone in the early history of Germanic linguistics, the First Grammatical Treatise (12th century) offers a wealth of information on Old Norse lexicon, grammar and phonology.
+In the 13th century, the Modistae or "speculative grammarians" introduced the notion of universal grammar. In the treatise De vulgari eloquentia ("On the Eloquence of Vernacular"), dating to 1303-1305, the Italian poet Dante presented a theory of language and discussed the origin of languages after the confusion of tongues following the events of the Tower of Babel. By recognizing the instrinsically human nature of language, Dante first recognized that — like customs and traditions — languages are bound to evolve over time and to differentiate in space giving birth to dialects. He argued that the wave of human populations migrating westward to Europe after the confusion of tongues were already differentiated into three linguistic families: the Greek family, one that can be defined as Slavo-Germanic, and the one that is today known as Romance family. Each of these families independently underwent differentiation into several branching languages. The Romance family, in particular, appeared to Dante as split into three closely related languages, namely Old French ("langue d'oïl"), Old Occitan ("langue d'oc") and Italian ("lingua del sì"). The writer then focused on the additional subdivision of Italian into 14 dialectal varieties, whence it could be possible to extract a noble and elevated vulgar language not inferior in dignity to Latin.
+The Renaissance and Baroque period saw an intensified interest in linguistics, notably for the purpose of Bible translations by the Jesuits, and also related to philosophical speculation on philosophical languages and the origin of language.
+In the 1600s, Joannes Goropius Becanus was the oldest representative of Dutch linguistics. He was the first person to publish a fragment of Gothic, mainly The Lord's Prayer. Franciscus Juniuns, Lambert ten Kate from Amsterdam and George Hickes from England are considered to be the founding fathers of Germanic linguistics.
+
+== Modern linguistics ==
+
+Modern linguistics did not begin until the late 18th century, and the Romantic or animist theses of  Johann Gottfried Herder and Johann Christoph Adelung remained influential well into the 19th century.
+In the history of American linguistics, there were hundreds of Indigenous languages that were never recorded. Many of the languages were spoken, not written, and so they are now inaccessible. Under these circumstances, linguists such as Franz Boas tried to prescribe sound methodical principles for the analysis of unfamiliar languages. Boas was an influential linguist and was followed by Edward Sapir and Leonard Bloomfield.
+
+=== Historical linguistics ===
+
+During the 18th century conjectural history, based on a mix of linguistics and anthropology, on the topic of both the origin and progress of language and society was fashionable. These thinkers contributed to the construction of academic paradigms in which some languages were labelled "primitive" relative to the English language. Hugh Blair wrote that for Native Americans, certain motions and actions were found to convey meaning as much as what was said verbally. Around the same time, James Burnett authored a 6 volume treatise that delved more deeply into the matter of "savage languages". Other writers theorized that Native American languages were "nothing but the natural and instinctive cries of the animal" without grammatical structure. The thinkers within this paradigm connected themselves with the Greeks and Romans, viewed as the only civilized persons of the ancient world, a view articulated by Thomas Sheridan who compiled an important 18th century pronunciation dictionary: "It was to the care taken in the cultivation of their languages, that Greece and Rome, owed that splendor, which eclipsed all the other nations of the world".
+In the 18th century James Burnett, Lord Monboddo analyzed numerous languages and deduced logical elements of the evolution of human languages.  His thinking was interleaved with his precursive concepts of biological evolution.  Some of his early concepts have been validated and are considered correct today. In his The Sanscrit Language (1786), Sir William Jones proposed that Sanskrit and Persian had resemblances to Classical Greek, Latin, Gothic, and Celtic languages. From this idea sprung the field of comparative linguistics and historical linguistics. Through the 19th century, European linguistics centered on the comparative history of the Indo-European languages, with a concern for finding their common roots and tracing their development.
+In the 1820s, Wilhelm von Humboldt observed that human language was a rule-governed system, anticipating a theme that was to become central in the formal work on syntax and semantics of language in the 20th century. Of this observation he said that it allowed language to make "infinite use of finite means" (Über den Dualis, 1827). Humboldt's work is associated with the movement of Romantic linguistics, which was inspired by Naturphilosophie and Romantic science. Other notable representatives of the movement include Friedrich Schlegel and Franz Bopp.
+It was only in the late 19th century that the Neogrammarian approach of Karl Brugmann and others introduced a rigid notion of sound law.
+Historical linguistics also led to the emergence of the semantics and some forms of pragmatics (Nerlich, 1992; Nerlich and Clarke, 1996).
+Historical linguistics continues today and linguistics have succeeded in grouping approximately 5000 languages of the world into a number of common ancestors.
+
+=== Structuralism ===
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+title: "History of linguistics"
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+tags: "science, encyclopedia"
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+instance: "kb-cron"
+---
+
+In Europe there was a development of structural linguistics, initiated by Ferdinand de Saussure, a Swiss professor of Indo-European and general linguistics, whose lectures on general linguistics, published posthumously by his students, set the direction of European linguistic analysis from the 1920s on; his approach has been widely adopted in other fields under the broad term "Structuralism".
+By the 20th century, the attention shifted from language change to the structure, which is governed by rules and principles. This structure turned more into grammar and by the 1920s structural linguistic, was developing into sophisticated methods of grammatical analysis.
+
+=== Descriptive linguistics ===
+
+During the second World War, North American linguists Leonard Bloomfield, William Mandeville Austin and several of his students and colleagues developed teaching materials for a variety of languages whose knowledge was needed for the war effort. This work led to an increasing prominence of the field of linguistics, which became a recognized discipline in most American universities only after the war.
+In 1965, William Stokoe, Carl G. Croneberg, and Dorothy C. Casterline linguists from Gallaudet University published an analysis which proved that American Sign Language fits the criteria for a natural language.
+
+=== Generative linguistics ===
+
+Generative linguistics focuses on modeling the subconscious rules governing language. It started with Noam Chomsky’s Transformational Grammar and has evolved into various theories like Government and Binding and the Minimalist Program. Core principles include the distinction between competence and performance, the role of innate grammar (Universal Grammar), and the use of explicit, formal models to describe linguistic knowledge.
+
+=== Other subfields ===
+
+From roughly 1980 onwards, pragmatic, functional, and cognitive approaches have steadily gained ground, both in the United States and in Europe.
+
+== See also ==
+History of grammar
+History of communication
+History of women in linguistics
+
+== Notes ==
+
+== References ==
+Keith Allan (2007). The Western Classical Tradition in Linguistics. London: Equinox.
+Roy Harris; Talbot J. Taylor (1989). Landmarks in Linguistic Thought: The Western Tradition from Socrates to Saussure. London: Routledge. ISBN 0-415-00290-7.
+John E. Joseph; Nigel Love; Talbot J. Taylor (2001). Landmarks in Linguistic Thought II: The Western Tradition in the Twentieth Century. London: Routledge. ISBN 0-415-06396-5.
+W. P. Lehmann, ed. (1967). A Reader in Nineteenth Century Historical Indo-European Linguistics. Indiana University Press. ISBN 0-253-34840-4. Archived from the original on 2008-04-26.
+François, Alexandre; Ponsonnet, Maïa (2013). "Descriptive linguistics" (PDF). In Jon R. McGee; Richard L. Warms (eds.). Theory in Social and Cultural Anthropology: An Encyclopedia. Vol. 1. SAGE Publications, Inc. pp. 184–187. ISBN 9781412999632.
+Bimal Krishna Matilal (1990). The Word and the World: India's Contribution to the Study of Language. Delhi; New York: Oxford University Press. ISBN 0-19-562515-3.
+James McElvenny (2024). A History of Modern Linguistics: From the beginnings to World War II. Edinburgh: Edinburgh University Press.
+Frederick J. Newmeyer (2005). The History of Linguistics. Linguistic Society of America. ISBN 0-415-11553-1. Archived from the original on 2007-02-10. Retrieved 2007-01-17.
+Mario Pei (1965). Invitation to Linguistics. Doubleday & Company. ISBN 0-385-06584-1.
+Robert Henry Robins (1997). A Short History of Linguistics. London: Longman. ISBN 0-582-24994-5.
+Kees Versteegh (1997). Landmarks in Linguistic Thought III: The Arabic Linguistic Tradition. London; New York: Routledge. ISBN 0-415-14062-5.
+Randy Allen Harris (1995) The Linguistics Wars, Oxford University Press, ISBN 9780199839063. Second edition published in 2022 as The Linguistics Wars: Chomsky, Lakoff, and the Battle Over Deep Structure, Oxford University Press, ISBN 9780199740338
+Brigitte Nerlich (1992). Semantic Theories in Europe, 1830-1930. Amsterdam: John Benjamins, ISBN 90-272-4546-0
+Brigitte Nerlich and David D. Clarke (1996). Language, Action, and Context. Amsterdam: John Benjamins, ISBN 90-272-4567-3
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+instance: "kb-cron"
+---
+
+The history of logic deals with the study of the development of the science of valid inference (logic). Formal logics developed in ancient times in India, China, and Greece. Greek methods, particularly Aristotelian logic (or term logic) as found in the Organon, found wide application and acceptance in Western science and mathematics for millennia. The Stoics, especially Chrysippus, began the development of predicate logic.
+Christian and Islamic philosophers such as Boethius (died 524), Avicenna (died 1037), Thomas Aquinas (died 1274) and William of Ockham (died 1347) further developed Aristotle's logic in the Middle Ages, reaching a high point in the mid-fourteenth century, with Jean Buridan. The period between the fourteenth century and the beginning of the nineteenth century saw largely decline and neglect, and at least one historian of logic regards this time as barren. Empirical methods ruled the day, as evidenced by Sir Francis Bacon's Novum Organon of 1620.
+Logic revived in the mid-nineteenth century, at the beginning of a revolutionary period when the subject developed into a rigorous and formal discipline which took as its exemplar the exact method of proof used in mathematics, a hearkening back to the Greek tradition. The development of the modern "symbolic" or "mathematical" logic during this period by the likes of Boole, Frege, Russell, and Peano is the most significant in the two-thousand-year history of logic, and is arguably one of the most important and remarkable events in human intellectual history.
+Progress in mathematical logic in the first few decades of the twentieth century, particularly arising from the work of Gödel and Tarski, had a significant impact on analytic philosophy and philosophical logic, particularly from the 1950s onwards, in subjects such as modal logic, temporal logic, deontic logic, and relevance logic.
+
+== Logic in India ==
+
+=== Hindu logic ===
+
+==== Origin ====
+The Nasadiya Sukta of the Rigveda (RV 10.129) contains ontological speculation in terms of various logical divisions that were later recast formally as the four circles of catuskoti: "A", "not A", "A and 'not A'", and "not A and not not A".
+
+Logic began independently in ancient India and continued to develop to early modern times without any known influence from Greek logic.
+
+==== Before Gautama ====
+Though the origins in India of public debate (pariṣad), one form of rational inquiry, are not clear, we know that public debates were common in preclassical India, for they are frequently alluded to in various Upaniṣads and in the early Buddhist literature. Public debate is not the only form of public deliberations in preclassical India. Assemblies (pariṣad or sabhā) of various sorts, comprising relevant experts, were regularly convened to deliberate on a variety of matters, including administrative, legal and religious matters.
+
+==== Dattatreya ====
+A philosopher named Dattatreya is stated in the Bhagavata Purana to have taught Anviksiki to Aiarka, Prahlada and others. It appears from the Markandeya purana that the Anviksiki-vidya expounded by him consisted of a mere disquisition on soul in accordance with the yoga philosophy. Dattatreya expounded the philosophical side of Anviksiki and not its logical aspect.
+
+==== Medhatithi Gautama ====
+While the teachers mentioned before dealt with some particular topics of Anviksiki, the credit of founding the Anviksiki in its special sense of a science is to be attributed to Medhatithi Gautama (c. 6th century BC). Guatama founded the anviksiki school of logic. The Mahabharata (12.173.45), around the 5th century BC, refers to the anviksiki and tarka schools of logic.
+
+==== Panini ====
+Pāṇini (c. 5th century BC) developed a form of logic (to which Boolean logic has some similarities) for his formulation of Sanskrit grammar. Logic is described by Chanakya (c. 350–283 BC) in his Arthashastra as an independent field of inquiry.
+
+==== Nyaya-Vaisheshika ====
+Two of the six Indian schools of thought deal with logic: Nyaya and Vaisheshika. The Nyāya Sūtras of Aksapada Gautama (c. 2nd century AD) constitute the core texts of the Nyaya school, one of the six orthodox schools of Hindu philosophy. This realist school developed a rigid five-member schema of inference involving an initial premise, a reason, an example, an application, and a conclusion. The idealist Buddhist philosophy became the chief opponent to the Naiyayikas.
+
+=== Jain logic ===
+
+Jains made its own unique contribution to this mainstream development of logic by also occupying itself with the basic epistemological issues, namely, with those concerning the nature of knowledge, how knowledge is derived, and in what way knowledge can be said to be reliable.
+The Jains have doctrines of relativity used for logic and reasoning:
+
+Anekāntavāda – the theory of relative pluralism or manifoldness;
+Syādvāda – the theory of conditioned predication and;
+Nayavāda – The theory of partial standpoints.
+These concepts in Jain philosophy made important contributions to the thought, especially in the areas of skepticism and relativity. [4]
+
+=== Buddhist logic ===
+
+==== Nagarjuna ====
+Nagarjuna (c. 150–250 AD), the founder of the Madhyamaka ("Middle Way") developed an analysis known as the catuṣkoṭi (Sanskrit), a "four-cornered" system of argumentation that involves the systematic examination and rejection of each of the four possibilities of a proposition, P:
+
+P; that is, being.
+not P; that is, not being.
+P and not P; that is, being and not being.
+not (P or not P); that is, neither being nor not being.Under propositional logic, De Morgan's laws would imply that the fourth case is equivalent to the third case, and would be therefore superfluous, with only 3 actual cases to consider.
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+instance: "kb-cron"
+---
+
+=== Dignaga ===
+However, Dignāga (c 480–540 AD) is sometimes said to have developed a formal syllogism, and it was through him and his successor, Dharmakirti, that Buddhist logic reached its height; it is contested whether their analysis actually constitutes a formal syllogistic system. In particular, their analysis centered on the definition of an inference-warranting relation, "vyapti", also known as invariable concomitance or pervasion. To this end, a doctrine known as "apoha" or differentiation was developed. This involved what might be called inclusion and exclusion of defining properties.
+Dignāga's famous "wheel of reason" (Hetucakra) is a method of indicating when one thing (such as smoke) can be taken as an invariable sign of another thing (like fire), but the inference is often inductive and based on past observation. Matilal remarks that Dignāga's analysis is much like John Stuart Mill's Joint Method of Agreement and Difference, which is inductive.
+
+== Logic in China ==
+
+In China, a contemporary of Confucius, Mozi, "Master Mo", is credited with founding the Mohist school, whose canons dealt with issues relating to valid inference and the conditions of correct conclusions. In particular, one of the schools that grew out of Mohism, the Logicians, are credited by some scholars for their early investigation of formal logic. Due to the harsh rule of Legalism in the subsequent Qin dynasty, this line of investigation disappeared in China until the introduction of Indian philosophy by Buddhists.
+
+== Logic in the ancient Mediterranean ==
+
+=== Prehistory of logic ===
+Valid reasoning has been employed in all periods of human history. However, logic studies the principles of valid reasoning, inference and demonstration. It is probable that the idea of demonstrating a conclusion first arose in connection with geometry, which originally meant the same as "land measurement". The ancient Egyptians discovered geometry, including the formula for the volume of a truncated pyramid. Ancient Babylon was also skilled in mathematics. Esagil-kin-apli's medical Diagnostic Handbook in the 11th century BC was based on a logical set of axioms and assumptions, while Babylonian astronomers in the 8th and 7th centuries BC employed an internal logic within their predictive planetary systems, an important contribution to the philosophy of science.
+
+=== Ancient Greece before Aristotle ===
+While the ancient Egyptians empirically discovered some truths of geometry, the great achievement of the ancient Greeks was to replace empirical methods by demonstrative proof. Both Thales and Pythagoras of the Pre-Socratic philosophers seemed aware of geometric methods.
+Fragments of early proofs are preserved in the works of Plato and Aristotle, and the idea of a deductive system was probably known in the Pythagorean school and the Platonic Academy. The proofs of Euclid of Alexandria are a paradigm of Greek geometry. The three basic principles of geometry are as follows:
+
+Certain propositions must be accepted as true without demonstration; such a proposition is known as an axiom of geometry.
+Every proposition that is not an axiom of geometry must be demonstrated as following from the axioms of geometry; such a demonstration is known as a proof or a "derivation" of the proposition.
+The proof must be formal; that is, the derivation of the proposition must be independent of the particular subject matter in question.
+Further evidence that early Greek thinkers were concerned with the principles of reasoning is found in the fragment called dissoi logoi, probably written at the beginning of the fourth century BC. This is part of a protracted debate about truth and falsity. In the case of the classical Greek city-states, interest in argumentation was also stimulated by the activities of the Rhetoricians or Orators and the Sophists, who used arguments to defend or attack a thesis, both in legal and political contexts.
+
+==== Thales ====
+It is said Thales, most widely regarded as the first philosopher in the Greek tradition, measured the height of the pyramids by their shadows at the moment when his own shadow was equal to his height. Thales was said to have had a sacrifice in celebration of discovering Thales' theorem just as Pythagoras had the Pythagorean theorem.
+Thales is the first known individual to use deductive reasoning applied to geometry, by deriving four corollaries to his theorem, and the first known individual to whom a mathematical discovery has been attributed. Indian and Babylonian mathematicians knew his theorem for special cases before he proved it. It is believed that Thales learned that an angle inscribed in a semicircle is a right angle during his travels to Babylon.
+
+==== Pythagoras ====
+
+Before 520 BC, on one of his visits to Egypt or Greece, Pythagoras might have met the c. 54 years older Thales. The systematic study of proof seems to have begun with the school of Pythagoras (i. e. the Pythagoreans) in the late sixth century BC. Indeed, the Pythagoreans, believing all was number, are the first philosophers to emphasize form rather than matter.
+
+==== Heraclitus and Parmenides ====
+The writing of Heraclitus (c. 535 – c. 475 BC) was the first place where the word logos was given special attention in ancient Greek philosophy, Heraclitus held that everything changes and all was fire and conflicting opposites, seemingly unified only by this Logos. He is known for his obscure sayings.
+
+This logos holds always but humans always prove unable to understand it, both before hearing it and when they have first heard it. For though all things come to be in accordance with this logos, humans are like the inexperienced when they experience such words and deeds as I set out, distinguishing each in accordance with its nature and saying how it is. But other people fail to notice what they do when awake, just as they forget what they do while asleep.
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+instance: "kb-cron"
+---
+
+The names of Gödel and Tarski dominate the 1930s, a crucial period in the development of metamathematics—the study of mathematics using mathematical methods to produce metatheories, or mathematical theories about other mathematical theories. Early investigations into metamathematics had been driven by Hilbert's program. Work on metamathematics culminated in the work of Gödel, who in 1929 showed that a given first-order sentence is deducible if and only if it is logically valid—i.e. it is true in every structure for its language. This is known as Gödel's completeness theorem. A year later, he proved two important theorems, which showed Hibert's program to be unattainable in its original form. The first is that no consistent system of axioms whose theorems can be listed by an effective procedure such as an algorithm or computer program is capable of proving all facts about the natural numbers. For any such system, there will always be statements about the natural numbers that are true, but that are unprovable within the system. The second is that if such a system is also capable of proving certain basic facts about the natural numbers, then the system cannot prove the consistency of the system itself. These two results are known as Gödel's incompleteness theorems, or simply Gödel's Theorem. Later in the decade, Gödel developed the concept of set-theoretic constructibility, as part of his proof that the axiom of choice and the continuum hypothesis are consistent with Zermelo–Fraenkel set theory.
+In proof theory, Gerhard Gentzen developed natural deduction and the sequent calculus. The former attempts to model logical reasoning as it 'naturally' occurs in practice and is most easily applied to intuitionistic logic, while the latter was devised to clarify the derivation of logical proofs in any formal system. Since Gentzen's work, natural deduction and sequent calculi have been widely applied in the fields of proof theory, mathematical logic and computer science. Gentzen also proved normalization and cut-elimination theorems for intuitionistic and classical logic which could be used to reduce logical proofs to a normal form.
+
+Alfred Tarski, a pupil of Łukasiewicz, is best known for his definition of truth and logical consequence, and the semantic concept of logical satisfaction. In 1933, he published (in Polish) The concept of truth in formalized languages, in which he proposed his semantic theory of truth: a sentence such as "snow is white" is true if and only if snow is white. Tarski's theory separated the metalanguage, which makes the statement about truth, from the object language, which contains the sentence whose truth is being asserted, and gave a correspondence (the T-schema) between phrases in the object language and elements of an interpretation. Tarski's approach to the difficult idea of explaining truth has been enduringly influential in logic and philosophy, especially in the development of model theory. Tarski also produced important work on the methodology of deductive systems, and on fundamental principles such as completeness, decidability, consistency and definability. According to Anita Feferman, Tarski "changed the face of logic in the twentieth century".
+Alonzo Church and Alan Turing proposed formal models of computability, giving independent negative solutions to Hilbert's Entscheidungsproblem in 1936 and 1937, respectively. The Entscheidungsproblem asked for a procedure that, given any formal mathematical statement, would algorithmically determine whether the statement is true. Church and Turing proved there is no such procedure; Turing's paper introduced the halting problem as a key example of a mathematical problem without an algorithmic solution.
+Church's system for computation developed into the modern λ-calculus, while the Turing machine became a standard model for a general-purpose computing device. It was soon shown that many other proposed models of computation were equivalent in power to those proposed by Church and Turing. These results led to the Church–Turing thesis that any deterministic algorithm that can be carried out by a human can be carried out by a Turing machine. Church proved additional undecidability results, showing that both Peano arithmetic and first-order logic are undecidable. Later work by Emil Post and Stephen Cole Kleene in the 1940s extended the scope of computability theory and introduced the concept of degrees of unsolvability.
+The results of the first few decades of the twentieth century also had an impact upon analytic philosophy and philosophical logic, particularly from the 1950s onwards, in subjects such as modal logic, temporal logic, deontic logic, and relevance logic.
+
+=== Logic after WWII ===
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+---
+
+After World War II, mathematical logic branched into four inter-related but separate areas of research: model theory, proof theory, computability theory, and set theory.
+In set theory, the method of forcing revolutionized the field by providing a robust method for constructing models and obtaining independence results.  Paul Cohen introduced this method in 1963 to prove the independence of the continuum hypothesis and the axiom of choice from Zermelo–Fraenkel set theory. His technique, which was simplified and extended soon after its introduction, has since been applied to many other problems in all areas of mathematical logic.
+Computability theory had its roots in the work of Turing, Church, Kleene, and Post in the 1930s and 40s. It developed into a study of abstract computability, which became known as recursion theory. The priority method, discovered independently by Albert Muchnik and Richard Friedberg in the 1950s, led to major advances in the understanding of the degrees of unsolvability and related structures.  Research into higher-order computability theory demonstrated its connections to set theory.  The fields of constructive analysis and computable analysis were developed to study the effective content of classical mathematical theorems; these in turn inspired the program of reverse mathematics. A separate branch of computability theory, computational complexity theory, was also characterized in logical terms as a result of investigations into descriptive complexity.
+Model theory applies the methods of mathematical logic to study models of particular mathematical theories. Alfred Tarski published much pioneering work in the field, which is named after a series of papers he published under the title Contributions to the theory of models.  In the 1960s, Abraham Robinson used model-theoretic techniques to develop calculus and analysis based on infinitesimals, a problem that first had been proposed by Leibniz. 
+In proof theory, the relationship between classical mathematics and intuitionistic mathematics was clarified via tools such as the realizability method invented by Georg Kreisel and Gödel's Dialectica interpretation. This work inspired the contemporary area of proof mining. The Curry–Howard correspondence emerged as a deep analogy between logic and computation, including a correspondence between systems of natural deduction and typed lambda calculi used in computer science. As a result, research into this class of formal systems began to address both logical and computational aspects; this area of research came to be known as modern type theory. Advances were also made in ordinal analysis and the study of independence results in arithmetic such as the Paris–Harrington theorem.
+This was also a period, particularly in the 1950s and afterwards, when the ideas of mathematical logic begin to influence philosophical thinking. For example, tense logic is a formalised system for representing, and reasoning about, propositions qualified in terms of time. The philosopher Arthur Prior played a significant role in its development in the 1960s. Modal logics extend the scope of formal logic to include the elements of modality (for example, possibility and necessity). The ideas of Saul Kripke, particularly about possible worlds, and the formal system now called Kripke semantics have had a profound impact on analytic philosophy. His best known and most influential work is Naming and Necessity (1980). Deontic logics are closely related to modal logics: they attempt to capture the logical features of obligation, permission and related concepts. Although some basic novelties syncretizing mathematical and philosophical logic were shown by Bolzano in the early 1800s, it was Ernst Mally, a pupil of Alexius Meinong, who was to propose the first formal deontic system in his Grundgesetze des Sollens, based on the syntax of Whitehead's and Russell's propositional calculus.
+Another logical system founded after World War II was fuzzy logic by Azerbaijani mathematician Lotfi Asker Zadeh in 1965.
+
+== See also ==
+
+History of deductive reasoning
+History of inductive reasoning
+History of abductive reasoning
+History of the function concept
+History of mathematics
+History of Philosophy
+Plato's beard
+Timeline of mathematical logic
+
+== Notes ==
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+category: "reference"
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+date_saved: "2026-05-05T03:59:53.898187+00:00"
+instance: "kb-cron"
+---
+
+== References ==
+Primary Sources
+Alexander of Aphrodisias, In Aristotelis An. Pr. Lib. I Commentarium, ed. Wallies, Berlin, C.I.A.G. vol. II/1, 1882.
+Avicenna, Avicennae Opera Venice 1508.
+Boethius Commentary on the Perihermenias, Secunda Editio, ed. Meiser, Leipzig, Teubner, 1880.
+Bolzano, Bernard Wissenschaftslehre, (1837) 4 Bde, Neudr., hrsg. W. Schultz, Leipzig I–II 1929, III 1930, IV 1931 (Theory of Science, four volumes, translated by Rolf George and Paul Rusnock, New York: Oxford University Press, 2014).
+Bolzano, Bernard Theory of Science (Edited, with an introduction, by Jan Berg. Translated from the German by Burnham Terrell – D. Reidel Publishing Company, Dordrecht and Boston 1973).
+Boole, George (1847) The Mathematical Analysis of Logic (Cambridge and London); repr. in Studies in Logic and Probability, ed. R. Rhees (London 1952).
+Boole, George (1854) The Laws of Thought (London and Cambridge); repr. as Collected Logical Works. Vol. 2, (Chicago and London: Open Court, 1940).
+Epictetus, Epicteti Dissertationes ab Arriano digestae, edited by Heinrich Schenkl, Leipzig, Teubner. 1894.
+Frege, G., Boole's Logical Calculus and the Concept Script, 1882, in Posthumous Writings transl. P. Long and R. White 1969, pp. 9–46.
+Gergonne, Joseph Diaz, (1816) Essai de dialectique rationelle, in Annales de mathématiques pures et appliquées 7, 1816/1817, 189–228.
+Jevons, W. S. The Principles of Science, London 1879.
+Ockham's Theory of Terms: Part I of the Summa Logicae, translated and introduced by Michael J. Loux (Notre Dame, IN: University of Notre Dame Press 1974). Reprinted: South Bend, IN: St. Augustine's Press, 1998.
+Ockham's Theory of Propositions: Part II of the Summa Logicae, translated by Alfred J. Freddoso and Henry Schuurman and introduced by Alfred J. Freddoso (Notre Dame, IN: University of Notre Dame Press, 1980). Reprinted: South Bend, IN: St. Augustine's Press, 1998.
+Peirce, C. S., (1896), "The Regenerated Logic", The Monist, vol. VII, No. 1, p pp. 19–40, The Open Court Publishing Co., Chicago, IL, 1896, for the Hegeler Institute. Reprinted (CP 3.425–455). Internet Archive The Monist 7.
+Sextus Empiricus, Against the Logicians. (Adversus Mathematicos VII and VIII). Richard Bett (trans.) Cambridge: Cambridge University Press, 2005. ISBN 0-521-53195-0.
+Zermelo, Ernst (1908). "Untersuchungen über die Grundlagen der Mengenlehre I". Mathematische Annalen. 65 (2): 261–281. doi:10.1007/BF01449999. S2CID 120085563. Archived from the original on 2017-09-08. Retrieved 2013-09-30. English translation in van Heijenoort, Jean (1967). "Investigations in the foundations of set theory". From Frege to Gödel: A Source Book in Mathematical Logic, 1879–1931. Source Books in the History of the Sciences. Harvard Univ. Press. pp. 199–215. ISBN 978-0-674-32449-7..
+Frege, Gottlob (1879). Begriffsschrift, a formula language, modeled upon that of arithmetic, for pure thought. translated in van Heijenoort 1967.
+Secondary Sources
+Barwise, Jon, (ed.), Handbook of Mathematical Logic, Studies in Logic and the Foundations of Mathematics, Amsterdam, North Holland, 1982 ISBN 978-0-444-86388-1 .
+Beaney, Michael, The Frege Reader, London: Blackwell 1997.
+Bochenski, I. M., A History of Formal Logic, Indiana, Notre Dame University Press, 1961.
+Boehner, Philotheus, Medieval Logic, Manchester 1950.
+Boyer, C.B. (1991) [1989], A History of Mathematics (2nd ed.), New York: Wiley, ISBN 978-0-471-54397-8
+Buroker, Jill Vance (transl. and introduction), A. Arnauld, P. Nicole Logic or the Art of Thinking, Cambridge University Press, 1996, ISBN 0-521-48249-6.
+Church, Alonzo, 1936–1938. "A bibliography of symbolic logic". Journal of Symbolic Logic 1: 121–218; 3:178–212.
+de Jong, Everard (1989), Galileo Galilei's "Logical Treatises" and Giacomo Zabarella's "Opera Logica": A Comparison, PhD dissertation, Washington, DC: Catholic University of America.
+Ebbesen, Sten "Early supposition theory (12th–13th Century)" Histoire, Épistémologie, Langage 3/1: 35–48 (1981).
+Farrington, B., The Philosophy of Francis Bacon, Liverpool 1964.
+Feferman, Anita B. (1999). "Alfred Tarski". American National Biography. 21. Oxford University Press. pp. 330–332. ISBN 978-0-19-512800-0.
+Feferman, Anita B.; Feferman, Solomon (2004). Alfred Tarski: Life and Logic. Cambridge University Press. ISBN 978-0-521-80240-6. OCLC 54691904.
+Gabbay, Dov and John Woods, eds, Handbook of the History of Logic 2004. 1. Greek, Indian and Arabic logic; 2. Mediaeval and Renaissance logic; 3. The rise of modern logic: from Leibniz to Frege; 4. British logic in the Nineteenth century; 5. Logic from Russell to Church; 6. Sets and extensions in the Twentieth century; 7. Logic and the modalities in the Twentieth century; 8. The many-valued and nonmonotonic turn in logic; 9. Computational Logic; 10. Inductive logic; 11. Logic: A history of its central concepts; Elsevier, ISBN 0-444-51611-5.
+Geach, P. T. Logic Matters, Blackwell 1972.
+Goodman, Lenn Evan (2003). Islamic Humanism. Oxford University Press, ISBN 0-19-513580-6.
+Goodman, Lenn Evan (1992). Avicenna. Routledge, ISBN 0-415-01929-X.
+Grattan-Guinness, Ivor, 2000. The Search for Mathematical Roots 1870–1940. Princeton University Press.
+Gracia, J. G. and Noone, T. B., A Companion to Philosophy in the Middle Ages, London 2003.
+Haaparanta, Leila (ed.) 2009. The Development of Modern Logic Oxford University Press.
+Heath, T. L., 1949. Mathematics in Aristotle, Oxford University Press.
+Heath, T. L., 1931, A Manual of Greek Mathematics, Oxford (Clarendon Press).
+Honderich, Ted (ed.). The Oxford Companion to Philosophy (New York: Oxford University Press, 1995) ISBN 0-19-866132-0.
+Kneale, William and Martha, 1962. The development of logic. Oxford University Press, ISBN 0-19-824773-7.
+Lukasiewicz, Aristotle's Syllogistic, Oxford University Press 1951.
+Potter, Michael (2004), Set Theory and its Philosophy, Oxford University Press.
+
+== External links ==
+The History of Logic from Aristotle to Gödel with annotated bibliographies on the history of logic
+Bobzien, Susanne. "Ancient Logic". In Zalta, Edward N. (ed.). Stanford Encyclopedia of Philosophy. ISSN 1095-5054. OCLC 429049174.
+Chatti, Saloua. "Avicenna (Ibn Sina): Logic". In Fieser, James; Dowden, Bradley (eds.). Internet Encyclopedia of Philosophy. ISSN 2161-0002. OCLC 37741658.
+Spruyt, Joke. "Peter of Spain". In Zalta, Edward N. (ed.). Stanford Encyclopedia of Philosophy. ISSN 1095-5054. OCLC 429049174.
+Paul Spade's "Thoughts Words and Things" – An Introduction to Late Mediaeval Logic and Semantic Theory (PDF)
+Open Access pdf download; Insights, Images, Bios, and links for 178 logicians by David Marans
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+
+In contrast to Heraclitus, Parmenides held that all is one and nothing changes. He may have been a dissident Pythagorean, disagreeing that One (a number) produced the many. "X is not" must always be false or meaningless. What exists can in no way not exist. Our sense perceptions with its noticing of generation and destruction are in grievous error. Instead of sense perception, Parmenides advocated logos as the means to Truth. He has been called the discoverer of logic,
+
+For this view, that That Which Is Not exists, can never predominate. You must debar your thought from this way of search, nor let ordinary experience in its variety force you along this way, (namely, that of allowing) the eye, sightless as it is, and the ear, full of sound, and the tongue, to rule; but (you must) judge by means of the Reason (Logos) the much-contested proof which is expounded by me.
+Zeno of Elea, a pupil of Parmenides, had the idea of a standard argument pattern found in the method of proof known as reductio ad absurdum. This is the technique of drawing an obviously false (that is, "absurd") conclusion from an assumption, thus demonstrating that the assumption is false. Therefore, Zeno and his teacher are seen as the first to apply the art of logic. Plato's dialogue Parmenides portrays Zeno as claiming to have written a book defending the monism of Parmenides by demonstrating the absurd consequence of assuming that there is plurality. Zeno famously used this method to develop his paradoxes in his arguments against motion. Such dialectic reasoning later became popular. The members of this school were called "dialecticians" (from a Greek word meaning "to discuss").
+
+==== Plato ====
+Let no one ignorant of geometry enter here.
+
+None of the surviving works of the great fourth-century philosopher Plato (428–347 BC) include any formal logic, but they include important contributions to the field of philosophical logic. Plato raises three questions:
+
+What is it that can properly be called true or false?
+What is the nature of the connection between the assumptions of a valid argument and its conclusion?
+What is the nature of definition?
+The first question arises in the dialogue Theaetetus, where Plato identifies thought or opinion with talk or discourse (logos). The second question is a result of Plato's theory of Forms. Forms are not things in the ordinary sense, nor strictly ideas in the mind, but they correspond to what philosophers later called universals, namely an abstract entity common to each set of things that have the same name. In both the Republic and the Sophist, Plato suggests that the necessary connection between the assumptions of a valid argument and its conclusion corresponds to a necessary connection between "forms". The third question is about definition. Many of Plato's dialogues concern the search for a definition of some important concept (justice, truth, the Good), and it is likely that Plato was impressed by the importance of definition in mathematics. What underlies every definition is a Platonic Form, the common nature present in different particular things. Thus, a definition reflects the ultimate object of understanding, and is the foundation of all valid inference. This had a great influence on Plato's student Aristotle, in particular Aristotle's notion of the essence of a thing.
+
+=== Aristotle ===
+
+The logic of Aristotle, and particularly his theory of the syllogism, has had an enormous influence on the history of logic and Western thought in general. Aristotle was the first logician to attempt a systematic analysis of logical syntax, of noun (or term), and of verb. He was the first formal logician, in that he demonstrated the principles of reasoning by employing variables to show the underlying logical form of an argument. He sought relations of dependence which characterize necessary inference, and distinguished the validity of these relations, from the truth of the premises. He was the first to explicitly discuss the principles of non-contradiction and excluded middle. 
+
+==== The Organon ====
+His logical works, called the Organon, are the earliest formal study of logic that have come down to modern times. Though it is difficult to determine the dates, the probable order of writing of Aristotle's logical works is:
+
+The Categories, a study of the ten kinds of primitive term.
+The Topics (with an appendix called On Sophistical Refutations), a discussion of dialectics.
+On Interpretation, an analysis of simple categorical propositions into simple terms, negation, and signs of quantity.
+The Prior Analytics, a formal analysis of what makes a syllogism (a valid argument, according to Aristotle).
+The Posterior Analytics, a study of scientific demonstration, containing Aristotle's mature views on logic.
+
+The Categories influence his work the Metaphysics, which itself had a profound influence on Western thought; the namesake of the subject of metaphysics.
+Aristotle also developed a theory of non-formal logic (i.e., the theory of fallacies), which is presented in Topics and Sophistical Refutations.
+On Interpretation contains a comprehensive treatment of the notions of opposition and conversion; chapter 7 is at the origin of the square of opposition (or logical square); chapter 9 contains the beginning of modal logic and the famous sea battle argument.
+The Prior Analytics contains his exposition of the syllogism, wherein three important advances are made for the first time in history: the use of variables, a purely formal treatment, and the use of an axiomatic system.
+
+=== Stoics ===
+
+The other great school of Greek logic is that of the Stoics. Stoic logic traces its roots back to the late 5th century BC philosopher Euclid of Megara, a pupil of Socrates and slightly older contemporary of Plato, probably following in the tradition of Parmenides and Zeno. His pupils and successors were called "Megarians", or "Eristics", and later the "Dialecticians". The two most important dialecticians of the Megarian school were Diodorus Cronus and Philo, who were active in the late 4th century BC. 
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+
+The Stoics adopted the Megarian logic and systemized it. The most important member of the school was Chrysippus (c. 278 – c. 206 BC), who was its third head, and who formalized much of Stoic doctrine. He is supposed to have written over 700 works, including at least 300 on logic, almost none of which survive. Unlike with Aristotle, we have no complete works by the Megarians or the early Stoics, and have to rely mostly on accounts (sometimes hostile) by later sources, including prominently Diogenes Laërtius, Sextus Empiricus, Galen, Aulus Gellius, Alexander of Aphrodisias, and Cicero.
+Three significant contributions of the Stoic school were (i) their account of modality, (ii) their theory of the Material conditional, and (iii) their account of meaning and truth.
+
+Modality. According to Aristotle, the Megarians of his day claimed there was no distinction between potentiality and actuality. Diodorus Cronus defined the possible as that which either is or will be, the impossible as what will not be true, and the contingent as that which either is already, or will be false. Diodorus is also famous for what is known as his Master argument, which states that each pair of the following 3 propositions contradicts the third proposition:
+Everything that is past is true and necessary.
+The impossible does not follow from the possible.
+What neither is nor will be is possible.
+Diodorus used the plausibility of the first two to prove that nothing is possible if it neither is nor will be true. Chrysippus, by contrast, denied the second premise and said that the impossible could follow from the possible.
+Conditional statements. The first logicians to debate conditional statements were Diodorus and his pupil Philo of Megara. Sextus Empiricus refers three times to a debate between Diodorus and Philo. Philo regarded a conditional as true unless it has both a true antecedent and a false consequent. Precisely, let T0 and T1 be true statements, and let F0 and F1 be false statements; then, according to Philo, each of the following conditionals is a true statement, because it is not the case that the consequent is false while the antecedent is true (it is not the case that a false statement is asserted to follow from a true statement):
+If T0, then T1
+If F0, then T0
+If F0, then F1
+The following conditional does not meet this requirement, and is therefore a false statement according to Philo:
+If T0, then F0
+Indeed, Sextus says "According to [Philo], there are three ways in which a conditional may be true, and one in which it may be false." Philo's criterion of truth is what would now be called a truth-functional definition of "if ... then"; it is the definition used in modern logic.
+In contrast, Diodorus allowed the validity of conditionals only when the antecedent clause could never lead to an untrue conclusion.
+Meaning and truth. The most important and striking difference between Megarian-Stoic logic and Aristotelian logic is that Megarian-Stoic logic concerns propositions, not terms, and is thus closer to modern propositional logic. The Stoics distinguished between utterance (phone), which may be noise, speech (lexis), which is articulate but which may be meaningless, and discourse (logos), which is meaningful utterance. The most original part of their theory is the idea that what is expressed by a sentence, called a lekton, is something real; this corresponds to what is now called a proposition. Sextus says that according to the Stoics, three things are linked together: that which signifies, that which is signified, and the object; for example, that which signifies is the word Dion, and that which is signified is what Greeks understand but barbarians do not, and the object is Dion himself.
+
+== Medieval logic ==
+
+=== Logic in the Middle East ===
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+
+The works of Al-Kindi, Al-Farabi, Avicenna, Al-Ghazali, Averroes and other Muslim logicians were based on Aristotelian logic and were important in communicating the ideas of the ancient world to the medieval West. Al-Farabi (Alfarabi) (873–950) was an Aristotelian logician who discussed the topics of future contingents, the number and relation of the categories, the relation between logic and grammar, and non-Aristotelian forms of inference. Al-Farabi also considered the theories of conditional syllogisms and analogical inference, which were part of the Stoic tradition of logic rather than the Aristotelian.
+Maimonides (1138-1204) wrote a Treatise on Logic (Arabic: Maqala Fi-Sinat Al-Mantiq), referring to Al-Farabi as the "second master", the first being Aristotle.
+Ibn Sina (Avicenna) (980–1037) was the founder of Avicennian logic, which replaced Aristotelian logic as the dominant system of logic in the Islamic world, and also had an important influence on Western medieval writers such as Albertus Magnus. Avicenna wrote on the hypothetical syllogism and on the propositional calculus, which were both part of the Stoic logical tradition. He developed an original "temporally modalized" syllogistic theory, involving temporal logic and modal logic. He also made use of inductive logic, such as the methods of agreement, difference, and concomitant variation which are critical to the scientific method. One of Avicenna's ideas had a particularly important influence on Western logicians such as William of Ockham: Avicenna's word for a meaning or notion (ma'na), was translated by the scholastic logicians as the Latin intentio; in medieval logic and epistemology, this is a sign in the mind that naturally represents a thing. This was crucial to the development of Ockham's conceptualism: A universal term (e.g., "man") does not signify a thing existing in reality, but rather a sign in the mind (intentio in intellectu) which represents many things in reality; Ockham cites Avicenna's commentary on Metaphysics V in support of this view.
+Fakhr al-Din al-Razi (b. 1149) criticised Aristotle's "first figure" and formulated an early system of inductive logic, foreshadowing the system of inductive logic developed by John Stuart Mill (1806–1873). Al-Razi's work was seen by later Islamic scholars as marking a new direction for Islamic logic, towards a Post-Avicennian logic. This was further elaborated by his student Afdaladdîn al-Khûnajî (d. 1249), who developed a form of logic revolving around the subject matter of conceptions and assents. In response to this tradition, Nasir al-Din al-Tusi (1201–1274) began a tradition of Neo-Avicennian logic which remained faithful to Avicenna's work and existed as an alternative to the more dominant Post-Avicennian school over the following centuries.
+The Illuminationist school was founded by Shahab al-Din Suhrawardi (1155–1191), who developed the idea of "decisive necessity", which refers to the reduction of all modalities (necessity, possibility, contingency and impossibility) to the single mode of necessity. Ibn al-Nafis (1213–1288) wrote a book on Avicennian logic, which was a commentary of Avicenna's Al-Isharat (The Signs) and Al-Hidayah (The Guidance). Ibn Taymiyyah (1263–1328), wrote the Ar-Radd 'ala al-Mantiqiyyin, where he argued against the usefulness, though not the validity, of the syllogism and in favour of inductive reasoning. Ibn Taymiyyah also argued against the certainty of syllogistic arguments and in favour of analogy; his argument is that concepts founded on induction are themselves not certain but only probable, and thus a syllogism based on such concepts is no more certain than an argument based on analogy. He further claimed that induction itself is founded on a process of analogy. His model of analogical reasoning was based on that of juridical arguments. This model of analogy has been used in the recent work of John F. Sowa.
+The Sharh al-takmil fi'l-mantiq written by Muhammad ibn Fayd Allah ibn Muhammad Amin al-Sharwani in the 15th century is the last major Arabic work on logic that has been studied. However, "thousands upon thousands of pages" on logic were written between the 14th and 19th centuries, though only a fraction of the texts written during this period have been studied by historians, hence little is known about the original work on Islamic logic produced during this later period.
+
+=== Logic in medieval Europe ===
+
+"Medieval logic" (also known as "Scholastic logic") generally means the form of Aristotelian logic developed in medieval Europe throughout roughly the period 1200–1600. For centuries after Stoic logic had been formulated, it was the dominant system of logic in the classical world. When the study of logic resumed after the Dark Ages, the main source was the work of the Christian philosopher Boethius, who was familiar with some of Aristotle's logic, but almost none of the work of the Stoics. Until the twelfth century, the only works of Aristotle available in the West were the Categories, On Interpretation, and Boethius's translation of the Isagoge of Porphyry (a commentary on the Categories). These works were known as the "Old Logic" (Logica Vetus or Ars Vetus). An important work in this tradition was the Logica Ingredientibus of Peter Abelard (1079–1142). His direct influence was small, but his influence through pupils such as John of Salisbury was great, and his method of applying rigorous logical analysis to theology shaped the way that theological criticism developed in the period that followed. The proof for the principle of explosion, also known as the principle of Pseudo-Scotus, the law according to which any proposition can be proven from a contradiction (including its negation), was first given by the 12th century French logician William of Soissons.
+By the early thirteenth century, the remaining works of Aristotle's Organon, including the Prior Analytics, Posterior Analytics, and the Sophistical Refutations (collectively known as the Logica Nova or "New Logic"), had been recovered in the West. Logical work until then was mostly paraphrasis or commentary on the work of Aristotle. The period from the middle of the thirteenth to the middle of the fourteenth century was one of significant developments in logic, particularly in three areas which were original, with little foundation in the Aristotelian tradition that came before. These were:
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+
+The theory of supposition. Supposition theory deals with the way that predicates (e.g., 'man') range over a domain of individuals (e.g., all men). In the proposition 'every man is an animal', does the term 'man' range over or 'supposit for' men existing just in the present, or does the range include past and future men? Can a term supposit for a non-existing individual? Some medievalists have argued that this idea is a precursor of modern first-order logic. "The theory of supposition with the associated theories of copulatio (sign-capacity of adjectival terms), ampliatio (widening of referential domain), and distributio constitute one of the most original achievements of Western medieval logic".
+The theory of syncategoremata. Syncategoremata are terms which are necessary for logic, but which, unlike categorematic terms, do not signify on their own behalf, but 'co-signify' with other words. Examples of syncategoremata are 'and', 'not', 'every', 'if', and so on.
+The theory of consequences. A consequence is a hypothetical, conditional proposition: two propositions joined by the terms 'if ... then'. For example, 'if a man runs, then God exists' (Si homo currit, Deus est). A fully developed theory of consequences is given in Book III of William of Ockham's work Summa Logicae. There, Ockham distinguishes between 'material' and 'formal' consequences, which are roughly equivalent to the modern material implication and logical implication respectively. Similar accounts are given by Jean Buridan and Albert of Saxony.
+The last great works in this tradition are the Logic of John Poinsot (1589–1644, known as John of St Thomas), the Metaphysical Disputations of Francisco Suarez (1548–1617), and the Logica Demonstrativa of Giovanni Girolamo Saccheri (1667–1733).
+
+== Traditional logic ==
+
+=== The textbook tradition ===
+
+Traditional logic generally means the textbook tradition that begins with Antoine Arnauld's and Pierre Nicole's Logic, or the Art of Thinking, better known as the Port-Royal Logic. Published in 1662, it was the most influential work on logic after Aristotle until the nineteenth century. The book presents a loosely Cartesian doctrine (that the proposition is a combining of ideas rather than terms, for example) within a framework that is broadly derived from Aristotelian and medieval term logic. Between 1664 and 1700, there were eight editions, and the book had considerable influence after that. The Port-Royal introduces the concepts of extension and intension. The account of propositions that Locke gives in the Essay is essentially that of the Port-Royal: "Verbal propositions, which are words, [are] the signs of our ideas, put together or separated in affirmative or negative sentences. So that proposition consists in the putting together or separating these signs, according as the things which they stand for agree or disagree."
+Dudley Fenner helped popularize Ramist logic, a reaction against Aristotle. Another influential work was the Novum Organum by Francis Bacon, published in 1620. The title translates as "new instrument". This is a reference to Aristotle's work known as the Organon. In this work, Bacon rejects the syllogistic method of Aristotle in favor of an alternative procedure "which by slow and faithful toil gathers information from things and brings it into understanding". This method is known as inductive reasoning, a method which starts from empirical observation and proceeds to lower axioms or propositions; from these lower axioms, more general ones can be induced. For example, in finding the cause of a phenomenal nature such as heat, three lists should be constructed:
+
+The presence list: a list of every situation where heat is found.
+The absence list: a list of every situation that is similar to at least one of those of the presence list, except for the lack of heat.
+The variability list: a list of every situation where heat can vary.
+Then, the form nature (or cause) of heat may be defined as that which is common to every situation of the presence list, and which is lacking from every situation of the absence list, and which varies by degree in every situation of the variability list.
+Other works in the textbook tradition include Isaac Watts's Logick: Or, the Right Use of Reason (1725), Richard Whately's Logic (1826), and John Stuart Mill's A System of Logic (1843). Although the latter was one of the last great works in the tradition, Mill's view that the foundations of logic lie in introspection influenced the view that logic is best understood as a branch of psychology, a view which dominated the next fifty years of its development, especially in Germany.
+
+=== Logic in Hegel's philosophy ===
+
+G.W.F. Hegel indicated the importance of logic to his philosophical system when he condensed his extensive Science of Logic into a shorter work published in 1817 as the first volume of his Encyclopaedia of the Philosophical Sciences. The "Shorter" or "Encyclopaedia" Logic, as it is often known, lays out a series of transitions which leads from the most empty and abstract of categories—Hegel begins with "Pure Being" and "Pure Nothing"—to the "Absolute", the category which contains and resolves all the categories which preceded it. Despite the title, Hegel's Logic is not really a contribution to the science of valid inference. Rather than deriving conclusions about concepts through valid inference from premises, Hegel seeks to show that thinking about one concept compels thinking about another concept (one cannot, he argues, possess the concept of "Quality" without the concept of "Quantity"); this compulsion is, supposedly, not a matter of individual psychology, because it arises almost organically from the content of the concepts themselves. His purpose is to show the rational structure of the "Absolute"—indeed of rationality itself. The method by which thought is driven from one concept to its contrary, and then to further concepts, is known as the Hegelian dialectic.
+Although Hegel's Logic has had little impact on mainstream logical studies, its influence can be seen elsewhere:
+
+Carl von Prantl's Geschichte der Logik im Abendland (1855–1867).
+The work of the British Idealists, such as F. H. Bradley's Principles of Logic (1883).
+The economic, political, and philosophical studies of Karl Marx, and in the various schools of Marxism.
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+
+=== Logic and psychology ===
+Between the work of Mill and Frege stretched half a century during which logic was widely treated as a descriptive science, an empirical study of the structure of reasoning, and thus essentially as a branch of psychology. The German psychologist Wilhelm Wundt, for example, discussed deriving "the logical from the psychological laws of thought", emphasizing that "psychological thinking is always the more comprehensive form of thinking." This view was widespread among German philosophers of the period:
+
+Theodor Lipps described logic as "a specific discipline of psychology".
+Christoph von Sigwart understood logical necessity as grounded in the individual's compulsion to think in a certain way.
+Benno Erdmann argued that "logical laws only hold within the limits of our thinking".
+Such was the dominant view of logic in the years following Mill's work. This psychological approach to logic was rejected by Gottlob Frege. It was also subjected to an extended and destructive critique by Edmund Husserl in the first volume of his Logical Investigations (1900), an assault which has been described as "overwhelming". Husserl argued forcefully that grounding logic in psychological observations implied that all logical truths remained unproven, and that skepticism and relativism were unavoidable consequences.
+Such criticisms did not immediately extirpate what is called "psychologism". For example, the American philosopher Josiah Royce, while acknowledging the force of Husserl's critique, remained "unable to doubt" that progress in psychology would be accompanied by progress in logic, and vice versa.
+
+== Rise of modern logic ==
+The period between the fourteenth century and the beginning of the nineteenth century had been largely one of decline and neglect, and is generally regarded as barren by historians of logic. The revival of logic occurred in the mid-nineteenth century, at the beginning of a revolutionary period where the subject developed into a rigorous and formalistic discipline whose exemplar was the exact method of proof used in mathematics. The development of the modern "symbolic" or "mathematical" logic during this period is the most significant in the 2000-year history of logic, and is arguably one of the most important and remarkable events in human intellectual history.
+A number of features distinguish modern logic from the old Aristotelian or traditional logic, the most important of which are as follows: Modern logic is fundamentally a calculus whose rules of operation are determined only by the shape and not by the meaning of the symbols it employs, as in mathematics. Many logicians were impressed by the "success" of mathematics, in that there had been no prolonged dispute about any truly mathematical result. C. S. Peirce noted that even though a mistake in the evaluation of a definite integral by Laplace led to an error concerning the moon's orbit that persisted for nearly 50 years, the mistake, once spotted, was corrected without any serious dispute. Peirce contrasted this with the disputation and uncertainty surrounding traditional logic, and especially reasoning in metaphysics. He argued that a truly "exact" logic would depend upon mathematical, i.e., "diagrammatic" or "iconic" thought. "Those who follow such methods will ... escape all error except such as will be speedily corrected after it is once suspected". Modern logic is also "constructive" rather than "abstractive"; i.e., rather than abstracting and formalising theorems derived from ordinary language (or from psychological intuitions about validity), it constructs theorems by formal methods, then looks for an interpretation in ordinary language. It is entirely symbolic, meaning that even the logical constants (which the medieval logicians called "syncategoremata") and the categoric terms are expressed in symbols.
+
+== Modern logic ==
+
+The development of modern logic falls into roughly five periods:
+
+The embryonic period from Leibniz to 1847, when the notion of a logical calculus was discussed and developed, particularly by Leibniz, but no schools were formed, and isolated periodic attempts were abandoned or went unnoticed.
+The algebraic period from Boole's Analysis to Schröder's Vorlesungen. In this period, there were more practitioners, and a greater continuity of development.
+The logicist period from the Begriffsschrift of Frege to the Principia Mathematica of Russell and Whitehead. The aim of the "logicist school" was to incorporate the logic of all mathematical and scientific discourse in a single unified system which, taking as a fundamental principle that all mathematical truths are logical, did not accept any non-logical terminology. The major logicists were Frege, Russell, and the early Wittgenstein. It culminates with the Principia, an important work which includes a thorough examination and attempted solution of the antinomies which had been an obstacle to earlier progress.
+The metamathematical period from 1910 to the 1930s, which saw the development of metalogic, in the finitist system of Hilbert, and the non-finitist system of Löwenheim and Skolem, the combination of logic and metalogic in the work of Gödel and Tarski. Gödel's incompleteness theorem of 1931 was one of the greatest achievements in the history of logic. Later in the 1930s, Gödel developed the notion of set-theoretic constructibility.
+The period after World War II, when mathematical logic branched into four inter-related but separate areas of research: model theory, proof theory, computability theory, and set theory, and its ideas and methods began to influence philosophy.
+
+=== Embryonic period ===
\ No newline at end of file
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+---
+title: "History of logic"
+chunk: 8/13
+source: "https://en.wikipedia.org/wiki/History_of_logic"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T03:59:53.898187+00:00"
+instance: "kb-cron"
+---
+
+The idea that inference could be represented by a purely mechanical process is found as early as Raymond Llull, who proposed a (somewhat eccentric) method of drawing conclusions by a system of concentric rings. The work of logicians such as the Oxford Calculators led to a method of using letters instead of writing out logical calculations (calculationes) in words, a method used, for instance, in the Logica magna by Paul of Venice. Three hundred years after Llull, the English philosopher and logician Thomas Hobbes suggested that all logic and reasoning could be reduced to the mathematical operations of addition and subtraction. The same idea is found in the work of Leibniz, who had read both Llull and Hobbes, and who argued that logic can be represented through a combinatorial process or calculus. But, like Llull and Hobbes, he failed to develop a detailed or comprehensive system, and his work on this topic was not published until long after his death. Leibniz says that ordinary languages are subject to "countless ambiguities" and are unsuited for a calculus, whose task is to expose mistakes in inference arising from the forms and structures of words; hence, he proposed to identify an alphabet of human thought comprising fundamental concepts which could be composed to express complex ideas, and create a calculus ratiocinator that would make all arguments "as tangible as those of the Mathematicians, so that we can find our error at a glance, and when there are disputes among persons, we can simply say: Let us calculate."
+
+Gergonne (1816) said that reasoning does not have to be about objects about which one has perfectly clear ideas, because algebraic operations can be carried out without having any idea of the meaning of the symbols involved. Bolzano anticipated a fundamental idea of modern proof theory when he defined logical consequence or "deducibility" in terms of variables:Hence I say that propositions 
+  
+    
+      
+        M
+      
+    
+    {\displaystyle M}
+  
+, 
+  
+    
+      
+        N
+      
+    
+    {\displaystyle N}
+  
+, 
+  
+    
+      
+        O
+      
+    
+    {\displaystyle O}
+  
+,... are deducible from propositions 
+  
+    
+      
+        A
+      
+    
+    {\displaystyle A}
+  
+, 
+  
+    
+      
+        B
+      
+    
+    {\displaystyle B}
+  
+, 
+  
+    
+      
+        C
+      
+    
+    {\displaystyle C}
+  
+, 
+  
+    
+      
+        D
+      
+    
+    {\displaystyle D}
+  
+,... with respect to variable parts 
+  
+    
+      
+        i
+      
+    
+    {\displaystyle i}
+  
+, 
+  
+    
+      
+        j
+      
+    
+    {\displaystyle j}
+  
+,..., if every class of ideas whose substitution for 
+  
+    
+      
+        i
+      
+    
+    {\displaystyle i}
+  
+, 
+  
+    
+      
+        j
+      
+    
+    {\displaystyle j}
+  
+,... makes all of 
+  
+    
+      
+        A
+      
+    
+    {\displaystyle A}
+  
+, 
+  
+    
+      
+        B
+      
+    
+    {\displaystyle B}
+  
+, 
+  
+    
+      
+        C
+      
+    
+    {\displaystyle C}
+  
+, 
+  
+    
+      
+        D
+      
+    
+    {\displaystyle D}
+  
+,... true, also makes all of 
+  
+    
+      
+        M
+      
+    
+    {\displaystyle M}
+  
+, 
+  
+    
+      
+        N
+      
+    
+    {\displaystyle N}
+  
+, 
+  
+    
+      
+        O
+      
+    
+    {\displaystyle O}
+  
+,... true. Occasionally, since it is customary, I shall say that propositions 
+  
+    
+      
+        M
+      
+    
+    {\displaystyle M}
+  
+, 
+  
+    
+      
+        N
+      
+    
+    {\displaystyle N}
+  
+, 
+  
+    
+      
+        O
+      
+    
+    {\displaystyle O}
+  
+,... follow, or can be inferred or derived, from 
+  
+    
+      
+        A
+      
+    
+    {\displaystyle A}
+  
+, 
+  
+    
+      
+        B
+      
+    
+    {\displaystyle B}
+  
+, 
+  
+    
+      
+        C
+      
+    
+    {\displaystyle C}
+  
+, 
+  
+    
+      
+        D
+      
+    
+    {\displaystyle D}
+  
+,.... Propositions 
+  
+    
+      
+        A
+      
+    
+    {\displaystyle A}
+  
+, 
+  
+    
+      
+        B
+      
+    
+    {\displaystyle B}
+  
+, 
+  
+    
+      
+        C
+      
+    
+    {\displaystyle C}
+  
+, 
+  
+    
+      
+        D
+      
+    
+    {\displaystyle D}
+  
+,... I shall call the premises, 
+  
+    
+      
+        M
+      
+    
+    {\displaystyle M}
+  
+, 
+  
+    
+      
+        N
+      
+    
+    {\displaystyle N}
+  
+, 
+  
+    
+      
+        O
+      
+    
+    {\displaystyle O}
+  
+,... the conclusions.This is now known as semantic validity.
+
+=== Algebraic period ===
+
+Modern logic begins with what is known as the "algebraic school", originating with Boole and including Peirce, Jevons, Schröder, and Venn. Their objective was to develop a calculus to formalise reasoning in the area of classes, propositions, and probabilities. The school begins with Boole's seminal work Mathematical Analysis of Logic which appeared in 1847, although De Morgan (1847) is its immediate precursor. The fundamental idea of Boole's system is that algebraic formulae can be used to express logical relations. This idea occurred to Boole in his teenage years, working as an usher in a private school in Lincoln, Lincolnshire. For example, let x and y stand for classes, let the symbol = signify that the classes have the same members, xy stand for the class containing all and only the members of x and y and so on. Boole calls these elective symbols, i.e. symbols which select certain objects for consideration. An expression in which elective symbols are used is called an elective function, and an equation of which the members are elective functions, is an elective equation. The theory of elective functions and their "development" is essentially the modern idea of truth-functions and their expression in disjunctive normal form.
+Boole's system admits of two interpretations, in class logic, and propositional logic. Boole distinguished between "primary propositions" which are the subject of syllogistic theory, and "secondary propositions", which are the subject of propositional logic, and showed how under different "interpretations" the same algebraic system could represent both. An example of a primary proposition is "All inhabitants are either Europeans or Asiatics." An example of a secondary proposition is "Either all inhabitants are Europeans or they are all Asiatics." These are easily distinguished in modern predicate logic, where it is also possible to show that the first follows from the second, but it is a significant disadvantage that there is no way of representing this in the Boolean system.
+In his Symbolic Logic (1881), John Venn used diagrams of overlapping areas to express Boolean relations between classes or truth-conditions of propositions. In 1869 Jevons realised that Boole's methods could be mechanised, and constructed a "logical machine" which he showed to the Royal Society the following year. In 1885 Allan Marquand proposed an electrical version of the machine that is still extant (picture at the Firestone Library).
\ No newline at end of file
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+++ b/data/en.wikipedia.org/wiki/History_of_logic-8.md
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+---
+title: "History of logic"
+chunk: 9/13
+source: "https://en.wikipedia.org/wiki/History_of_logic"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T03:59:53.898187+00:00"
+instance: "kb-cron"
+---
+
+The defects in Boole's system (such as the use of the letter v for existential propositions) were all remedied by his followers. Jevons published Pure Logic, or the Logic of Quality apart from Quantity in 1864, where he suggested a symbol to signify exclusive or, which allowed Boole's system to be greatly simplified. This was usefully exploited by Schröder when he set out theorems in parallel columns in his Vorlesungen (1890–1905). Peirce (1880) showed how all the Boolean elective functions could be expressed by the use of a single primitive binary operation, "neither ... nor ..." and equally well "not both ... and ...", however, like many of Peirce's innovations, this remained unknown or unnoticed until Sheffer rediscovered it in 1913. Boole's early work also lacks the idea of the logical sum which originates in Peirce (1867), Schröder (1877) and Jevons (1890), and the concept of inclusion, first suggested by Gergonne (1816) and clearly articulated by Peirce (1870).
+
+The success of Boole's algebraic system suggested that all logic must be capable of algebraic representation, and there were attempts to express a logic of relations in such form, of which the most ambitious was Schröder's monumental Vorlesungen über die Algebra der Logik ("Lectures on the Algebra of Logic", vol iii 1895), although the original idea was again anticipated by Peirce.
+Boole's unwavering acceptance of Aristotle's logic is emphasized by the historian of logic John Corcoran in an accessible introduction to Laws of Thought. Corcoran also wrote a point-by-point comparison of Prior Analytics and Laws of Thought. According to Corcoran, Boole fully accepted and endorsed Aristotle's logic. Boole's goals were "to go under, over, and beyond" Aristotle's logic by 1) providing it with mathematical foundations involving equations, 2) extending the class of problems it could treat—from assessing validity to solving equations—and 3) expanding the range of applications it could handle—e.g. from propositions having only two terms to those having arbitrarily many.
+More specifically, Boole agreed with what Aristotle said; Boole's 'disagreements', if they might be called that, concern what Aristotle did not say. 
+First, in the realm of foundations, Boole reduced the four propositional forms of Aristotelian logic to formulas in the form of equations—by itself a revolutionary idea. 
+Second, in the realm of logic's problems, Boole's addition of equation solving to logic—another revolutionary idea—involved Boole's doctrine that Aristotle's rules of inference (the "perfect syllogisms") must be supplemented by rules for equation solving. 
+Third, in the realm of applications, Boole's system could handle multi-term propositions and arguments whereas Aristotle could handle only two-termed subject-predicate propositions and arguments. For example, Aristotle's system could not deduce "No quadrangle that is a square is a rectangle that is a rhombus" from "No square that is a quadrangle is a rhombus that is a rectangle" or from "No rhombus that is a rectangle is a square that is a quadrangle".
+
+=== Logicist period ===
+
+After Boole, the next great advances were made by the German mathematician Gottlob Frege. Frege's objective was the program of Logicism, i.e. demonstrating that arithmetic is identical with logic. Frege went much further than any of his predecessors in his rigorous and formal approach to logic, and his calculus or Begriffsschrift is important. Frege also tried to show that the concept of number can be defined by purely logical means, so that (if he was right) logic includes arithmetic and all branches of mathematics that are reducible to arithmetic. He was not the first writer to suggest this. In his pioneering work Die Grundlagen der Arithmetik (The Foundations of Arithmetic), sections 15–17, he acknowledges the efforts of Leibniz, J. S. Mill as well as Jevons, citing the latter's claim that "algebra is a highly developed logic, and number but logical discrimination."
+Frege's first work, the Begriffsschrift ("concept script") is a rigorously axiomatised system of propositional logic, relying on just two connectives (negational and conditional), two rules of inference (modus ponens and substitution), and six axioms. Frege referred to the "completeness" of this system, but was unable to prove this. The most significant innovation, however, was his explanation of the quantifier in terms of mathematical functions. Traditional logic regards the sentence "Caesar is a man" as of fundamentally the same form as "all men are mortal." Sentences with a proper name subject were regarded as universal in character, interpretable as "every Caesar is a man". At the outset Frege abandons the traditional "concepts subject and predicate", replacing them with argument and function respectively, which he believes "will stand the test of time". He goes on to say that it is "easy to see how regarding a content as a function of an argument leads to the formation of concepts. Furthermore, the demonstration of the connection between the meanings of the words if, and, not, or, there is, some, all, and so forth, deserves attention". Frege argued that the quantifier expression "all men" does not have the same logical or semantic form as "all men", and that the universal proposition "every A is B" is a complex proposition involving two functions, namely ' – is A' and ' – is B' such that whatever satisfies the first, also satisfies the second. In modern notation, this would be expressed as
+
+  
+    
+      
+        ∀
+        
+        x
+        
+          
+            (
+          
+        
+        A
+        (
+        x
+        )
+        →
+        B
+        (
+        x
+        )
+        
+          
+            )
+          
+        
+      
+    
+    {\displaystyle \forall \;x{\big (}A(x)\rightarrow B(x){\big )}}
+  
\ No newline at end of file
diff --git a/data/en.wikipedia.org/wiki/History_of_logic-9.md b/data/en.wikipedia.org/wiki/History_of_logic-9.md
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index 000000000..1d35e4a55
--- /dev/null
+++ b/data/en.wikipedia.org/wiki/History_of_logic-9.md
@@ -0,0 +1,260 @@
+---
+title: "History of logic"
+chunk: 10/13
+source: "https://en.wikipedia.org/wiki/History_of_logic"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T03:59:53.898187+00:00"
+instance: "kb-cron"
+---
+
+In English, "for all x, if Ax then Bx". Thus only singular propositions are of subject-predicate form, and they are irreducibly singular, i.e. not reducible to a general proposition. Universal and particular propositions, by contrast, are not of simple subject-predicate form at all. If "all mammals" were the logical subject of the sentence "all mammals are land-dwellers", then to negate the whole sentence we would have to negate the predicate to give "all mammals are not land-dwellers". But this is not the case. This functional analysis of ordinary-language sentences later had a great impact on philosophy and linguistics.
+This means that in Frege's calculus, Boole's "primary" propositions can be represented in a different way from "secondary" propositions. "All inhabitants are either men or women" is
+
+  
+    
+      
+        ∀
+        
+        x
+        
+          
+            (
+          
+        
+        I
+        (
+        x
+        )
+        →
+        
+          
+            (
+          
+        
+        M
+        (
+        x
+        )
+        ∨
+        W
+        (
+        x
+        )
+        
+          
+            )
+          
+        
+        
+          
+            )
+          
+        
+      
+    
+    {\displaystyle \forall \;x{\Big (}I(x)\rightarrow {\big (}M(x)\lor W(x){\big )}{\Big )}}
+  
+
+whereas "All the inhabitants are men or all the inhabitants are women" is
+
+  
+    
+      
+        ∀
+        
+        x
+        
+          
+            (
+          
+        
+        I
+        (
+        x
+        )
+        →
+        M
+        (
+        x
+        )
+        
+          
+            )
+          
+        
+        ∨
+        ∀
+        
+        x
+        
+          
+            (
+          
+        
+        I
+        (
+        x
+        )
+        →
+        W
+        (
+        x
+        )
+        
+          
+            )
+          
+        
+      
+    
+    {\displaystyle \forall \;x{\big (}I(x)\rightarrow M(x){\big )}\lor \forall \;x{\big (}I(x)\rightarrow W(x){\big )}}
+  
+
+As Frege remarked in a critique of Boole's calculus:
+
+"The real difference is that I avoid [the Boolean] division into two parts ... and give a homogeneous presentation of the lot. In Boole the two parts run alongside one another, so that one is like the mirror image of the other, but for that very reason stands in no organic relation to it."
+As well as providing a unified and comprehensive system of logic, Frege's calculus also resolved the ancient problem of multiple generality. The ambiguity of "every girl kissed a boy" is difficult to express in traditional logic, but Frege's logic resolves this through the different scope of the quantifiers. Thus
+
+  
+    
+      
+        ∀
+        
+        x
+        
+          
+            (
+          
+        
+        G
+        (
+        x
+        )
+        →
+        ∃
+        
+        y
+        
+          
+            (
+          
+        
+        B
+        (
+        y
+        )
+        ∧
+        K
+        (
+        x
+        ,
+        y
+        )
+        
+          
+            )
+          
+        
+        
+          
+            )
+          
+        
+      
+    
+    {\displaystyle \forall \;x{\Big (}G(x)\rightarrow \exists \;y{\big (}B(y)\land K(x,y){\big )}{\Big )}}
+  
+
+means that to every girl there corresponds some boy (any one will do) who the girl kissed. But
+
+  
+    
+      
+        ∃
+        
+        x
+        
+          
+            (
+          
+        
+        B
+        (
+        x
+        )
+        ∧
+        ∀
+        
+        y
+        
+          
+            (
+          
+        
+        G
+        (
+        y
+        )
+        →
+        K
+        (
+        y
+        ,
+        x
+        )
+        
+          
+            )
+          
+        
+        
+          
+            )
+          
+        
+      
+    
+    {\displaystyle \exists \;x{\Big (}B(x)\land \forall \;y{\big (}G(y)\rightarrow K(y,x){\big )}{\Big )}}
+  
+
+means that there is some particular boy whom every girl kissed. Without this device, the project of logicism would have been doubtful or impossible. Using it, Frege provided a definition of the ancestral relation, of the many-to-one relation, and of mathematical induction.
+
+This period overlaps with the work of what is known as the "mathematical school", which included Dedekind, Pasch, Peano, Hilbert, Zermelo, Huntington, Veblen and Heyting. Their objective was the axiomatisation of branches of mathematics like geometry, arithmetic, analysis and set theory. Most notable was Hilbert's Program, which sought to ground all of mathematics to a finite set of axioms, proving its consistency by "finitistic" means and providing a procedure which would decide the truth or falsity of any mathematical statement. The standard axiomatization of the natural numbers is named the Peano axioms eponymously. Peano maintained a clear distinction between mathematical and logical symbols. While unaware of Frege's work, he independently recreated his logical apparatus based on the work of Boole and Schröder.
+The logicist project received a near-fatal setback with the discovery of a paradox in 1901 by Bertrand Russell. This proved Frege's naive set theory led to a contradiction. Frege's theory contained the axiom that for any formal criterion, there is a set of all objects that meet the criterion. Russell showed that a set containing exactly the sets that are not members of themselves would contradict its own definition (if it is not a member of itself, it is a member of itself, and if it is a member of itself, it is not). This contradiction is now known as Russell's paradox. One important method of resolving this paradox was proposed by Ernst Zermelo. Zermelo set theory was the first axiomatic set theory. It was developed into the now-canonical Zermelo–Fraenkel set theory (ZF). Russell's paradox symbolically is as follows:
+
+  
+    
+      
+        
+          Let 
+        
+        R
+        =
+        {
+        x
+        ∣
+        x
+        ∉
+        x
+        }
+        
+          , then 
+        
+        R
+        ∈
+        R
+        
+        ⟺
+        
+        R
+        ∉
+        R
+      
+    
+    {\displaystyle {\text{Let }}R=\{x\mid x\not \in x\}{\text{, then }}R\in R\iff R\not \in R}
+  
+
+The monumental Principia Mathematica, a three-volume work on the foundations of mathematics, written by Russell and Alfred North Whitehead and published 1910–1913 also included an attempt to resolve the paradox, by means of an elaborate system of types: a set of elements is of a different type than is each of its elements (set is not the element; one element is not the set) and one cannot speak of the "set of all sets". The Principia was an attempt to derive all mathematical truths from a well-defined set of axioms and inference rules in symbolic logic.
+
+=== Metamathematical period ===
\ No newline at end of file
diff --git a/data/en.wikipedia.org/wiki/History_of_mathematics-0.md b/data/en.wikipedia.org/wiki/History_of_mathematics-0.md
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+---
+title: "History of mathematics"
+chunk: 1/13
+source: "https://en.wikipedia.org/wiki/History_of_mathematics"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T03:59:56.476741+00:00"
+instance: "kb-cron"
+---
+
+The history of mathematics deals with the origin of discoveries in mathematics and the mathematical methods and notation of the past. Before the modern age and worldwide spread of knowledge, written examples of new mathematical developments have come to light only in a few locales. From 3000 BC the Mesopotamian states of Sumer, Akkad and Assyria, followed closely by Ancient Egypt and the Levantine state of Ebla began using arithmetic, algebra and geometry for taxation, commerce, trade, and in astronomy, to record time and formulate calendars.
+The earliest mathematical texts available are from Mesopotamia and Egypt – Plimpton 322 (Babylonian c. 2000 – 1900 BC), the Rhind Mathematical Papyrus (Egyptian c. 1800 BC) and the Moscow Mathematical Papyrus (Egyptian c. 1890 BC). All these texts mention the so-called Pythagorean triples, so, by inference, the Pythagorean theorem seems to be the most ancient and widespread mathematical development, after basic arithmetic and geometry.
+The study of mathematics as a "demonstrative discipline" began in the 6th century BC with the Pythagoreans, who coined the term "mathematics" from the ancient Greek μάθημα (mathema), meaning "subject of instruction". Greek mathematics greatly refined the methods (especially through the introduction of deductive reasoning and mathematical rigor in proofs) and expanded the subject matter of mathematics. The ancient Romans used applied mathematics in surveying, structural engineering, mechanical engineering, bookkeeping, creation of lunar and solar calendars, and even arts and crafts. Chinese mathematics made early contributions, including a place value system and the first use of negative numbers. The Hindu–Arabic numeral system and the rules for the use of its operations, in use throughout the world today, evolved over the course of the first millennium AD in India and were transmitted to the Western world via Islamic mathematics through the work of Khwārizmī. Islamic mathematics, in turn, developed and expanded the mathematics known to these civilizations. Contemporaneous with but independent of these traditions were the mathematics developed by the Maya civilization of Mexico and Central America, where the concept of zero was given a standard symbol in Maya numerals.
+Many Greek and Arabic texts on mathematics were translated into Latin from the 12th century, leading to further development of mathematics in Medieval Europe. From ancient times through the Middle Ages, periods of mathematical discovery were often followed by centuries of stagnation. Beginning in Renaissance Italy in the 15th century, new mathematical developments, interacting with new scientific discoveries, were made at an increasing pace that continues through the present day. This includes the groundbreaking work of both Isaac Newton and Gottfried Wilhelm Leibniz in the development of infinitesimal calculus during the 17th century and subsequent discoveries of German mathematicians like Carl Friedrich Gauss and David Hilbert.
+
+== Prehistoric ==
+The origins of mathematical thought lie in the concepts of number, patterns in nature, magnitude, and form. Modern studies of animal cognition have shown that these concepts are not unique to humans. Such concepts would have been part of everyday life in hunter-gatherer societies. The idea of the "number" concept evolving gradually over time is supported by the existence of languages that preserve the distinction between "one", "two", and "many", but not of numbers larger than two.
+The use of yarn by Neanderthals some 40,000 years ago at a site in Abri du Maras in the south of France suggests they knew basic concepts in mathematics. The Ishango bone, found near the headwaters of the Nile river (northeastern Congo), may be more than 20,000 years old and consists of a series of marks carved in three columns running the length of the bone. Common interpretations are that the Ishango bone shows either a tally of the earliest known demonstration of sequences of prime numbers or a six-month lunar calendar. Peter Rudman argues that the development of the concept of prime numbers could only have come about after the concept of division, which he dates to after 10,000 BC, with prime numbers probably not being understood until about 500 BC. He also writes that "no attempt has been made to explain why a tally of something should exhibit multiples of two, prime numbers between 10 and 20, and some numbers that are almost multiples of 10." The Ishango bone, according to scholar Alexander Marshack, may have influenced the later development of mathematics in Egypt as, like some entries on the Ishango bone, Egyptian arithmetic also made use of multiplication by 2; this however, is disputed.
+Predynastic Egyptians of the 5th millennium BC pictorially represented geometric designs. It has been claimed that megalithic monuments in England and Scotland, dating from the 3rd millennium BC, incorporate geometric ideas such as circles, ellipses, and Pythagorean triples in their design. All of the above are disputed, however, and the currently oldest undisputed mathematical documents are from Babylonian and dynastic Egyptian sources.
+
+== Babylonian ==
+
+Babylonian mathematics refers to any mathematics of the peoples of Mesopotamia (modern Iraq) from the days of the early Sumerians through the Hellenistic period, almost to the dawn of Christianity. The majority of Babylonian mathematical work comes from two widely separated periods: The first few hundred years of the second millennium BC (Old Babylonian period) and the last few centuries of the first millennium BC (Seleucid period). It is named Babylonian mathematics due to the central role of Babylon as a place of study.
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+title: "History of mathematics"
+chunk: 2/13
+source: "https://en.wikipedia.org/wiki/History_of_mathematics"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T03:59:56.476741+00:00"
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+---
+
+In contrast to the sparsity of sources in Egyptian mathematics, knowledge of Babylonian mathematics is derived from more than 400 clay tablets unearthed since the 1850s. Written in Cuneiform script, tablets were inscribed whilst the clay was moist, and baked hard in an oven or by the heat of the sun. Some of these appear to be graded homework.
+The earliest evidence of written mathematics dates back to the ancient Sumerians, who built the earliest civilization in Mesopotamia. They developed a complex system of metrology from 3000 BC that was chiefly concerned with administrative/financial counting, such as grain allotments, workers, weights of silver, or even liquids, among other things. From around 2500 BC onward, the Sumerians wrote multiplication tables on clay tablets and dealt with geometrical exercises and division problems. The earliest traces of the Babylonian numerals also date back to this period.
+
+Babylonian mathematics was written using a sexagesimal (base-60) numeral system. From this derives the modern-day usage of 60 seconds in a minute, 60 minutes in an hour, and 360 (60 × 6) degrees in a circle, as well as the use of seconds and minutes of arc to denote fractions of a degree. It is thought the sexagesimal system was initially used by Sumerian scribes because 60 can be evenly divided by 2, 3, 4, 5, 6, 10, 12, 15, 20 and 30, and for scribes (doling out the aforementioned grain allotments, recording weights of silver, etc.) being able to easily calculate by hand was essential, and so a sexagesimal system is pragmatically easier to calculate by hand with; however, there is the possibility that using a sexagesimal system was an ethno-linguistic phenomenon (that might not ever be known), and not a mathematical/practical decision. Also, unlike the Egyptians, Greeks, and Romans, the Babylonians had a place-value system, where digits written in the left column represented larger values, much as in the decimal system. The power of the Babylonian notational system lay in that it could be used to represent fractions as easily as whole numbers; thus, multiplying two numbers that contained fractions was no different from multiplying integers, similar to modern notation. The notational system of the Babylonians was the best of any civilization until the Renaissance, and its power allowed it to achieve remarkable computational accuracy; for example, the Babylonian tablet YBC 7289 gives an approximation of √2 accurate to five decimal places. The Babylonians lacked, however, an equivalent of the decimal point, and so the place value of a symbol often had to be inferred from the context. By the Seleucid period, the Babylonians had developed a zero symbol as a placeholder for empty positions; however, it was only used for intermediate positions. This zero sign does not appear in terminal positions; thus, the Babylonians came close but did not develop a true place value system.
+Other topics covered by Babylonian mathematics include fractions, algebra, quadratic and cubic equations, and the calculation of regular numbers and their reciprocal pairs. The tablets also include multiplication tables and methods for solving linear, quadratic equations, and cubic equations, a remarkable achievement for the time. Tablets from the Old Babylonian period also contain the earliest known statement of the Pythagorean theorem. However, as with Egyptian mathematics, Babylonian mathematics shows no awareness of the difference between exact and approximate solutions, or the solvability of a problem, and most importantly, no explicit statement of the need for proofs or logical principles.
+
+== Egyptian ==
+
+Egyptian mathematics refers to mathematics written in the Egyptian language. From the Hellenistic period, Greek replaced Egyptian as the written language of Egyptian scholars. Archaeological evidence has suggested that the Ancient Egyptian counting system had origins in Sub-Saharan Africa. Also, fractal geometry designs which are widespread among Sub-Saharan African cultures are also found in Egyptian architecture and cosmological signs. Megalithic structures located in Nabta Playa, Upper Egypt featured astronomy, calendar arrangements in alignment with the heliacal rising of Sirius and supported calibration the yearly calendar for the annual Nile flood.
+The most extensive Egyptian mathematical text is the Rhind papyrus (sometimes also called the Ahmes Papyrus after its author), dated to c. 1650 BC but likely a copy of an older document from the Middle Kingdom of about 2000–1800 BC. It is an instruction manual for students in arithmetic and geometry. In addition to giving area formulas and methods for multiplication, division and working with unit fractions, it also contains evidence of other mathematical knowledge, including composite and prime numbers; arithmetic, geometric and harmonic means; and simplistic understandings of both the Sieve of Eratosthenes and perfect number theory (namely, that of the number 6). It also shows how to solve first order linear equations as well as arithmetic and geometric series.
+Another significant Egyptian mathematical text is the Moscow papyrus, also from the Middle Kingdom period, dated to c. 1890 BC. It consists of what are today called word problems or story problems, which were apparently intended as entertainment. One problem is considered to be of particular importance because it gives a method for finding the volume of a frustum (truncated pyramid).
+Finally, the Berlin Papyrus 6619 (c. 1800 BC) shows that ancient Egyptians could solve a second-order algebraic equation.
+
+== Greek ==
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+---
+
+This century saw the development of the two forms of non-Euclidean geometry, where the parallel postulate of Euclidean geometry no longer holds.
+The Russian mathematician Nikolai Ivanovich Lobachevsky and his rival, the Hungarian mathematician János Bolyai, independently defined and studied hyperbolic geometry, where uniqueness of parallels no longer holds. In this geometry the sum of angles in a triangle add up to less than 180°. Elliptic geometry was developed later in the 19th century by the German mathematician Bernhard Riemann; here no parallel can be found and the angles in a triangle add up to more than 180°. Riemann also developed Riemannian geometry, which unifies and vastly generalizes the three types of geometry, and he defined the concept of a manifold, which generalizes the ideas of curves and surfaces, and set the mathematical foundations for the theory of general relativity.
+The 19th century saw the beginning of a great deal of abstract algebra. Hermann Grassmann in Germany gave a first version of vector spaces, William Rowan Hamilton in Ireland developed noncommutative algebra.The British mathematician George Boole devised an algebra that soon evolved into what is now called Boolean algebra, in which the only numbers were 0 and 1. Boolean algebra is the starting point of mathematical logic and has important applications in electrical engineering and computer science. 
+Augustin-Louis Cauchy, Bernhard Riemann,  and Karl Weierstrass reformulated the calculus in a more rigorous fashion.
+Also, for the first time, the limits of mathematics were explored. Paolo Ruffini, Niels Henrik Abel, and Évariste Galois proved there is no general algebraic method for solving polynomial equations of degree greater than four (Abel–Ruffini theorem). Other 19th-century mathematicians used this in their proofs that straight edge and compass alone are not sufficient to trisect an arbitrary angle, to construct the side of a cube twice the volume of a given cube, nor to construct a square equal in area to a given circle. Mathematicians had vainly attempted to solve these problems since the ancient Greeks. On the other hand, the limitation of three dimensions in geometry was surpassed in the 19th century through considerations of parameter space and hypercomplex numbers.
+Abel and Galois's investigations into the solutions of various polynomial equations laid the groundwork for further developments of group theory, and the associated fields of abstract algebra. In the 20th century physicists and other scientists have seen group theory as the ideal way to study symmetry.
+
+In the later 19th century, Georg Cantor established the first foundations of set theory, which enabled the rigorous treatment of the notion of infinity and has become the common language of nearly all mathematics. Cantor's set theory, and the rise of mathematical logic in the hands of Peano, L.E.J. Brouwer, David Hilbert, Bertrand Russell, and A.N. Whitehead, initiated a long running debate on the foundations of mathematics.
+The 19th century saw the founding of a number of national mathematical societies: the London Mathematical Society in 1865, the Société mathématique de France in 1872, the Circolo Matematico di Palermo in 1884, the Edinburgh Mathematical Society in 1883, and the American Mathematical Society in 1888. The first international, special-interest society, the Quaternion Association, was formed in 1899, in the context of a vector controversy. In 1897, Kurt Hensel introduced p-adic numbers.
+
+=== 20th century ===
+The 20th century saw mathematics become a major profession. By the end of the century, thousands of new Ph.D.s in mathematics were being awarded every year, and jobs were available in both teaching and industry. An effort to catalogue the areas and applications of mathematics was undertaken in Klein's encyclopedia.
+In a 1900 speech to the International Congress of Mathematicians, David Hilbert set out a list of 23 unsolved problems in mathematics. These problems, spanning many areas of mathematics, formed a central focus for much of 20th-century mathematics. 10 have been solved, 7 partially solved, and 2 are still open. The remaining 4 are too loosely formulated to be stated as solved or not.
+
+Notable historical conjectures were finally proven. In 1976, Wolfgang Haken and Kenneth Appel proved the four color theorem, controversial at the time for the use of a computer to do so. Andrew Wiles, building on the work of others, proved Fermat's Last Theorem in 1995. Paul Cohen and Kurt Gödel proved that the continuum hypothesis is independent of (could neither be proved nor disproved from) the standard axioms of set theory. In 1998, Thomas Callister Hales proved the Kepler conjecture, also using a computer.
+Mathematical collaborations of unprecedented size and scope took place. An example is the classification of finite simple groups (also called the "enormous theorem"), whose proof between 1955 and 2004 required 500-odd journal articles by about 100 authors, and filling tens of thousands of pages. A group of French mathematicians, including Jean Dieudonné and André Weil, publishing under the pseudonym "Nicolas Bourbaki", attempted to exposit all of known mathematics as a coherent rigorous whole. The resulting several dozen volumes has had a controversial influence on mathematical education.
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+
+Differential geometry came into its own when Albert Einstein used it in general relativity. Entirely new areas of mathematics such as mathematical logic, topology, and John von Neumann's game theory changed the kinds of questions that could be answered by mathematical methods. All kinds of structures were abstracted using axioms and given names like metric spaces, topological spaces etc. The concept of an abstract structure was itself abstracted and led to category theory. Grothendieck and Serre recast algebraic geometry using sheaf theory. Large advances were made in the qualitative study of dynamical systems that Poincaré had begun in the 1890s.
+Measure theory was developed in the late 19th and early 20th centuries. Applications of measures include the Lebesgue integral, Kolmogorov's axiomatisation of probability theory, and ergodic theory. Knot theory greatly expanded. Quantum mechanics aided the development of functional analysis, a branch of mathematics developed by Stefan Banach and his collaborators who formed the Lwów School of Mathematics. Other new areas include Laurent Schwartz's distribution theory, fixed point theory, singularity theory and René Thom's catastrophe theory, model theory, and Mandelbrot's fractals. Lie theory with its Lie groups and Lie algebras became one of the major areas of study.
+Nonstandard analysis, introduced by Abraham Robinson, rehabilitated the infinitesimal approach to calculus, which had fallen into disrepute in favour of the theory of limits, by extending the field of real numbers to the Hyperreal numbers which include infinitesimal and infinite quantities. An even larger number system, the surreal numbers were discovered by John Horton Conway in connection with combinatorial games.
+The development and continual improvement of computers, at first mechanical analog machines and then digital electronic machines, allowed industry to deal with larger and larger amounts of data to facilitate mass production and distribution and communication, and new areas of mathematics were developed to deal with this: Alan Turing's computability theory; complexity theory; Derrick Henry Lehmer's use of ENIAC to further number theory and the Lucas–Lehmer primality test; Rózsa Péter's recursive function theory; Claude Shannon's information theory; signal processing; data analysis; optimization and other areas of operations research. In the preceding centuries much mathematical focus was on calculus and continuous functions, but the rise of computing and communication networks led to an increasing importance of discrete concepts and the expansion of combinatorics including graph theory. The speed and data processing abilities of computers also enabled the handling of mathematical problems that were too time-consuming to deal with by pencil and paper calculations, leading to areas such as numerical analysis and computer algebra. Some of the most important methods and algorithms of the 20th century are: the simplex algorithm, the fast Fourier transform, error-correcting codes, the Kalman filter from control theory and the RSA algorithm of public-key cryptography.
+At the same time, deep insights were made about the limitations to mathematics. In 1929 and 1930, it was proved by Mojżesz Presburger, that the truth or falsity of all statements formulated about the natural numbers plus either addition or multiplication (but not both), was decidable, i.e. could be determined by some algorithm. In 1931, Kurt Gödel found that this was not the case for the natural numbers plus both addition and multiplication; this system, known as Peano arithmetic, was in fact incomplete. (Peano arithmetic is adequate for a good deal of number theory, including the notion of prime number.) A consequence of Gödel's two incompleteness theorems is that in any mathematical system that includes Peano arithmetic (including all of analysis and geometry), truth necessarily outruns proof, i.e. there are true statements that cannot be proved within the system. Hence mathematics cannot be reduced to mathematical logic, and David Hilbert's dream of making all of mathematics complete and consistent needed to be reformulated.
+
+One of the more colorful figures in 20th-century mathematics was Srinivasa Ramanujan (1887–1920), an Indian autodidact who conjectured or proved over 3000 theorems, including properties of highly composite numbers, the partition function and its asymptotics, and mock theta functions. He also made major investigations in the areas of gamma functions, modular forms, divergent series, hypergeometric series and prime number theory.
+Paul Erdős published more papers than any other mathematician in history, working with hundreds of collaborators. Mathematicians have a game equivalent to the Kevin Bacon Game, which leads to the Erdős number of a mathematician. This describes the "collaborative distance" between a person and Erdős, as measured by joint authorship of mathematical papers.
+Emmy Noether has been described by many as the most important woman in the history of mathematics. She studied the theories of rings, fields, and algebras.
+As in most areas of study, the explosion of knowledge in the scientific age has led to specialization: by the end of the century, there were hundreds of specialized areas in mathematics, and the Mathematics Subject Classification was dozens of pages long. More and more mathematical journals were published and, by the end of the century, the development of the World Wide Web led to online publishing.
+
+=== 21st century ===
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+title: "History of mathematics"
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+date_saved: "2026-05-05T03:59:56.476741+00:00"
+instance: "kb-cron"
+---
+
+In 2000, the Clay Mathematics Institute announced the seven Millennium Prize Problems. In 2003 the Poincaré conjecture was solved by Grigori Perelman (who declined to accept an award, as he was critical of the mathematics establishment).
+Most mathematical journals now have online versions as well as print versions, and many online-only journals are launched. There is an increasing drive toward open access publishing, first made popular by arXiv.
+Many other important problems have been solved in this century. Examples include the Green–Tao theorem (2004), existence of bounded gaps between arbitrarily large primes (2013), and the modularity theorem (2001). The AKS primality test was published in 2002, which is the first algorithm that can determine whether a number is prime or composite in polynomial time. A proof of Goldbach's weak conjecture was published by Harald Helfgott in 2013; as of 2025, the proof has not yet been fully reviewed. The first einstein was discovered in 2023.
+In addition, a lot of work has been done toward long-lasting projects which began in the twentieth century. For example, the classification of finite simple groups was completed in 2008. Similarly, work on the Langlands program has progressed significantly, and there have been proofs of the fundamental lemma (2008), as well as a proposed proof of the geometric Langlands correspondence in 2024.
+
+== Future ==
+
+There are many observable trends in mathematics, the most notable being that the subject is growing ever larger as computers are ever more important and powerful; the volume of data being produced by science and industry, facilitated by computers, continues expanding exponentially. As a result, there is a corresponding growth in the demand for mathematics to help process and understand this big data. Math science careers are also expected to continue to grow, with the US Bureau of Labor Statistics estimating (in 2018) that "employment of mathematical science occupations is projected to grow 27.9 percent from 2016 to 2026."
+
+== See also ==
+
+== Notes ==
+
+== References ==
+
+=== Works cited ===
+
+== Further reading ==
+
+=== General ===
+Aaboe, Asger (1964). Episodes from the Early History of Mathematics. New York: Random House.
+Bell, E. T. (1937). Men of Mathematics. Simon and Schuster.
+Burton, David M. (1997). The History of Mathematics: An Introduction. McGraw Hill.
+Grattan-Guinness, Ivor (2003). Companion Encyclopedia of the History and Philosophy of the Mathematical Sciences. The Johns Hopkins University Press. ISBN 978-0-8018-7397-3.
+Kline, Morris. Mathematical Thought from Ancient to Modern Times.
+Struik, D. J. (1987). A Concise History of Mathematics, fourth revised edition. Dover Publications, New York.
+
+=== Books on a specific period ===
+Gillings, Richard J. (1972). Mathematics in the Time of the Pharaohs. Cambridge, MA: MIT Press.
+Heath, Thomas Little (1921). A History of Greek Mathematics. Oxford, Claredon Press.
+van der Waerden, B. L. (1983). Geometry and Algebra in Ancient Civilizations, Springer, ISBN 0-387-12159-5.
+
+=== Books on a specific topic ===
+Corry, Leo (2015), A Brief History of Numbers, Oxford University Press, ISBN 978-0198702597
+Hoffman, Paul (1998). The Man Who Loved Only Numbers: The Story of Paul Erdős and the Search for Mathematical Truth. Hyperion. ISBN 0-7868-6362-5.
+Menninger, Karl W. (1969). Number Words and Number Symbols: A Cultural History of Numbers. MIT Press. ISBN 978-0-262-13040-0.
+Stigler, Stephen M. (1990). The History of Statistics: The Measurement of Uncertainty before 1900. Belknap Press. ISBN 978-0-674-40341-3.
+
+== External links ==
+
+=== Documentaries ===
+BBC (2008). The Story of Maths.
+Renaissance Mathematics, BBC Radio 4 discussion with Robert Kaplan, Jim Bennett & Jackie Stedall (In Our Time, Jun 2, 2005)
+
+=== Educational material ===
+MacTutor History of Mathematics archive (John J. O'Connor and Edmund F. Robertson; University of St Andrews, Scotland). An award-winning website containing detailed biographies on many historical and contemporary mathematicians, as well as information on notable curves and various topics in the history of mathematics.
+History of Mathematics Home Page (David E. Joyce; Clark University). Articles on various topics in the history of mathematics with an extensive bibliography.
+The History of Mathematics (David R. Wilkins; Trinity College, Dublin). Collections of material on the mathematics between the 17th and 19th century.
+Earliest Known Uses of Some of the Words of Mathematics (Jeff Miller). Contains information on the earliest known uses of terms used in mathematics.
+Earliest Uses of Various Mathematical Symbols (Jeff Miller). Contains information on the history of mathematical notations.
+Mathematical Words: Origins and Sources (John Aldrich, University of Southampton) Discusses the origins of the modern mathematical word stock.
+Biographies of Women Mathematicians (Larry Riddle; Agnes Scott College).
+Mathematicians of the African Diaspora (Scott W. Williams; University at Buffalo).
+Notes for MAA minicourse: teaching a course in the history of mathematics. (2009) (V. Frederick Rickey & Victor J. Katz).
+Ancient Rome: The Odometer Of Vitruv. Pictorial (moving) re-construction of Vitusius' Roman ododmeter.
+
+=== Bibliographies ===
+A Bibliography of Collected Works and Correspondence of Mathematicians archive dated 2007/3/17 (Steven W. Rockey; Cornell University Library).
+
+=== Organizations ===
+International Commission for the History of Mathematics
+
+=== Journals ===
+Historia Mathematica
+Convergence Archived 2020-09-08 at the Wayback Machine, the Mathematical Association of America's online Math History Magazine
+History of Mathematics Archived 2006-10-04 at the Wayback Machine Math Archives (University of Tennessee, Knoxville)
+History/Biography The Math Forum (Drexel University)
+History of Mathematics (Courtright Memorial Library).
+History of Mathematics Web Sites Archived 2009-05-25 at the Wayback Machine (David Calvis; Baldwin-Wallace College)
+Historia de las Matemáticas (Universidad de La La guna)
+História da Matemática (Universidade de Coimbra)
+Using History in Math Class
+Mathematical Resources: History of Mathematics (Bruno Kevius)
+History of Mathematics (Roberta Tucci)
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+title: "History of mathematics"
+chunk: 3/13
+source: "https://en.wikipedia.org/wiki/History_of_mathematics"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T03:59:56.476741+00:00"
+instance: "kb-cron"
+---
+
+Greek mathematics refers to the mathematics written in the Greek language from the time of Thales of Miletus (~600 BC) to the closure of the Academy of Athens in 529 AD. Greek mathematicians lived in cities spread over the entire Eastern Mediterranean, from Italy to North Africa, but were united by culture and language. Greek mathematics of the period following Alexander the Great is sometimes called Hellenistic mathematics.
+Greek mathematics was much more sophisticated than the mathematics that had been developed by earlier cultures. All surviving records of pre-Greek mathematics show the use of inductive reasoning, that is, repeated observations used to establish rules of thumb. Greek mathematicians, by contrast, used deductive reasoning. The Greeks used logic to derive conclusions from definitions and axioms, and used mathematical rigor to prove them.
+Greek mathematics is thought to have begun with Thales of Miletus (c. 624 – c. 546 BC) and Pythagoras of Samos (c. 582 – c. 507 BC). Although the extent of the influence is disputed, they were probably inspired by Egyptian and Babylonian mathematics. According to legend, Pythagoras traveled to Egypt to learn mathematics, geometry, and astronomy from Egyptian priests.
+Thales used geometry to solve problems such as calculating the height of pyramids and the distance of ships from the shore. He is credited with the first use of deductive reasoning applied to geometry, by deriving four corollaries to Thales' Theorem. As a result, he has been hailed as the first true mathematician and the first known individual to whom a mathematical discovery has been attributed. Pythagoras established the Pythagorean School, whose doctrine it was that mathematics ruled the universe and whose motto was "All is number". It was the Pythagoreans who coined the term "mathematics", and with whom the study of mathematics for its own sake begins. The Pythagoreans are credited with the first proof of the Pythagorean theorem, though the statement of the theorem has a long history, and with the proof of the existence of irrational numbers. Although he was preceded by the Babylonians, Indians and the Chinese, the Neopythagorean mathematician Nicomachus (60–120 AD) provided one of the earliest Greco-Roman multiplication tables, whereas the oldest extant Greek multiplication table is found on a wax tablet dated to the 1st century AD (now found in the British Museum). The association of the Neopythagoreans with the Western invention of the multiplication table is evident in its later Medieval name: the mensa Pythagorica.
+Plato (428/427 BC – 348/347 BC) is important in the history of mathematics for inspiring and guiding others. His Platonic Academy, in Athens, became the mathematical center of the world in the 4th century BC, and it was from this school that the leading mathematicians of the day, such as Eudoxus of Cnidus (c. 390 – c. 340 BC), came. Plato also discussed the foundations of mathematics, clarified some of the definitions (e.g. that of a line as "breadthless length").
+Eudoxus developed the method of exhaustion, a precursor of modern integration and a theory of ratios that avoided the problem of incommensurable magnitudes. The former allowed the calculations of areas and volumes of curvilinear figures, while the latter enabled subsequent geometers to make significant advances in geometry. Though he made no specific technical mathematical discoveries, Aristotle (384–c. 322 BC) contributed significantly to the development of mathematics by laying the foundations of logic.
+
+In the 3rd century BC, the premier center of mathematical education and research was the Musaeum of Alexandria. It was there that Euclid (c. 300 BC) taught, and wrote the Elements, widely considered the most successful and influential textbook of all time. The Elements introduced mathematical rigor through the axiomatic method and is the earliest example of the format still used in mathematics today, that of definition, axiom, theorem, and proof. Although most of the contents of the Elements were already known, Euclid arranged them into a single, coherent logical framework. The Elements was known to all educated people in the West up through the middle of the 20th century and its contents are still taught in geometry classes today. In addition to the familiar theorems of Euclidean geometry, the Elements was meant as an introductory textbook to all mathematical subjects of the time, such as number theory, algebra and solid geometry, including proofs that the square root of two is irrational and that there are infinitely many prime numbers. Euclid also wrote extensively on other subjects, such as conic sections, optics, spherical geometry, and mechanics, but only half of his writings survive.
+
+Archimedes (c. 287–212 BC) of Syracuse, widely considered the greatest mathematician of antiquity, used the method of exhaustion to calculate the area under the arc of a parabola with the summation of an infinite series, in a manner not too dissimilar from modern calculus. He also showed one could use the method of exhaustion to calculate the value of π with as much precision as desired, and obtained the most accurate value of π then known, 3+⁠10/71⁠ < π < 3+⁠10/70⁠. He also studied the spiral bearing his name, obtained formulas for the volumes of surfaces of revolution (paraboloid, ellipsoid, hyperboloid), and an ingenious method of exponentiation for expressing very large numbers. While he is also known for his contributions to physics and several advanced mechanical devices, Archimedes himself placed far greater value on the products of his thought and general mathematical principles. He regarded as his greatest achievement his finding of the surface area and volume of a sphere, which he obtained by proving these are 2/3 the surface area and volume of a cylinder circumscribing the sphere.
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+title: "History of mathematics"
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+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T03:59:56.476741+00:00"
+instance: "kb-cron"
+---
+
+Apollonius of Perga (c. 262–190 BC) made significant advances to the study of conic sections, showing that one can obtain all three varieties of conic section by varying the angle of the plane that cuts a double-napped cone. He also coined the terminology in use today for conic sections, namely parabola ("place beside" or "comparison"), "ellipse" ("deficiency"), and "hyperbola" ("a throw beyond"). His work Conics is one of the best known and preserved mathematical works from antiquity, and in it he derives many theorems concerning conic sections that would prove invaluable to later mathematicians and astronomers studying planetary motion, such as Isaac Newton. While neither Apollonius nor any other Greek mathematicians made the leap to coordinate geometry, Apollonius' treatment of curves is in some ways similar to the modern treatment, and some of his work seems to anticipate the development of analytical geometry by Descartes some 1800 years later.
+Around the same time, Eratosthenes of Cyrene (c. 276–194 BC) devised the Sieve of Eratosthenes for finding prime numbers. The 3rd century BC is generally regarded as the "Golden Age" of Greek mathematics, with advances in pure mathematics henceforth in relative decline. Nevertheless, in the centuries that followed significant advances were made in applied mathematics, most notably trigonometry, largely to address the needs of astronomers. Hipparchus of Nicaea (c. 190–120 BC) is considered the founder of trigonometry for compiling the first known trigonometric table, and to him is also due the systematic use of the 360 degree circle. Heron of Alexandria (c. 10–70 AD) is credited with Heron's formula for finding the area of a scalene triangle and with being the first to recognize the possibility of negative numbers possessing square roots. Menelaus of Alexandria (c. 100 AD) pioneered spherical trigonometry through Menelaus' theorem. The most complete and influential trigonometric work of antiquity is the Almagest of Ptolemy (c. AD 90–168), a landmark astronomical treatise whose trigonometric tables would be used by astronomers for the next thousand years. Ptolemy is also credited with Ptolemy's theorem for deriving trigonometric quantities, and the most accurate value of π outside of China until the medieval period, 3.1416.
+
+Following a period of stagnation after Ptolemy, the period between 250 and 350 AD is sometimes referred to as the "Silver Age" of Greek mathematics. During this period, Diophantus made significant advances in algebra, particularly indeterminate analysis, which is also known as "Diophantine analysis". The study of Diophantine equations and Diophantine approximations is a significant area of research to this day. His main work was the Arithmetica, a collection of 150 algebraic problems dealing with exact solutions to determinate and indeterminate equations. The Arithmetica had a significant influence on later mathematicians, such as Pierre de Fermat, who arrived at his famous Last Theorem after trying to generalize a problem he had read in the Arithmetica (that of dividing a square into two squares). Diophantus also made significant advances in notation, the Arithmetica being the first instance of algebraic symbolism and syncopation.
+
+Among the last great Greek mathematicians is Pappus of Alexandria (4th century AD). He is known for his hexagon theorem and centroid theorem, as well as the Pappus configuration and Pappus graph. His Collection is a major source of knowledge on Greek mathematics as most of it has survived. Pappus is considered the last major innovator in Greek mathematics, with subsequent work consisting mostly of commentaries on earlier work.
+The first woman mathematician recorded was Hypatia of Alexandria (AD 350–415), who wrote many works on applied mathematics. Because of a political dispute, the Christian community in Alexandria had her stripped publicly and executed. Her death is sometimes taken as the end of the era of the Alexandrian Greek mathematics, although work did continue in Athens for another century with figures such as Proclus, Simplicius and Eutocius. Although Proclus and Simplicius were more philosophers than mathematicians, their commentaries on earlier works are valuable sources on Greek mathematics. The closure of the neo-Platonic Academy of Athens by the emperor Justinian in 529 AD is traditionally held as marking the end of the era of Greek mathematics, although the Greek tradition continued unbroken in the Byzantine empire with mathematicians such as Anthemius of Tralles and Isidore of Miletus, the architects of the Hagia Sophia. Nevertheless, Byzantine mathematics consisted mostly of commentaries, with little in the way of innovation, and the centers of mathematical innovation were to be found elsewhere by this time.
+
+== Roman ==
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+title: "History of mathematics"
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+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T03:59:56.476741+00:00"
+instance: "kb-cron"
+---
+
+Although ethnic Greek mathematicians continued under the rule of the late Roman Republic and subsequent Roman Empire, there were no noteworthy native Latin mathematicians in comparison. Ancient Romans such as Cicero (106–43 BC), an influential Roman statesman who studied mathematics in Greece, believed that Roman surveyors and calculators were far more interested in applied mathematics than the theoretical mathematics and geometry that were prized by the Greeks. It is unclear if the Romans first derived their numerical system directly from the Greek precedent or from Etruscan numerals used by the Etruscan civilization centered in what is now Tuscany, central Italy.
+Using calculation, Romans were adept at both instigating and detecting financial fraud, as well as managing taxes for the treasury. Siculus Flaccus, one of the Roman gromatici (i.e. land surveyor), wrote the Categories of Fields, which aided Roman surveyors in measuring the surface areas of allotted lands and territories. Aside from managing trade and taxes, the Romans also regularly applied mathematics to solve problems in engineering, including the erection of architecture such as bridges, road-building, and preparation for military campaigns. Arts and crafts such as Roman mosaics, inspired by previous Greek designs, created illusionist geometric patterns and rich, detailed scenes that required precise measurements for each tessera tile, the opus tessellatum pieces on average measuring eight millimeters square and the finer opus vermiculatum pieces having an average surface of four millimeters square.
+The creation of the Roman calendar also necessitated basic mathematics. The first calendar allegedly dates back to 8th century BC during the Roman Kingdom and included 356 days plus a leap year every other year. In contrast, the lunar calendar of the Republican era contained 355 days, roughly ten-and-one-fourth days shorter than the solar year, a discrepancy that was solved by adding an extra month into the calendar after the 23rd of February. This calendar was supplanted by the Julian calendar, a solar calendar organized by Julius Caesar (100–44 BC) and devised by Sosigenes of Alexandria to include a leap day every four years in a 365-day cycle. This calendar, which contained an error of 11 minutes and 14 seconds, was later corrected by the Gregorian calendar organized by Pope Gregory XIII (r. 1572–1585), virtually the same solar calendar used in modern times as the international standard calendar.
+At roughly the same time, the Han Chinese and the Romans both invented the wheeled odometer device for measuring distances traveled, the Roman model first described by the Roman civil engineer and architect Vitruvius (c. 80 BC – c. 15 BC). The device was used at least until the reign of emperor Commodus (r. 177 – 192 AD), but its design seems to have been lost until experiments were made during the 15th century in Western Europe. Perhaps relying on similar gear-work and technology found in the Antikythera mechanism, the odometer of Vitruvius featured chariot wheels measuring 4 feet (1.2 m) in diameter turning four-hundred times in one Roman mile (roughly 4590 ft/1400 m). With each revolution, a pin-and-axle device engaged a 400-tooth cogwheel that turned a second gear responsible for dropping pebbles into a box, each pebble representing one mile traversed.
+
+== Chinese ==
+
+An analysis of early Chinese mathematics has demonstrated its unique development compared to other parts of the world, leading scholars to assume an entirely independent development. The oldest extant mathematical text from China is the Zhoubi Suanjing (周髀算經), variously dated to between 1200 BC and 100 BC, though a date of about 300 BC during the Warring States Period appears reasonable. However, the Tsinghua Bamboo Slips, containing the earliest known decimal multiplication table (although ancient Babylonians had ones with a base of 60), is dated around 305 BC and is perhaps the oldest surviving mathematical text of China.
+
+Of particular note is the use in Chinese mathematics of a decimal positional notation system, the so-called "rod numerals" in which distinct ciphers were used for numbers between 1 and 10, and additional ciphers for powers of ten. Thus, the number 123 would be written using the symbol for "1", followed by the symbol for "100", then the symbol for "2" followed by the symbol for "10", followed by the symbol for "3". This was the most advanced number system in the world at the time, apparently in use several centuries before the common era and well before the development of the Indian numeral system. Rod numerals allowed the representation of numbers as large as desired and allowed calculations to be carried out on the suan pan, or Chinese abacus. The date of the invention of the suan pan is not certain, but the earliest written mention dates from AD 190, in Xu Yue's Supplementary Notes on the Art of Figures.
+The oldest extant work on geometry in China comes from the philosophical Mohist canon c. 330 BC, compiled by the followers of Mozi (470–390 BC). The Mo Jing described various aspects of many fields associated with physical science, and provided a small number of geometrical theorems as well. It also defined the concepts of circumference, diameter, radius, and volume.
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+title: "History of mathematics"
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+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T03:59:56.476741+00:00"
+instance: "kb-cron"
+---
+
+In 212 BC, the Emperor Qin Shi Huang commanded all books in the Qin Empire other than officially sanctioned ones be burned. This decree was not universally obeyed, but as a consequence of this order little is known about ancient Chinese mathematics before this date. After the book burning of 212 BC, the Han dynasty (202 BC–220 AD) produced works of mathematics which presumably expanded on works that are now lost. The most important of these is The Nine Chapters on the Mathematical Art, the full title of which appeared by AD 179, but existed in part under other titles beforehand. It consists of 246 word problems involving agriculture, business, employment of geometry to figure height spans and dimension ratios for Chinese pagoda towers, engineering, surveying, and includes material on right triangles. It created mathematical proof for the Pythagorean theorem, and a mathematical formula for Gaussian elimination. The treatise also provides values of π, which Chinese mathematicians originally approximated as 3 until Liu Xin (d. 23 AD) provided a figure of 3.1457 and subsequently Zhang Heng (78–139) approximated pi as 3.1724, as well as 3.162 by taking the square root of 10. Liu Hui commented on the Nine Chapters in the 3rd century AD and gave a value of π accurate to 5 decimal places (i.e. 3.14159). Though more of a matter of computational stamina than theoretical insight, in the 5th century AD Zu Chongzhi computed the value of π to seven decimal places (between 3.1415926 and 3.1415927), which remained the most accurate value of π for almost the next 1000 years. He also established a method which would later be called Cavalieri's principle to find the volume of a sphere.
+The high-water mark of Chinese mathematics occurred in the 13th century during the latter half of the Song dynasty (960–1279), with the development of Chinese algebra. The most important text from that period is the Precious Mirror of the Four Elements by Zhu Shijie (1249–1314), dealing with the solution of simultaneous higher order algebraic equations using a method similar to Horner's method. The Precious Mirror also contains a diagram of Pascal's triangle with coefficients of binomial expansions through the eighth power, though both appear in Chinese works as early as 1100. The Chinese also made use of the complex combinatorial diagram known as the magic square and magic circles, described in ancient times and perfected by Yang Hui (AD 1238–1298).
+Even after European mathematics began to flourish during the Renaissance, European and Chinese mathematics were separate traditions, with significant Chinese mathematical output in decline from the 13th century onwards. Jesuit missionaries such as Matteo Ricci carried mathematical ideas back and forth between the two cultures from the 16th to 18th centuries, though at this point far more mathematical ideas were entering China than leaving.
+Japanese mathematics, Korean mathematics, and Vietnamese mathematics are traditionally viewed as stemming from Chinese mathematics and belonging to the Confucian-based East Asian cultural sphere. Korean and Japanese mathematics were heavily influenced by the algebraic works produced during China's Song dynasty, whereas Vietnamese mathematics was heavily indebted to popular works of China's Ming dynasty (1368–1644). For instance, although Vietnamese mathematical treatises were written in either Chinese or the native Vietnamese Chữ Nôm script, all of them followed the Chinese format of presenting a collection of problems with algorithms for solving them, followed by numerical answers. Mathematics in Vietnam and Korea were mostly associated with the professional court bureaucracy of mathematicians and astronomers, whereas in Japan it was more prevalent in the realm of private schools.
+
+== Indian ==
+
+The earliest civilization on the Indian subcontinent is the Indus Valley civilization (mature second phase: 2600 to 1900 BC) that flourished in the Indus river basin. Their cities were laid out with geometric regularity, but no known mathematical documents survive from this civilization.
+The oldest extant mathematical records from India are the Sulba Sutras (dated variously between the 8th century BC and the 2nd century AD), appendices to religious texts which give simple rules for constructing altars of various shapes, such as squares, rectangles, parallelograms, and others. As with Egypt, the preoccupation with temple functions points to an origin of mathematics in religious ritual. The Sulba Sutras give methods for constructing a circle with approximately the same area as a given square, which imply several different approximations of the value of π. In addition, they compute the square root of 2 to several decimal places, list Pythagorean triples, and give a statement of the Pythagorean theorem. All of these results are present in Babylonian mathematics, indicating Mesopotamian influence. It is not known to what extent the Sulba Sutras influenced later Indian mathematicians. As in China, there is a lack of continuity in Indian mathematics; significant advances are separated by long periods of inactivity.
+Pāṇini (c. 5th century BC) formulated the rules for Sanskrit grammar. His notation was similar to modern mathematical notation, and used metarules, transformations, and recursion. Pingala (roughly 3rd–1st centuries BC) in his treatise of prosody uses a device corresponding to a binary numeral system. His discussion of the combinatorics of meters corresponds to an elementary version of the binomial theorem. Pingala's work also contains the basic ideas of Fibonacci numbers (called mātrāmeru).
+The next significant mathematical documents from India after the Sulba Sutras are the Siddhantas, astronomical treatises from the 4th and 5th centuries AD (Gupta period) showing strong Hellenistic influence. They are significant in that they contain the first instance of trigonometric relations based on the half-chord, as is the case in modern trigonometry, rather than the full chord, as was the case in Ptolemaic trigonometry. Through a series of translation errors, the words "sine" and "cosine" derive from the Sanskrit "jiya" and "kojiya".
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+title: "History of mathematics"
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+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T03:59:56.476741+00:00"
+instance: "kb-cron"
+---
+
+Around 500 AD, Aryabhata wrote the Aryabhatiya, a slim volume, written in verse, intended to supplement the rules of calculation used in astronomy and mathematical mensuration, though with no feeling for logic or deductive methodology. It is in the Aryabhatiya that the decimal place-value system first appears. Several centuries later, the Muslim mathematician Abu Rayhan Biruni described the Aryabhatiya as a "mix of common pebbles and costly crystals".
+In the 7th century, Brahmagupta identified the Brahmagupta theorem, Brahmagupta's identity and Brahmagupta's formula, and for the first time, in Brahma-sphuta-siddhanta, he lucidly explained the use of zero as both a placeholder and decimal digit, and explained the Hindu–Arabic numeral system. It was from a translation of this Indian text on mathematics (c. 770) that Islamic mathematicians were introduced to this numeral system, which they adapted as Arabic numerals. Islamic scholars carried knowledge of this number system to Europe by the 12th century, and it has now displaced all older number systems throughout the world. Various symbol sets are used to represent numbers in the Hindu–Arabic numeral system, all of which evolved from the Brahmi numerals. Each of the roughly dozen major scripts of India has its own numeral glyphs. In the 10th century, Halayudha's commentary on Pingala's work contains a study of the Fibonacci sequence and Pascal's triangle.
+In the 12th century, Bhāskara II, who lived in southern India, wrote extensively on the mathematical knowledge of his time. In his astronomical work, he described results that have been interpreted by later scholars as resembling early infinitesimal methods. His writings include ideas approximately equivalent to infinitesimals and a special case of the mean value theorem  in inverse interpolation of sine.He also made significant contributions to algebra, including methods for solving indeterminate equations of the type later known as Pell equations, which he treated using cyclic procedures such as the chakravāla method. In the 14th century, Narayana Pandita completed his Ganita Kaumudi.
+Also in the 14th century, Madhava of Sangamagrama, the founder of the Kerala School of Mathematics, found the Madhava–Leibniz series and obtained from it a transformed series, whose first 21 terms he used to compute the value of π as 3.14159265359. Madhava also found the Madhava-Gregory series to determine the arctangent, the Madhava-Newton power series to determine sine and cosine and the Taylor approximation for sine and cosine functions. In the 16th century, Jyesthadeva consolidated many of the Kerala School's developments and theorems in the Yukti-bhāṣā.  has been argued that certain ideas of calculus like infinite series and taylor series of some trigonometry functions, were transmitted to Europe in the 16th century via Jesuit missionaries and traders who were active around the ancient port of Muziris at the time and, as a result, directly influenced later European developments in analysis and calculus. However, other scholars argue that the Kerala School did not formulate a systematic theory of differentiation and integration, and that there is not any direct evidence of their results being transmitted outside Kerala.
+
+== Islamic empires ==
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+title: "History of mathematics"
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+source: "https://en.wikipedia.org/wiki/History_of_mathematics"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T03:59:56.476741+00:00"
+instance: "kb-cron"
+---
+
+The Islamic Empire established across the Middle East, Central Asia, North Africa, Iberia, and in parts of India in the 8th century made significant contributions towards mathematics. Although most Islamic texts on mathematics were written in Arabic, they were not all written by Arabs, since much like the status of Greek in the Hellenistic world, Arabic was used as the written language of non-Arab scholars throughout the Islamic world at the time.
+In the 9th century, the Persian mathematician Muḥammad ibn Mūsā al-Khwārizmī wrote an important book on the Hindu–Arabic numerals and one on methods for solving equations. His book On the Calculation with Hindu Numerals, written about 825, along with the work of Al-Kindi, were instrumental in spreading Indian mathematics and Indian numerals to the West. The word algorithm is derived from the Latinization of his name, Algoritmi, and the word algebra from the title of one of his works, Al-Kitāb al-mukhtaṣar fī hīsāb al-ğabr wa’l-muqābala (The Compendious Book on Calculation by Completion and Balancing). He gave an exhaustive explanation for the algebraic solution of quadratic equations with positive roots, and he was the first to teach algebra in an elementary form and for its own sake. He also discussed the fundamental method of "reduction" and "balancing", referring to the transposition of subtracted terms to the other side of an equation, that is, the cancellation of like terms on opposite sides of the equation. This is the operation which al-Khwārizmī originally described as al-jabr. His algebra was also no longer concerned "with a series of problems to be resolved, but an exposition which starts with primitive terms in which the combinations must give all possible prototypes for equations, which henceforward explicitly constitute the true object of study." He also studied an equation for its own sake and "in a generic manner, insofar as it does not simply emerge in the course of solving a problem, but is specifically called on to define an infinite class of problems."
+In Egypt, Abu Kamil extended algebra to the set of irrational numbers, accepting square roots and fourth roots as solutions and coefficients to quadratic equations. He also developed techniques used to solve three non-linear simultaneous equations with three unknown variables. One unique feature of his works was trying to find all the possible solutions to some of his problems, including one where he found 2676 solutions. His works formed an important foundation for the development of algebra and influenced later mathematicians, such as al-Karaji and Fibonacci.
+Further developments in algebra were made by Al-Karaji in his treatise al-Fakhri, where he extends the methodology to incorporate integer powers and integer roots of unknown quantities. Something close to a proof by mathematical induction appears in a book written by Al-Karaji around 1000 AD, who used it to prove the binomial theorem, Pascal's triangle, and the sum of integral cubes. The historian of mathematics, F. Woepcke, praised Al-Karaji for being "the first who introduced the theory of algebraic calculus." Also in the 10th century, Abul Wafa translated the works of Diophantus into Arabic. Ibn al-Haytham was the first mathematician to derive the formula for the sum of the fourth powers, using a method that is readily generalizable for determining the general formula for the sum of any integral powers. He performed an integration in order to find the volume of a paraboloid, and was able to generalize his result for the integrals of polynomials up to the fourth degree. He thus came close to finding a general formula for the integrals of polynomials, but he was not concerned with any polynomials higher than the fourth degree.
+In the late 11th century, Omar Khayyam wrote Discussions of the Difficulties in Euclid, a book about what he perceived as flaws in Euclid's Elements, especially the parallel postulate. He was also the first to find the general geometric solution to cubic equations. He was also very influential in calendar reform.
+In the 13th century, Nasir al-Din Tusi (Nasireddin) made advances in spherical trigonometry. He also wrote influential work on Euclid's parallel postulate. In the 15th century, Ghiyath al-Kashi computed the value of π to the 16th decimal place. Kashi also had an algorithm for calculating nth roots, which was a special case of the methods given many centuries later by Ruffini and Horner.
+Other achievements of Muslim mathematicians during this period include the addition of the decimal point notation to the Arabic numerals, the discovery of all the modern trigonometric functions besides the sine, al-Kindi's introduction of cryptanalysis and frequency analysis, the development of analytic geometry by Ibn al-Haytham, the beginning of algebraic geometry by Omar Khayyam, and the development of an algebraic notation by al-Qalasādī.
+During the time of the Ottoman Empire and Safavid Empire from the 15th century, the development of Islamic mathematics became stagnant.
+
+== Maya ==
+
+In the Pre-Columbian Americas, the Maya civilization that flourished in Mexico and Central America during the 1st millennium AD developed a unique tradition of mathematics that, due to its geographic isolation, was entirely independent of existing European, Egyptian, and Asian mathematics. Maya numerals used a base of twenty, the vigesimal system, instead of a base of ten that forms the basis of the decimal system used by most modern cultures. The Maya used mathematics to create the Maya calendar as well as to predict astronomical phenomena in their native Maya astronomy. While the concept of zero had to be inferred in the mathematics of many contemporary cultures, the Maya developed a standard symbol for it.
+
+== Medieval European ==
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+title: "History of mathematics"
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+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T03:59:56.476741+00:00"
+instance: "kb-cron"
+---
+
+Medieval European interest in mathematics was driven by concerns quite different from those of modern mathematicians. One driving element was the belief that mathematics provided the key to understanding the created order of nature, frequently justified by Plato's Timaeus and the biblical passage (in the Book of Wisdom) that God had ordered all things in measure, and number, and weight.
+Boethius provided a place for mathematics in the curriculum in the 6th century when he coined the term quadrivium to describe the study of arithmetic, geometry, astronomy, and music. He wrote De institutione arithmetica, a free translation from the Greek of Nicomachus's Introduction to Arithmetic; De institutione musica, also derived from Greek sources; and a series of excerpts from Euclid's Elements. His works were theoretical, rather than practical, and were the basis of mathematical study until the recovery of Greek and Arabic mathematical works.
+In the 12th century, European scholars traveled to Spain and Sicily seeking scientific Arabic texts, including al-Khwārizmī's The Compendious Book on Calculation by Completion and Balancing, translated into Latin by Robert of Chester, and the complete text of Euclid's Elements, translated in various versions by Adelard of Bath, Herman of Carinthia, and Gerard of Cremona. These and other new sources sparked a renewal of mathematics.
+Leonardo of Pisa, now known as Fibonacci, serendipitously learned about the Hindu–Arabic numerals on a trip to what is now Béjaïa, Algeria with his merchant father. (Europe was still using Roman numerals.) There, he observed a system of arithmetic (specifically algorism) which due to the positional notation of Hindu–Arabic numerals was much more efficient and greatly facilitated commerce. Leonardo wrote Liber Abaci in 1202 (updated in 1254) introducing the technique to Europe and beginning a long period of popularizing it. The book also brought to Europe what is now known as the Fibonacci sequence (known to Indian mathematicians for hundreds of years before that) which Fibonacci used as an unremarkable example.
+The 14th century saw the development of new mathematical concepts to investigate a wide range of problems. One important contribution was development of mathematics of local motion. Thomas Bradwardine proposed that speed (V) increases in arithmetic proportion as the ratio of force (F) to resistance (R) increases in geometric proportion. Bradwardine expressed this by a series of specific examples, but although the logarithm had not yet been conceived, we can express his conclusion anachronistically by writing:
+V = log (F/R). Bradwardine's analysis is an example of transferring a mathematical technique used by al-Kindi and Arnald of Villanova to quantify the nature of compound medicines to a different physical problem.
+
+One of the 14th-century Oxford Calculators, William of Heytesbury, lacking differential calculus and the concept of limits, proposed to measure instantaneous speed "by the path that would be described by [a body] if... it were moved uniformly at the same degree of speed with which it is moved in that given instant".
+Heytesbury and others mathematically determined the distance covered by a body undergoing uniformly accelerated motion (today solved by integration), stating that "a moving body uniformly acquiring or losing that increment [of speed] will traverse in some given time a [distance] completely equal to that which it would traverse if it were moving continuously through the same time with the mean degree [of speed]".
+Nicole Oresme at the University of Paris and the Italian Giovanni di Casali independently provided graphical demonstrations of this relationship, asserting that the area under the line depicting the constant acceleration, represented the total distance traveled. In a later mathematical commentary on Euclid's Elements, Oresme made a more detailed general analysis in which he demonstrated that a body will acquire in each successive increment of time an increment of any quality that increases as the odd numbers. Since Euclid had demonstrated the sum of the odd numbers are the square numbers, the total quality acquired by the body increases as the square of the time.
+
+== Renaissance ==
+
+During the Renaissance, the development of mathematics and of accounting were intertwined. While there is no direct relationship between algebra and accounting, the teaching of the subjects and the books published often intended for the children of merchants who were sent to reckoning schools (in Flanders and Germany) or abacus schools (known as abbaco in Italy), where they learned the skills useful for trade and commerce. There is probably no need for algebra in performing bookkeeping operations, but for complex bartering operations or the calculation of compound interest, a basic knowledge of arithmetic was mandatory and knowledge of algebra was very useful.
+Piero della Francesca (c. 1415 – c. 1492) wrote books on solid geometry and linear perspective, including De Prospectiva Pingendi (On Perspective for Painting), Trattato d’Abaco (Abacus Treatise), and De quinque corporibus regularibus (On the Five Regular Solids).
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+---
+title: "History of mathematics"
+chunk: 10/13
+source: "https://en.wikipedia.org/wiki/History_of_mathematics"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T03:59:56.476741+00:00"
+instance: "kb-cron"
+---
+
+Luca Pacioli's Summa de Arithmetica, Geometria, Proportioni et Proportionalità (Italian: "Review of Arithmetic, Geometry, Ratio and Proportion") was first printed and published in Venice in 1494. It included a 27-page treatise on bookkeeping, "Particularis de Computis et Scripturis" (Italian: "Details of Calculation and Recording"). It was written primarily for, and sold mainly to, merchants who used the book as a reference text, as a source of pleasure from the mathematical puzzles it contained, and to aid the education of their sons. In Summa Arithmetica, Pacioli introduced symbols for plus and minus for the first time in a printed book, symbols that became standard notation in Italian Renaissance mathematics. Summa Arithmetica was also the first known book printed in Italy to contain algebra. Pacioli obtained many of his ideas from Piero Della Francesca whom he plagiarized.
+In Italy, during the first half of the 16th century, Scipione del Ferro and Niccolò Fontana Tartaglia discovered solutions for cubic equations. Gerolamo Cardano published them in his 1545 book Ars Magna, together with a solution for the quartic equations, discovered by his student Lodovico Ferrari. In 1572 Rafael Bombelli published his L'Algebra in which he showed how to deal with the imaginary quantities that could appear in Cardano's formula for solving cubic equations.
+Simon Stevin's De Thiende ('the art of tenths'), first published in Dutch in 1585, contained the first systematic treatment of decimal notation in Europe, which influenced all later work on the real number system.
+Driven by the demands of navigation and the growing need for accurate maps of large areas, trigonometry grew to be a major branch of mathematics. Bartholomaeus Pitiscus was the first to use the word, publishing his Trigonometria in 1595. Regiomontanus's table of sines and cosines was published in 1533.
+During the Renaissance the desire of artists to represent the natural world realistically, together with the rediscovered philosophy of the Greeks, led artists to study mathematics. They were also the engineers and architects of that time, and so had need of mathematics in any case. The art of painting in perspective, and the developments in geometry that were involved, were studied intensely.
+
+== Mathematics during the Scientific Revolution ==
+
+=== 16th century ===
+In the 16th century, Viète laid down the foundations of algebra in 1591. This was foundational for the mathematics of Descartes.
+
+=== 17th century ===
+
+The 17th century saw an unprecedented increase of mathematical and scientific ideas across Europe. Tycho Brahe had gathered a large quantity of mathematical data describing the positions of the planets in the sky. By his position as Brahe's assistant, Johannes Kepler was first exposed to and seriously interacted with the topic of planetary motion. Kepler's calculations were made simpler by the contemporaneous invention of logarithms by John Napier and Jost Bürgi. Kepler succeeded in formulating mathematical laws of planetary motion.
+The analytic geometry developed by René Descartes (1596–1650) allowed those orbits to be plotted on a graph, in Cartesian coordinates.
+Building on earlier work by many predecessors, Isaac Newton discovered the laws of physics that explain Kepler's Laws, and brought together the concepts now known as calculus. Independently, Gottfried Wilhelm Leibniz, developed calculus and much of the calculus notation still in use today. He also refined the binary number system, which is the foundation of nearly all digital (electronic, solid-state, discrete logic) computers.
+Science and mathematics had become an international endeavor, which would soon spread over the entire world.
+In addition to the application of mathematics to the studies of the heavens, applied mathematics began to expand into new areas, with the correspondence of Pierre de Fermat and Blaise Pascal. Pascal and Fermat set the groundwork for the investigations of probability theory and the corresponding rules of combinatorics in their discussions over a game of gambling. Pascal, with his wager, attempted to use the newly developing probability theory to argue for a life devoted to religion, on the grounds that even if the probability of success was small, the rewards were infinite. In some sense, this foreshadowed the development of utility theory in the 18th and 19th centuries.
+
+=== 18th century ===
+
+The most influential mathematician of the 18th century was arguably Leonhard Euler (1707–83). His contributions range from founding the study of graph theory with the Seven Bridges of Königsberg problem to standardizing many modern mathematical terms and notations. For example, he named the square root of minus 1 with the symbol i, and he popularized the use of the Greek letter 
+  
+    
+      
+        π
+      
+    
+    {\displaystyle \pi }
+  
+ to stand for the ratio of a circle's circumference to its diameter. He made numerous contributions to the study of topology, graph theory, calculus, combinatorics, and complex analysis, as evidenced by the multitude of theorems and notations named for him.
+Other important European mathematicians of the 18th century included Joseph Louis Lagrange, who did pioneering work in number theory, algebra, differential calculus, and the calculus of variations, and Pierre-Simon Laplace, who, in the age of Napoleon, did important work on the foundations of celestial mechanics and on statistics.
+
+== Modern ==
+
+=== 19th century ===
+
+Throughout the 19th century mathematics became increasingly abstract. Carl Friedrich Gauss (1777–1855) did revolutionary work on functions of complex variables, in geometry, and on the convergence of series, leaving aside his many contributions to science. He also gave the first satisfactory proofs of the fundamental theorem of algebra and quadratic reciprocity law.
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+---
+title: "Legal history"
+chunk: 1/3
+source: "https://en.wikipedia.org/wiki/Legal_history"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T03:59:51.266004+00:00"
+instance: "kb-cron"
+---
+
+Legal history or the history of law is the study of how law has evolved and why it has changed. Legal history is closely connected to the development of civilizations and operates in the wider context of social history. Certain jurists and historians of legal process have seen legal history as the recording of the evolution of laws and the technical explanation of how these laws have evolved, with the view of better understanding the origins of various legal concepts; some consider legal history a branch of intellectual history. Twentieth-century historians viewed legal history in a more contextualised manner – more in line with the thinking of social historians. They have looked at legal institutions as complex systems of rules, players and symbols and have seen these elements interact with society to change, adapt, resist or promote certain aspects of civil society. Such legal historians have tended to analyze case histories through the lens of social-science inquiry, using statistical methods to analyse class distinctions among litigants, petitioners, and other players in various legal processes. By analyzing case outcomes, transaction costs, and the number of settled cases, they have begun examining legal institutions, practices, procedures, and briefs, offering a more nuanced picture of law and society than traditional legal studies of jurisprudence, case law, and civil codes can achieve.
+
+== Ancient world ==
+
+Ancient Egyptian law, dating as far back as 3000 BC, was based on the concept of Ma'at, and was characterised by tradition, rhetorical speech, social equality and impartiality. By the 22nd century BC, Ur-Nammu, an ancient Sumerian ruler, formulated the first extant law code, consisting of casuistic statements ("if... then..."). Around 1760 BC, King Hammurabi further developed Babylonian law by codifying and inscribing it in stone. Hammurabi placed several copies of his law code throughout the kingdom of Babylon as stelae, for the entire public to see; this became known as the Codex Hammurabi. The most intact copy of these stelae was discovered in the 19th century by British Assyriologists, and has since been fully transliterated and translated into various languages, including English, German, and French. Ancient Greek has no single word for "law" as an abstract concept, retaining instead the distinction between divine law (thémis), human decree (nómos) and custom (díkē). Yet Ancient Greek law contained major constitutional innovations in the development of democracy.
+
+== Southern Asia ==
+
+Ancient India and China represent distinct traditions of law, and had historically independent schools of legal theory and practice. The Arthashastra, dating from the 400 BC, and the Manusmriti from 100 BCE were influential treatises in India, texts that were considered authoritative legal guidance. Manu's central philosophy was tolerance and pluralism, and was cited across South East Asia. During the Muslim conquests in the Indian subcontinent, sharia was established by the Muslim sultanates and empires, most notably Mughal Empire's Fatawa-e-Alamgiri, compiled by Emperor Aurangzeb and various scholars of Islam. After British colonialism, Hindu tradition, along with Islamic law, was supplanted by the common law when India became part of the British Empire. Malaysia, Brunei, Singapore and Hong Kong also adopted the common law.
+
+== Eastern Asia ==
+
+The eastern Asian legal tradition reflects a unique blend of secular and religious influences. Japan was the first country to begin modernising its legal system along western lines, by importing bits of the French, but mostly the German Civil Code. This partly reflected Germany's status as a rising power in the late nineteenth century. Similarly, traditional Chinese law gave way to westernisation towards the final years of the Qing dynasty in the form of six private law codes based mainly on the Japanese model of German law. Today Taiwanese law retains the closest affinity to the codifications from that period, because of the split between Chiang Kai-shek's nationalists, who fled there, and Mao Zedong's communists who won control of the mainland in 1949. The current legal infrastructure in the People's Republic of China was heavily influenced by soviet Socialist law, which essentially inflates administrative law at the expense of private law rights. Today, however, because of rapid industrialisation China has been reforming, at least in terms of economic (if not social and political) rights. A new contract code in 1999 represented a turn away from administrative domination. Furthermore, after negotiations lasting fifteen years, in 2001 China joined the World Trade Organization.
+
+Yassa of the Mongol Empire
+
+== Canon law ==
+
+The legal history of the Catholic Church is the history of Catholic canon law, the oldest continuously functioning legal system in the West. Canon law originates much later than Roman law but predates the evolution of modern European civil law traditions. The cultural exchange between the secular (Roman/Barbarian) and ecclesiastical (canon) law produced the jus commune and greatly influenced both civil and common law.
+The history of Latin canon law can be divided into four periods: the jus antiquum, the jus novum, the jus novissimum and the Code of Canon Law. In relation to the Code, history can be divided into the jus vetus (all law before the Code) and the jus novum (the law of the Code, or jus codicis). Eastern canon law developed separately.
+In the twentieth century, canon law was comprehensively codified. On 27 May 1917, Pope Benedict XV codified the 1917 Code of Canon Law.
+John XXIII, together with his intention to call the Second Vatican Council, announced his intention to reform canon law, which culminated in the 1983 Code of Canon Law, promulgated by John Paul II on 25 January 1983. John Paul II also brought to a close the long process of codifying the Eastern Catholic canon law common to all 23 sui juris Eastern Catholic Churches on 18 October 1990 by promulgating the Code of Canons of the Eastern Churches.
+
+== Islamic law ==
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+title: "Legal history"
+chunk: 2/3
+source: "https://en.wikipedia.org/wiki/Legal_history"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T03:59:51.266004+00:00"
+instance: "kb-cron"
+---
+
+One of the major legal systems developed during the Middle Ages was Islamic law and jurisprudence. Some important legal institutions were developed by Islamic jurists during the classical period of Islamic law and jurisprudence. One such institution was the Hawala, an early informal value transfer system mentioned in texts of Islamic jurisprudence as early as the 8th century. Hawala itself later influenced the development of the Aval in French civil law and the Avallo in Italian law.
+
+== European laws ==
+
+=== Roman Empire ===
+
+Roman law was heavily influenced by Greek teachings. It forms the bridge to the modern legal world, over the centuries between the rise and decline of the Roman Empire. Roman law, in the days of the Roman Republic and Empire, was heavily procedural, and there was no professional legal class. Instead a lay person, iudex, was chosen to adjudicate. Precedents were not reported, so any case law that developed was disguised and almost unrecognised. Each case was to be decided afresh from the laws of the state, which mirrors the (theoretical) unimportance of judges' decisions for future cases in civil law systems today. During the 6th century AD in the Eastern Roman Empire, the Emperor Justinian codified and consolidated the laws that had existed in Rome so that what remained was one twentieth of the mass of legal texts from before. This became known as the Corpus Juris Civilis. As one legal historian wrote, "Justinian consciously looked back to the golden age of Roman law and aimed to restore it to the peak it had reached three centuries before."
+
+=== Middle Ages ===
+
+During the Byzantine Empire, the Justinian Code was expanded and remained in force until the Empire fell, though it was never officially introduced to the West. Instead, following the fall of the Western Empire and in former Roman countries, the ruling classes relied on the Theodosian Code to govern natives and Germanic customary law for the Germanic incomers – a system known as folk-right – until the two laws blended. Since the Roman court system had broken down, legal disputes were adjudicated according to Germanic custom by assemblies of learned lawspeakers in rigid ceremonies and in oral proceedings that relied heavily on testimony.
+After much of the West was consolidated under Charlemagne, law became centralized to strengthen the royal court system and, consequently, case law, and folk-right was abolished. However, once Charlemagne's kingdom definitively splintered, Europe became feudalistic, and law was generally not governed above the county, municipal, or lordship level, thereby creating a highly decentralized legal culture that favored the development of customary law founded on localized case law. However, in the 11th century, crusaders, having pillaged the Byzantine Empire, returned with Byzantine legal texts including the Justinian Code, and scholars at the University of Bologna were the first to use them to interpret their own customary laws. Medieval European legal scholars began researching the Roman law and using its concepts and prepared the way for the partial resurrection of Roman law as the modern civil law in a large part of the world. There was, however, a great deal of resistance so that civil law rivaled customary law for much of the late Middle Ages.
+After the Norman conquest of England, which introduced Norman legal concepts into medieval England, the English King's powerful judges developed a body of precedent that became the common law. In particular, Henry II instituted legal reforms and developed a system of royal courts administered by a small number of judges who lived in Westminster and traveled throughout the kingdom. Henry II also instituted the Assize of Clarendon in 1166, which allowed for jury trials and reduced the number of trials by combat. Louis IX of France also undertook major legal reforms and, inspired by ecclesiastical court procedure, extended Canon-law evidence and inquisitorial-trial systems to the royal courts. In 1280 and 1295, measures were instituted by the Court of Arches and other authorities in London to improve the conduct of lawyers in the courts. Also, judges no longer moved on circuits, becoming fixed to their jurisdictions, and jurors were nominated by parties to the legal dispute rather than by the sheriff. In addition, by the 10th century, the Law Merchant, first founded on Scandinavian trade customs, then solidified by the Hanseatic League, took shape so that merchants could trade using familiar standards, rather than the many splintered types of local law. A precursor to modern commercial law, the Law Merchant emphasised the freedom of contract and alienability of property.
+
+=== Modern European law ===
+
+The two main traditions of modern European law are the codified legal systems of most of continental Europe, and the English tradition based on case law.
+As nationalism grew in the 18th and 19th centuries, lex mercatoria was incorporated into national law through new civil codes. Of these, the French Napoleonic Code and the German Bürgerliches Gesetzbuch became the most influential. As opposed to English common law, which consists of massive tomes of case law, codes in small books are easy to export and for judges to apply. However, today there are signs that civil and common law are converging. European Union law is codified in treaties, but develops through the precedent set down by the European Court of Justice.
+
+== African law ==
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+title: "Legal history"
+chunk: 3/3
+source: "https://en.wikipedia.org/wiki/Legal_history"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T03:59:51.266004+00:00"
+instance: "kb-cron"
+---
+
+The African law system is based on common law and civilian law. Many legal systems in Africa were based on ethnic customs and traditions before colonization took over their original system. The people listened to their elders and relied on them as mediators during disputes. Several states didn't keep written records, as their laws were often passed orally. In the Mali Empire, the Kouroukan Fouga was proclaimed in 1222–1236 AD as the state's official constitution. It defined regulations in both constitutional and civil matters. The provisions of the constitution are still transmitted to this day by griots under oath. During colonization, authorities in Africa developed an official legal system called the Native Courts. After colonialism, the major faiths that stayed were Buddhism, Hinduism, and Judaism.
+
+== United States ==
+The United States legal system developed primarily from the English common law system (except for the state of Louisiana, which continued to follow the French civil law system after being admitted to statehood). Some concepts from Spanish law, such as the prior appropriation doctrine and community property, persist in some US states, particularly those that were part of the Mexican Cession in 1848.
+Under the doctrine of federalism, each state has its own separate court system, and the ability to legislate within areas not reserved to the federal government.
+
+== Global Legal Traditions ==
+A comprehensive view of legal history must encompass legal systems beyond the Western tradition. Scholars have increasingly focused on non-Western frameworks, such as Islamic law, which emphasizes religious principles; Confucian legal traditions, where moral conduct is integral to law; and the adaptive nature of African customary law. By comparing these diverse systems with Western legal developments, researchers have highlighted both striking differences and unexpected similarities, thereby enriching our understanding of law as a global phenomenon.
+
+== See also ==
+Legal biography
+Association of Young Legal Historians (AYLH)
+Constitution of the Roman Republic
+
+== Notes ==
+
+== References ==
+Farah, Paolo (August 2006). "Five Years of China WTO Membership. EU and US Perspectives about China's Compliance with Transparency Commitments and the Transitional Review Mechanism". Legal Issues of Economic Integration. 33 (3): 263–304. doi:10.54648/LEIE2006016. S2CID 153128973. SSRN 916768.
+Barretto, Vicente (2006). Dicionário de Filosofia do Direito. Unisinos Editora. ISBN 85-7431-266-5.
+Della Rocca, Fernando (1959). Manual of Canon Law. The Bruce Publishing Company.
+Glenn, H. Patrick (2000). Legal Traditions of the World. Oxford University Press. ISBN 0-19-876575-4.
+Sadakat Kadri, The Trial: A History from Socrates to O.J. Simpson, HarperCollins 2005. ISBN 0-00-711121-5
+Kelly, J.M. (1992). A Short History of Western Legal Theory. Oxford University Press. ISBN 0-19-876244-5.
+Gordley, James R.; von Mehren; Arthur Taylor (2006). An Introduction to the Comparative Study of Private Law. Cambridge University Press. ISBN 978-0-521-68185-8.
+Otto, Martin (2011). "Law". European History Online. Retrieved November 11, 2011.
+Sealy, L.S.; Hooley, R.J.A. (2003). Commercial Law. LexisNexis Butterworths.
+Stein, Peter (1999). Roman Law in European History. Cambridge University Press. pp. 32. ISBN 0-521-64372-4.
+Kempin, Jr., Frederick G. (1963). Legal History: Law and Social Change. Englewood Cliffs, New Jersey: Prentice-Hall.
+
+== Further reading ==
+The Oxford History of the Laws of England. 13 Vols. Oxford University Press, 2003–. (Six volumes to date: Vol. I (Canon Law and Ecclesiastical Jurisdiction from 597 to the 1640s), vol. II (871–1216), vol. VI (1483–1558), vols. XI–XIII (1820–1914))
+The Oxford International Encyclopedia of Legal History. Ed. Stanley N. Katz. 6 Vols. Oxford University Press, 2009. (OUP catalogue. Oxford Reference Online)
+Potz, Richard: Islam and Islamic Law in European Legal History, European History Online, Mainz: Institute of European History, 2011, retrieved: November 28, 2011.
+
+== External links ==
+
+The Legal History Project (Resources and interviews)
+Some legal history materials
+The Schoyen Collection
+The Roman Law Library by Yves Lassard and Alexandr Koptev.
+CHD Centre for Legal History – Faculty of Law, University of Rennes 1
+Centre for Legal History – Edinburgh Law School
+The European Society for History of Law
+Collection of Historical Statutory Material – Cornell Law Library
+Historical Laws of Hong Kong Online – University of Hong Kong Libraries, Digital Initiatives
+Basic Law Drafting History Online -University of Hong Kong Libraries, Digital Initiatives
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