Scrape wikipedia-science: 3705 new, 2848 updated, 6714 total (kb-cron)

data/en.wikipedia.org/wiki/AHFS_Drug_Information_Book-0.md

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+---
+title: "AHFS Drug Information Book"
+chunk: 1/1
+source: "https://en.wikipedia.org/wiki/AHFS_Drug_Information_Book"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T08:47:23.323678+00:00"
+instance: "kb-cron"
+---
+
+The AHFS DI is one of several compendiums approved by the Social Security Act (Section 1861(t)(2)(B)(ii)(I)) as a source of off-label anti-cancer drug use. It was originally published in 1959 as the American Hospital Formulary Service (AHFS) by the American Society of Health-System Pharmacists.
+It is also the only one left of the originally authorized compendiums.
+
+
+== References ==
+
+
+== Further reading ==
+"Gain a solid understanding of compendia and its impact on patient access". Formulary Journal. 2012-07-01. Retrieved 2018-03-30.
+
+
+== External links ==
+Official website

data/en.wikipedia.org/wiki/A_Colour_Atlas_of_Urology-0.md

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+---
+title: "A Colour Atlas of Urology"
+chunk: 1/1
+source: "https://en.wikipedia.org/wiki/A_Colour_Atlas_of_Urology"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T08:47:33.835758+00:00"
+instance: "kb-cron"
+---
+
+A Colour Atlas of Urology is a medical textbook of urology images first published by Wolfe Medical Publications in 1983. It is co-authored by Reginald Wyndham Lloyd-Davies, James G. Gow and D. R. Davies. 1,188 Images include those of pathological specimens, photographs at endoscopy of the bladder and diagrams that explain urological diagnostic procedures. 70 images relate to lesions of the penis and scrotum. A second edition was published in 1994.
+A review in the Postgraduate Medical Journal noted that the X-ray of lung metastases was back to front. Another review considered it a complete work covering everything a urologist could possibly see in their profession. The British Journal of Venereal Diseases noted that the book was aimed at urologists but suggested that genitourinary physicians might be interested in it. All three reviews reported that the book was expensive.
+
+
+== Publication ==
+A Colour Atlas of Urology is co-authored by Reginald Wyndham Lloyd-Davies, James G. Gow and D. R. Davies, and was first published by Wolfe Medical Publications in 1983 at a cost of £48. A second edition, with co-author Helen Parkhouse, was published in 1994.
+
+
+== Content ==
+1,188 images include those of pathological specimens, photographs at endoscopy of the bladder and diagrams that explain urological diagnostic procedures. It contains a collection of X-rays including a comparison of spread to bone from prostate cancer and Paget's disease. 70 images relate to lesions of the penis and scrotum. These include priapism, spermatocele, and hydrocele.
+
+
+== Reviews ==
+J. P. Hopewell, in the Postgraduate Medical Journal, called the book "impressive and interesting" but noted that the X-ray of lung metastases was back to front and felt that improvement could have been made on the X-rays of  polycystic kidney disease. W. Hendry, in the British Journal of Surgery, considered it a complete work covering everything a urologist could possibly see in their profession. A. McMillan, in the British Journal of Venereal Diseases noted that the book was aimed at urologists but suggested that genitourinary physicians might be interested in it. All three reviews reported that the book was expensive.
+
+
+== References ==
+
+
+== External links ==
+Lloyd-Davies, R. W. (Reginald Wyndham) (1989). A colour atlas of urology. Netherlands: Wolfe. ISBN 978-0-7234-1607-4.

data/en.wikipedia.org/wiki/A_Letter_to_a_Friend-0.md

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+---
+title: "A Letter to a Friend"
+chunk: 1/1
+source: "https://en.wikipedia.org/wiki/A_Letter_to_a_Friend"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T08:48:05.233170+00:00"
+instance: "kb-cron"
+---
+
+A Letter to a Friend (written 1656; published posthumously in 1690), by Sir Thomas Browne, the 17th century English philosopher and physician, is a medical treatise of case-histories and witty speculations upon the human condition.
+
+
+== Publication ==
+The Letter was first published as a folio pamphlet in 1690, after having been left out of the 1686 posthumous collection of Browne's complete works. Few copies of this pamphlet are extant; several of those which have survived did so because they were bound as an addition to his complete works. It was then included in his 1712 Poshumous Works printed by Edmund Curll, and a 1716 collection titled Christian Morals edited by John Jeffrey.
+
+
+== Morgellons ==
+Browne's pamphlet is the source of a term Mary Leitao coined in 2001 to describe her son's skin condition. She chose the name "Morgellons disease" based on a skin condition described by Browne in Letter to a Friend, thus:
+
+Hairs which have most amused me have not been in the Face or Head, but on the Back, and not in Men but Children, as I long ago observed in that endemial Distemper33 of little Children in Languedock, called the Morgellons, wherein they critically break out with harsh Hairs on their Backs, which takes off the Unquiet Symptomes of the Disease, and delivers them from Coughs and Convulsions34.
+There is, however, no suggestion that the symptoms described by Browne are linked to the alleged modern cases of Morgellons. In 1935, Charles Ernest Kellett MD FRCP (1903–1978), who lectured in the history of medicine at the University of Newcastle medical school, wrote a detailed criticism of Browne's Morgellons reference.
+
+
+== References ==
+
+
+== External links ==
+
+Full text with comments

data/en.wikipedia.org/wiki/A_Topological_Picturebook-0.md

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+---
+title: "A Topological Picturebook"
+chunk: 1/1
+source: "https://en.wikipedia.org/wiki/A_Topological_Picturebook"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T08:47:02.165515+00:00"
+instance: "kb-cron"
+---
+
+A Topological Picturebook is a book on mathematical visualization in low-dimensional topology by George K. Francis. It was originally published by Springer in 1987, and reprinted in paperback in 2007. The Basic Library List Committee of the Mathematical Association of America has recommended its inclusion in undergraduate mathematics libraries.
+
+
+== Topics ==
+Although the book includes some computer-generated images, most of it is centered on hand drawing techniques. After an introductory chapter on topological surfaces, the cusps in the outlines of surfaces formed when viewing them from certain angles, and the self-intersections of immersed surfaces, the next two chapters are centered on drawing techniques: chapter two concerns ink, paper, cross-hatching, and shading techniques for indicating the curvature of surfaces, while chapter three provides some basic techniques of graphical perspective.
+The remaining five chapters of the book provide case studies of different visualization problems in mathematics, called by the book "picture stories". The mathematical topics visualized in these chapters include the Penrose triangle and related optical illusions; the Roman surface and Boy's surface, two different immersions of the projective plane, and deformations between them; sphere eversion and the Morin surface; group theory, the mapping class groups of surfaces, and the braid groups; and knot theory, Seifert surfaces, the Hopf fibration of space by linked circles, and the construction of knot complements by gluing polyhedra.
+
+
+== Audience and reception ==
+Reviewer Athanase Papadopoulos calls the book "a drawing manual for mathematicians". However, reviewer Dave Auckly disagrees, writing that, although the book explains the principles of Francis's own visualizations, it is not really a practical guide to constructing visualizations more generally. Auckly also calls the chapter on perspective "a bizarre mix of mathematical formulas and artistic constructions". Nevertheless, he reviews it positively as "mathematics book loaded with pictures", aimed at undergraduates interested in mathematics.
+More generally, Bill Satzer suggests that the book can provide inspiration for other mathematical illustrators, and for how mathematics is taught and imagined, and Dušan Repovš sees the book as an encouragement to professional mathematicians to more heavily illustrate their work. Jeffrey Weeks sees the book as an embodiment of the principle that abstract mathematical results can often be best appreciated through concrete examples. Thomas Banchoff writes that most readers from a general audience will be "captivated" by the intricate artworks of the book, and professional mathematicians will find sufficient depth in its explanation of these works. However, Weeks writes that the book fails at another stated purpose, allowing artists to appreciate the mathematics behind the artworks it presents, because the mathematics is too advanced for easy understanding by a general audience.
+
+
+== References ==

data/en.wikipedia.org/wiki/A_Treatise_on_the_Circle_and_the_Sphere-0.md

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+---
+title: "A Treatise on the Circle and the Sphere"
+chunk: 1/1
+source: "https://en.wikipedia.org/wiki/A_Treatise_on_the_Circle_and_the_Sphere"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T08:47:06.833342+00:00"
+instance: "kb-cron"
+---
+
+A Treatise on the Circle and the Sphere is a mathematics book on circles, spheres, and inversive geometry. It was written by Julian Coolidge and published by the Clarendon Press in 1916. The Chelsea Publishing Company published a corrected reprint in 1971. After the American Mathematical Society acquired Chelsea Publishing it was reprinted again in 1997.
+
+
+== Topics ==
+As is now standard in inversive geometry, the book extends the Euclidean plane to its one-point compactification, and considers Euclidean lines to be a degenerate case of circles, passing through the point at infinity. It identifies every circle with the inversion through it, and studies circle inversions as a group, the group of Möbius transformations of the extended plane. Another key tool used by the book are the "tetracyclic coordinates" of a circle, quadruples of complex numbers 
+  
+    
+      
+        a
+        ,
+        b
+        ,
+        c
+        ,
+        d
+      
+    
+    {\displaystyle a,b,c,d}
+  
+ describing the circle in the complex plane as the solutions to the equation 
+  
+    
+      
+        a
+        z
+        
+          
+            
+              z
+              ¯
+            
+          
+        
+        +
+        b
+        z
+        +
+        c
+        
+          
+            
+              z
+              ¯
+            
+          
+        
+        +
+        d
+        =
+        0
+      
+    
+    {\displaystyle az{\bar {z}}+bz+c{\bar {z}}+d=0}
+  
+. It applies similar methods in three dimensions to identify spheres (and planes as degenerate spheres) with the inversions through them, and to coordinatize spheres by "pentacyclic coordinates".
+Other topics described in the book include:
+
+Tangent circles and pencils of circles
+Steiner chains, rings of circles tangent to two given circles
+Ptolemy's theorem on the sides and diagonals of quadrilaterals inscribed in circles
+Triangle geometry, and circles associated with triangles, including the nine-point circle, Brocard circle, and Lemoine circle
+The Problem of Apollonius on constructing a circle tangent to three given circles, and the Malfatti problem of constructing three mutually-tangent circles, each tangent to two sides of a given triangle
+The work of Wilhelm Fiedler on "cyclography", constructions involving circles and spheres
+The Mohr–Mascheroni theorem, that in straightedge and compass constructions, it is possible to use only the compass
+Laguerre transformations, analogues of Möbius transformations for oriented projective geometry
+Dupin cyclides, shapes obtained from cylinders and tori by inversion
+
+
+== Legacy ==
+At the time of its original publication this book was called encyclopedic, and "likely to become and remain the standard for a long period". It has since been called a classic, in part because of its unification of aspects of the subject previously studied separately in synthetic geometry, analytic geometry, projective geometry, and differential geometry. At the time of its 1971 reprint, it was still considered "one of the most complete publications on the circle and the sphere", and "an excellent reference".
+
+
+== References ==
+
+
+== External links ==
+A Treatise on the Circle and the Sphere (1916 edition) at the Internet Archive

data/en.wikipedia.org/wiki/Aequanimitas-0.md

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+---
+title: "Aequanimitas"
+chunk: 1/1
+source: "https://en.wikipedia.org/wiki/Aequanimitas"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T08:47:22.189252+00:00"
+instance: "kb-cron"
+---
+
+Aequanimitas was one of Sir William Osler's most famous essays, delivered to new doctors in 1889 as his farewell address at the Pennsylvania School of Medicine, prior to his transfer to Johns Hopkins. It was published in the same year and in 1904 appeared in his collection of essays titled Aequanimitas with Other Addresses to Medical Students, Nurses and Practitioners of Medicine. A second edition was produced in 1906, and a third in 1932. In the essay, Osler advocates two qualities "imperturbability" and "equanimity", which he defined as "coolness and presence of mind under all circumstances".
+Between 1932 and 1953, Eli Lilly & Company distributed more than 150,000 copies of the third edition to medical graduates.
+Through the years Osler's ideal of "Aequanimitas" has been analysed by various academics. Daniel Sokol, medical ethics and law expert, reasons in the British Medical Journal in 2007, that whatever interpretation is made of Aequanimitas, it "tackles head-on a timeless question: what makes a good doctor?".
+
+
+== Publication ==
+
+
+=== The essay ===
+Aequanimitas was an essay by  Sir William Osler, delivered to new doctors on 1 May 1889 as his farewell address at the Pennsylvania School of Medicine. It was published in the same year.
+Aequanimitas refers to staying calm and composed. In the essay, Osler advocates two qualities "imperturbability" and "equanimity", which he defined as "coolness and presence of mind under all circumstances".
+
+
+=== 1904 and 1906 ===
+In 1904, Aequanimitas was published by H. K. Lewis in Aequanimitas with Other Addresses to Medical Students, Nurses and Practitioners of Medicine, a collection of his essays. A second edition was produced in 1906 by P. Blakiston's Son & Co. in Philadelphia, and H.K. Lewis  in London.
+
+
+=== Eli Lilly & Company ===
+Following Osler's death, an expanded version of the book appeared as a third edition in 1932. It omits the essays "A Way of life", "A  man's redemption of man" and "The old humanities and new science", and became more widely available than the previous editions.
+Between 1932 and 1953, Eli Lilly & Company distributed more than 150,000 copies of the third edition to medical graduates. These volumes were not all the same. There were at least seven different publications in English and one in each of Spanish and Portuguese. There were variations in the type of paper, book size, title page, information on the spine, and printing information. There were also differences in the congratulatory letters from Eli Lilly, placed in each book.
+
+
+== Interpretation ==
+Through the years Osler's ideal of "Aequanimitas" has been criticised on the grounds that it excludes empathy, sympathy, or emotional resonance with patients. One of the strongest critiques was presented by Gerald Weissmann in his book The Woods Hole Cantata (1985). It had  been published the previous year in Hospital Practice, as an essay entitled "Against Aequanimitas". Weissmann's assessment of Osler led him to conclude that Osler's advice held "the public tone of the academic snob". After reciting Osler's description of "imperturbability", Weissmann held the opinion that "the Oslerian view is not only devoid of passion, but [also] of joy".
+Osler however, did not that day in 1889 intend to give the graduating medical students comprehensive advice about how to practice medicine. His involvement was a relatively small part of a busy commencement programme, in which the principal honoree was the retiring professor of surgery, David Hayes Agnew ("Agnew day"). Charles S. Bryan later explains that Osler deliberately confined his remarks to two of the qualities the students would need in practice. Osler emphasized the need to balance "head" and "heart". In his interpretation the balance varies according to the nature of the task at hand and Aequanimitas is best understood as emotions appropriate to the circumstances rather than as indifference as suggested by the critiques.
+Daniel Sokol, medical ethics and law expert, reasons in the British Medical Journal in 2007, that whatever interpretation is made of Aequanimitas, it "tackles head-on a timeless question: what makes a good doctor?".
+
+
+== Legacy ==
+Japan's prime minister's physician, Shigeaki Hinohara, was given a copy of Aequanimitas in the early days of the United States Military Occupation of Japan after the Second World War. Hinohara subsequently translated the title address and paraphrased the rest. In 1948, he published a book entitled The Life of Dr. Osler—Pioneer of American Medicine.
+The term aequanimitas has become a motto. At Johns Hopkins, it appears on ties and scarves worn by the housestaff, and was mentioned in the television programme House.
+A similar concept to aequanimitas was addressed by Steve Jobs at Stanford University in 2005. Daniel Goleman's notion of emotional intelligence has been described as a modern variation of aequanimitas.
+
+
+== References ==
+
+
+== Further reading ==
+Aequanimitas P. Blakiston's Son & Co (1910)
+
+
+== External links ==
+"Home Page – Osler Library Archives – Osler Library of the History of Medicine – McGill University". osler.library.mcgill.ca.

data/en.wikipedia.org/wiki/Al-Hawi-0.md

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+---
+title: "Al-Hawi"
+chunk: 1/1
+source: "https://en.wikipedia.org/wiki/Al-Hawi"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T08:47:24.437406+00:00"
+instance: "kb-cron"
+---
+
+Kitab al-Hawi or Al-Hawi or Kitāb al-Ḥāwī fī al-ṭibb translated as The Comprehensive Book on Medicine is an extensive medical encyclopedia authored by the Persian polymath Abu Bakr Muhammad ibn Zakariya al-Razi (865–925), commonly known in the West as Rhazes in the 10th century. This monumental work is a compendium of Greek, Syrian, and early Arabic medical knowledge, as well as some Indian medical practices.
+It was first translated into Latin in 1279 under the title Continens by Faraj ben Salim, a physician of Sicilian-Jewish origin employed by Charles of Anjou.
+The oldest partial remaining copy of this work belongs to the National Library of Medicine in Bethesda, Maryland dated 1094 CE.
+
+
+== Historical context and composition ==
+The Kitab al-Hawi was composed around the year 900 and spans 22 volumes. It was later published by the Dairat'l-Macarif-il-Osmania (Osmania Oriental Publications Bureau) in Hyderabad, India.
+
+
+== Contents and significance ==
+The book covers a wide range of medical topics, including theoretical  and practical medicine. Al-Razi's approach was notably comprehensive, as he not only included medical knowledge from Greek and Syrian sources but also incorporated insights from Indian medical traditions.
+Al-Razi frequently recommended various treatments, including those that might be considered magical remedies by today's standards. For instance, he addressed conditions such as quartan fever and recommended specific practices for their treatment.
+
+
+== Legacy ==
+The Kitab al-Hawi had a profound influence on the development of medical knowledge in the medieval Islamic world and subsequently in Europe. It was translated into Latin in the 12th century and became one of the main sources of medical knowledge in medieval Europe.
+
+
+== See also ==
+Medicine in the medieval Islamic world
+Islamic Golden Age
+Graeco-Arabic translation movement
+Unani medicine#Islamic Golden Age (786–1258)
+
+
+== References ==

data/en.wikipedia.org/wiki/An_Atlas_of_Illustrations_of_Clinical_Medicine,_Surgery_and_Pathology-0.md

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+---
+title: "An Atlas of Illustrations of Clinical Medicine, Surgery and Pathology"
+chunk: 1/1
+source: "https://en.wikipedia.org/wiki/An_Atlas_of_Illustrations_of_Clinical_Medicine,_Surgery_and_Pathology"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T08:47:27.931520+00:00"
+instance: "kb-cron"
+---
+
+An Atlas of Illustrations of Clinical Medicine, Surgery and Pathology is a medical book of images first published in 1901 by John Bale, Sons & Danielsson. It contains the widely cited photograph taken by Allan Warner of two 13-year-old boys from the same class, who after coming into contact with smallpox, the vaccinated boy remained well and the boy who did not receive the vaccine developed the disease.
+
+
+== References ==

data/en.wikipedia.org/wiki/Articella-0.md

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+---
+title: "Articella"
+chunk: 1/1
+source: "https://en.wikipedia.org/wiki/Articella"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T08:47:26.761166+00:00"
+instance: "kb-cron"
+---
+
+The Articella ('little art') or Ars medicinae ('art of medicine') is a Latin collection of medical treatises bound together in one volume that was used mainly as a textbook and reference manual between the 13th and the 16th centuries. In medieval times, several versions of this anthology circulated in manuscript form among medical students. Between 1476 and 1534, printed editions of the Articella were also published in several European cities.
+The earliest surviving manuscript of the collection was copied just after 1100. The original five texts, in their standard order, are the Isagoge Ioannitii ad Tegni Galieni by Hunayn ibn Ishaq; the Hippocratic Aphorisms and Prognostics; the De urinis of Theophilus Protospatharius; and the De pulsibus of Philaretus. The collection is usually supposed to have grown around Hunayn's Isagoge, an abridged introduction to Galen's classical Greek treatise Ars medica (Techne iatrike) translated from Arabic into Latin by Constantine the African in the 11th century. It circulated independently of the Articella. In the late 12th century, Galen's Ars was added to the Articella as a sixth text under the title Tegni. It was later moved into second place.
+In the mid-13th century, the emergence of formal medical education in several European universities fueled a demand for comprehensive textbooks. Instructors from the influential Salernitan medical school in southern Italy popularized the practice of binding other treatises together with their manuscript copies of the Isagoge.
+
+
+== See also ==
+Medieval medicine of Western Europe
+
+
+== References ==
+
+
+== Bibliography ==
+Cornelius O'Boyle. Thirteenth- and Fourteenth-Century Copies of the "Ars Medicine": A Checklist and Contents Descriptions of the Manuscripts. Articella Studies: Texts and Interpretations in Medieval and Renaissance Medical Teaching, no. 1. Cambridge: Cambridge Wellcome Unit for the History of Medicine, and CSIC Barcelona, Department of History of Science, 1998.
+Jon Arrizabalaga. The "Articella" in the Early Press, c. 1476-1534. Articella Studies: Texts and Interpretations in Medieval and Renaissance Medical Teaching, no. 2. Cambridge: Cambridge Wellcome Unit for the History of Medicine, and CSIC Barcelona, Department of History of Science, 1998.
+Papers of the Articella Project Meeting, Cambridge, December 1995. Articella Studies: Texts and Interpretations in Medieval and Renaissance Medical Teaching, no. 3. Cambridge: Cambridge Wellcome Unit for the History of Medicine, and CSIC Barcelona, Department of History of Science, 1998.
+
+
+== External links ==
+ 
+Medieval manuscripts - Articella

data/en.wikipedia.org/wiki/Autism's_False_Prophets-0.md

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+---
+title: "Autism's False Prophets"
+chunk: 1/1
+source: "https://en.wikipedia.org/wiki/Autism's_False_Prophets"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T08:47:30.278207+00:00"
+instance: "kb-cron"
+---
+
+Autism's False Prophets: Bad Science, Risky Medicine, and the Search for a Cure is a 2008 book by Paul Offit, a vaccine expert and chief of infectious diseases at Children's Hospital of Philadelphia. The book focuses on the controversy surrounding the now-discredited link between vaccines and autism. The scientific consensus is that no convincing scientific evidence supports these claims, and a 2011 pharmacotherapy journal article described the vaccine-autism connection as "the most damaging medical hoax of the last 100 years".
+
+
+== Summary ==
+Offit describes the origins and development of claims regarding the MMR vaccine and the vaccine preservative thiomersal, as well as subsequent scientific evidence which has disproved a link with autism. The book discusses possible explanations for the persistence of these claims in the face of scientific evidence to the contrary, as well as the proliferation of potentially risky and unproven treatments for autism. The author takes a critical view of several advocates of a vaccine–autism link, including Andrew Wakefield, David Kirby, Mark Geier, and Boyd Haley, raising scientific and, in some cases, ethical and legal concerns. The book also explores divisions within the autism community on the topic of vaccines, as some parents consider the ongoing narrow focus on vaccines a distraction from more scientifically promising avenues of research. In this vein, Offit interviews Kathleen Seidel, a mother of an autistic child who has published investigations critical of those who profit from promoting vaccine–autism claims.
+Offit also touches on the heated and bitter debate surrounding vaccine claims. He describes receiving death threats, hate mail, and threats against his children as a result of his advocacy for vaccination. Offit declined to do a book tour for Autism's False Prophets, citing concerns about his physical safety and comparing the intensity of hatred and threats directed at him to that experienced by abortion providers. Author's royalties from the book are being donated to the Center for Autism Research at Children's Hospital of Philadelphia.
+
+
+== Reception ==
+The book was the nucleus of profiles of Offit in Newsweek and The Philadelphia Inquirer. The New York Post reviewed the book positively, concluding: "Although arguably the most courageous and most knowledgeable scientist about vaccines in the United States, Offit lives in fear for his life and that of his family." The Wall Street Journal also praised the book as "an invaluable chronicle that relates some of the many ways in which the vulnerabilities of anxious parents have been exploited."
+The Philadelphia Inquirer wrote that the book "names names and calls nonsense nonsense", and provides "important insight into the fatal flaws of the key arguments of vaccine alarmists." The Inquirer applauded Offit's focus on slanted and sensationalist media coverage of the vaccine–autism issue, but faulted Offit for not holding scientists themselves sufficiently accountable for their failure to communicate the facts to the public.
+The Rocky Mountain News noted that the book "turned the tables" on those who see a pharmaceutical-industry conspiracy behind vaccination, by pointing out that the advocates of the autism–vaccine link receive large sums of money from lawyers and lobbyists. The News applauded the book's deconstruction of "misinformation" from Don Imus, Jenny McCarthy, Joseph Lieberman, and Robert F. Kennedy, Jr., among others, but found Offit's "sarcasm and brow-beating of those he disagrees with" to be "grating".
+Salon reviewed the book as an "enlightening, highly readable, and ... timely" work which "deconstruct[s] the anti-vaccine movement as one driven by bad science, litigious greed, hype and ego." Salon faulted Offit for minimizing the work that autism advocacy groups have done to raise awareness, create support networks, and obtain research funding; the review noted that Offit focuses instead on aggressive and scientifically "slanted" groups like Defeat Autism Now! and Generation Rescue. The review concluded that the book "effectively pulls back the curtain on the anti-vaccine movement to reveal a crusade grounded less in fact and more in greed and opportunism".
+Science called the book "forceful" and "an easy-to-read medical thriller about the consequences of greed, hubris, and intellectual sloppiness." The review noted that Offit did not discuss the irrationality of human decision-making in the presence of relative risk and both anecdotal and empirical evidence, and mentioned that Offit did not carefully discuss the role of regression. In conclusion, the review observed that the book has emboldened the media to apply scientific principles, and called for using the book's momentum to shift resources from the autism–vaccination debate to research into causes and treatments.
+The Journal of Autism and Developmental Disorders said the book "makes an important contribution to popular debates about the etiology and treatment of autism spectrum disorders. The book is arguably the most detailed and thorough history available of the current anti-vaccine movement". The review noted one possible weakness: the book gives light coverage to the public's fundamental misunderstanding of the epidemiology of autism, in that the public fears an "autism epidemic" that may not in fact be occurring. The review concluded with a call to scientists and physicians to follow Offit's lead in communicating to the public even uncomfortable truths about autism.
+Four months after its release, The New York Times reported that the book had been endorsed widely by pediatricians, autism researchers, vaccine companies, and medical journalists, and was "galvanizing a backlash against the antivaccine movement in the United States." Many doctors are critical of "false equivalence" in media coverage of the vaccine issue, and now argue that reporters should treat the antivaccine lobby with the same level of indifference as AIDS denialism and other fringe theories.
+Later in 2009, the New England Journal of Medicine reported that the book effectively advocated for vaccines and refuted the vaccine–autism myth. It noted that a particular strength of the book is its outline of the scientific method and the basic principles of probability and causality, and its coverage of the difficulty of explaining science to the public, such as the difference between causality and coincidence. It noted as a weakness the book's several diversions into topics such as breast implants.
+Other largely favorable reviews appeared in BioScience, in Health Affairs, in the Journal of Child Neurology, and in the Journal of Clinical Investigation.
+In a guest column for The Atlanta Journal-Constitution, neurologist Jon Poling panned Offit's book as "a novel of perceived good and evil". Poling, whose daughter was federally compensated for vaccine injuries, criticized Offit for attacking those with whom he disagrees: "In the story, Offit takes no prisoners, smearing characters in the vaccine-autism controversy as effortlessly as a rich cream cheese."
+
+
+== See also ==
+MMR vaccine and autism
+Thiomersal and vaccines
+Folk epidemiology of autism
+
+
+== References ==
+
+
+== External links ==
+Columbia University Press web page for Autism's False Prophets
+Excerpt from the book's prologue

data/en.wikipedia.org/wiki/Bad_Pharma-0.md

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data/en.wikipedia.org/wiki/Big_Pharma_(book)-0.md

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+---
+title: "Big Pharma (book)"
+chunk: 1/1
+source: "https://en.wikipedia.org/wiki/Big_Pharma_(book)"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T08:47:32.673802+00:00"
+instance: "kb-cron"
+---
+
+Big Pharma: How the World's Biggest Drug Companies Control Illness is a 2006 book by British journalist Jacky Law. The book examines the history of the pharmaceutical industry.
+Before the book, Law was the associate editor of Scrip Magazine.
+
+
+== Reception ==
+Ike Iheanacho writes about the book that "The author is clearly no great fan of the industry. But, refreshingly, she avoids the sort of lazy polemic that casts major pharmaceutical companies as an evil empire that continually foists its products on unwilling and unsuspecting healthcare professionals and patients."
+
+
+== See also ==
+Bad Pharma (2012) by Ben Goldacre
+Side Effects (2008) by Alison Bass
+Lists about the pharmaceutical industry
+
+
+== References ==
+
+
+== External links ==
+Excerpt from the book

data/en.wikipedia.org/wiki/Current_Reviews_in_Obstetrics_and_Gynaecology-0.md

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

data/en.wikipedia.org/wiki/Diagnosis_Mercury-0.md

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+---
+title: "Diagnosis Mercury"
+chunk: 1/1
+source: "https://en.wikipedia.org/wiki/Diagnosis_Mercury"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T08:47:39.612590+00:00"
+instance: "kb-cron"
+---
+
+Diagnosis Mercury: Money, Politics and Poison is a 2008 book by Jane Hightower. The book explains that mercury is a poison and that the majority of mercury in the environment comes from coal-fired power plants.  But the book is mainly concerned with human exposure from the eating of large predatory fish such as swordfish, shark, king mackerel, large tuna, etc. The book also discusses industrial mercury poisonings, such as those in Minamata, Japan, in the 1950s and Ontario, Canada, in the 1970s.
+
+
+== See also ==
+Mercury in fish
+Minamata Convention on Mercury
+
+
+== References ==
+
+
+== External links ==
+Diagnosis: Mercury
+Mercury poisoning symptoms and fish recommendations
+Mercury poisoning time line
+Mercury guidelines
+Author Bio at California Pacific Medical Center
+Mercury Facts

data/en.wikipedia.org/wiki/Die_Homosexualität_des_Mannes_und_des_Weibes-0.md

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+---
+title: "Die Homosexualität des Mannes und des Weibes"
+chunk: 1/1
+source: "https://en.wikipedia.org/wiki/Die_Homosexualität_des_Mannes_und_des_Weibes"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T08:47:40.768630+00:00"
+instance: "kb-cron"
+---
+
+Die Homosexualität des Mannes und des Weibes is a classic 1914 book on homosexuality in men and women that was written by German sexologist Magnus Hirschfeld. A second edition was published in 1920. Hirschfeld was himself gay and an occasional crossdresser, known by other Berlin crossdressers as "Aunt Magnesia".
+The book was part of the series Handbuch der Gesamten Sexualwissenschaft in Einzeldarstellungen and was the third volume of this series. Die Homosexualität des Mannes und des Weibes was not translated until 2000, under the title The Homosexuality of Men and Women by Michael Lombardi-Nash. It has been said that the book was the most significant and authoritative text on homosexuality of its time. The book has often been overlooked in the English-speaking academia.
+
+
+== See also ==
+Die Transvestiten: Eine Untersuchung über den Erotischen Verkleidungstrieb (Hirschfeld, 1910)
+
+
+== References ==

data/en.wikipedia.org/wiki/Donguibogam-0.md

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+---
+title: "Donguibogam"
+chunk: 1/1
+source: "https://en.wikipedia.org/wiki/Donguibogam"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T08:47:44.248506+00:00"
+instance: "kb-cron"
+---
+
+The Dongui Bogam (Korean: 동의보감; translated as "Principles and Practice of Eastern Medicine") is a Korean book compiled by the royal physician, Heo Jun and was first published in 1613 during the Joseon period of Korea.
+The book is regarded as important in traditional Korean medicine, and is one of the classics of Oriental medicine today. In July 2009, it was added to UNESCO’s Memory of the World International Register. The original edition of Dongui Bogam is currently preserved by the Korean National Library. The original was written in Hanja and only part of it was transcribed in Korean for wide reading use, as only officials understood in Hanmun. It was translated to English in 2013.
+
+
+== Name ==
+The title literally translates as "A Precious Mirror of Eastern Medicine". The phrase "Precious Mirror" (보감 寶鑑) is a metaphorical idiom meaning 'something which can be modeled after'. Meanwhile, the phrase "Eastern Medicine" (동의 東醫) is not the antonym to 'Western Medicine'; "Dongguk" (동국 東國), meaning "Eastern Country," was one of the names of Korea, which means the country to the east of China. Therefore, the title can be rendered as "An Exemplary Explanation of Korean Medicine" and is listed in UNESCO Memory of the World as "Principles and Practice of Eastern Medicine".
+
+
+== Background ==
+Known as one of the classics in the history of Eastern medicine, it was published and used in many countries including China and Japan, and remains a key reference work for the study of Eastern medicine. Its categorization and ordering of symptoms and remedies under the different human organs affected, rather than the disease itself, was a revolutionary development at that time. It contains insights that in some cases did not enter the medical knowledge of Europe until the twentieth century.
+Work on the Dongui Bogam started in the 29th year of King Seonjo's reign (1596) by the main physicians of Naeuiwon (내의원, "royal clinic"), with the objective to create a comprehensive compilation of traditional medicine. Main physician Heo Jun led the project, but work was interrupted due to the second Japanese invasion of Korea in 1597. King Seonjo did not see the project come to fruition, but Heo Jun steadfastedly stuck to the project and finally completed the work in 1610, the 2nd year of King Gwanghaegun's reign.
+It "synthesized 2000 years of traditional medical knowledge" from Korea and China, and included Taoist, Buddhist, and Confucian ideas.
+
+
+== The book ==
+The Dongui Bogam consists of 25 volumes. In contrast to Hyangyak jipseongbang (향약집성방, "Compilation of Native Korean Prescriptions"), written in 1433, Dongui Bogam is more systematic. It not only refers to Korean medicinal texts, but also Chinese medicinal texts, and records illnesses practically with their respective remedies.
+
+
+=== Contents ===
+The book is divided into 5 chapters: Naegyeongpyeon (내경편, 内景篇, Internal Medicine), Oehyeongpyeon (외형편, 外形篇, External Medicine), Japbyeongpyeon (잡병편, 難病編, Miscellaneous Diseases), Tangaekpyeon (탕액편, 湯液編, Remedies), and Chimgupyeon (침구편, 鍼灸編, Acupuncture), respectively.
+
+Naegyeongpyeon primarily deals with physiologic functions and equivalent disorders of internal organs. The interactions of five organs - liver, lungs, kidneys, heart, and spleen - are thoroughly explained.
+Oehyeongpyeon explains the function of visible parts of the human body - skin, muscles, blood vessels, tendons, and bones - and the various related illnesses.
+Japbyeongpyeon deals with diagnosis and healing methods of various illnesses and disorders such as anxiety, over-excitement, stroke, cold, nausea, edema, jaundice, carbunculosis, and others. This chapter also has a section for pediatrics and gynecology.
+Tangaekpyeon details methods for creating remedies and medical potions such as the collection of medicinal herbs and plants, creating and handling of medication, correct prescription and administration of medicine. All herbal medicine is categorized with explanations regarding their strength, gathering period and their common names for easy understanding.
+Chimgupyeon explains the acupuncture procedures for various ailments and disorders.
+Dongui Bogam offered not only medical facts, but also philosophical values of Eastern Asia. Heo Jun conveyed the message that maintaining the body's energies in balance leads to one's good health.  The first page of the book is an anatomical map of the human body, linking human body with heaven and earth which embodies the Asian perspective of nature.
+
+
+=== Editions ===
+There have been several print editions of Dongui Bogam besides the original Naeuiwon edition, within Korea and abroad. The first Chinese edition was printed in 1763 with additional prints in 1796, and 1890. The Japanese edition was first printed in 1724, and then 1799.
+
+
+== UNESCO Memory of the World Register and controversy ==
+In 2009, UNESCO decided to add Dongui Bogam to the cultural heritage list due to its contribution as a historical relic and it was placed on UNESCO’s Memory of the World International Register, becoming Korea's seventh cultural heritage to be thus included. However, doctors clashed over Dongui Bogam after the official listing. The Korean Medical Association (KMA) downplayed the book's importance saying that "it shouldn’t be taken as anything more than a recognition of the book's value as a historical relic. It should not be taken as an acknowledgement of traditional medicine for its superior effectiveness", saying that the book is full of quackery such as how to bear a son or how to make yourself invisible. The KMA emphasized that Dongui Bogam was merely a cultural artifact and not science. The Association of Korean Oriental Medicine (AKOM) criticized the doctors of KMA for the lack of their appreciation of the influence of Dongui Bogam and history, saying it is necessary "to inherit and advance traditional medicine".
+
+
+== See also ==
+Heo Jun
+Traditional Korean medicine
+
+
+== References ==
+
+
+== External links ==
+
+Donguibogam: Principles and Practice of Eastern Medicine on the UNESCO Memory of the World international register
+400 years of Dongui Bogam, Dongui Bogam Organization
+Donguibogam, precious book of Korean medicine, article published in the UNESCO Courier

data/en.wikipedia.org/wiki/Endemic_Goiter-0.md

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+---
+title: "Endemic Goiter"
+chunk: 1/1
+source: "https://en.wikipedia.org/wiki/Endemic_Goiter"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T08:47:45.385720+00:00"
+instance: "kb-cron"
+---
+
+Endemic Goiter: The Adaptation of Man to Iodine Deficiency is a monograph about a study of endemic goiters conducted in Mendoza Province, Argentina by the Massachusetts General Hospital and the University of Cuyo. Written by John B. Stanbury, Gordon L. Brownell, Douglas S. Riggs, Hector Perinetti, Juan Itoiz and Enrique B. Del Castillo, it was published in 1954 by Harvard University Press as part of their Harvard University Monographs in Medicine and Public Health series. The study itself was conducted just before the addition of iodine was made mandatory in Mendoza, and it suggested that a thyroid deprived of iodine absorbed iodide in blood more quickly than their iodine-satiated counterparts. 
+Contemporaneous reviews in The Quarterly Review of Biology, Archives of Internal Medicine, Science, and the American Journal of Clinical Pathology all praised the book for what they felt was clear, well-articulated research on the part of the authors. The reviews also felt that the work had provided a great deal of knowledge on thyroids, and several recommended it to wider audience, or just endocrinologists. The Journal of the American Medical Association differed in its assessment, feeling that the book was "too complex and theoretical" for general practitioners, though recommended it for specialists.
+
+
+== References ==

data/en.wikipedia.org/wiki/Ending_Aging-0.md

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+---
+title: "Ending Aging"
+chunk: 1/1
+source: "https://en.wikipedia.org/wiki/Ending_Aging"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T08:47:46.562153+00:00"
+instance: "kb-cron"
+---
+
+Ending Aging: The Rejuvenation Breakthroughs that Could Reverse Human Aging in Our Lifetime is a 2007 book written by biogerontologist Aubrey de Grey, with his research assistant Michael Rae. Ending Aging describes de Grey's proposal for eliminating aging as a cause of debilitation and death in humans, and restoring the body to an indefinitely youthful state, a project that he calls the "strategies for engineered negligible senescence" ("SENS"). De Grey argues that defeating aging is feasible, possibly within a few decades, and he outlines steps that can be taken to hasten the development of regenerative medicine treatments for each side of aging.
+
+
+== Editions ==
+St. Martin's Press, 1st edition (hardcover, 389 pages), released September 4, 2007: ISBN 0-312-36706-6
+St. Martin's Griffin, 1st reprint edition with new afterword (paperback, 448 pages), released October 14, 2008: ISBN 0-312-36707-4
+
+
+== Translations ==
+German: Niemals alt!: So lässt sich das Altern umkehren. Fortschritte der Verjüngungsforschung, transcript Verlag, Bielefeld 2010
+Spanish: El Fin del Envejecimiento. Los avances que podrían revertir el envejecimiento humano durante nuestra vida, Lola Books, Berlín 2013
+Italian: La fine dell'invecchiamento: Come la scienza potrà esaudire il sogno dell'eterna giovinezza, D Editore, Roma 2016
+Portuguese: O fim do envelhecimento: Os avanços que poderiam reverter o envelhecimento humano durante nossa vida, NTZ, 2018
+The book has not been officially translated into Russian, but there is an unofficial non-commercial fan translation named "Отменить Старение", which is distributed on the Internet in PDF format.
+
+
+== See also ==
+Life extension
+Rejuvenation
+Longevity escape velocity
+SENS Research Foundation
+Methuselah Foundation
+Pro-aging trance
+
+
+== References ==
+
+
+=== Other References ===

data/en.wikipedia.org/wiki/Epidemiology_in_Country_Practice-0.md

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+---
+title: "Epidemiology in Country Practice"
+chunk: 1/1
+source: "https://en.wikipedia.org/wiki/Epidemiology_in_Country_Practice"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T08:47:47.739445+00:00"
+instance: "kb-cron"
+---
+
+Epidemiology in Country Practice is a book by  William Pickles (1885–1969), a rural general practitioner (GP) physician in Wensleydale, North Yorkshire, England, first published in 1939. The book reports on how careful observations can lead to correlations between transmission of infective disease between families, farms and villages.
+It contains the detailed observational studies of a 1928 epidemic of catarrhal jaundice and a 1929 epidemic of Bornholm disease which were published in the British Medical Journal (BMJ) in 1930 and 1933 respectively.
+
+
+== Background ==
+William Pickles first realised the possibilities for epidemiological studies for a GP after he read James Mackenzie's The Principles of Diagnosis and Treatment in Heart Affections in the 1920s.
+With the assistance of his wife Gertie, who kept the charts, Pickles recorded his observations on a 1928 epidemic of catarrhal jaundice and a 1929 epidemic of Bornholm Disease in his district. His findings were published in the British Medical Journal in 1930 and 1933 respectively and in 1935 he presented them at the Royal Society of Medicine. The work was praised by Major Greenwood who wrote that Pickles's work would mark a "new era in epidemiology". His observations led to new understandings of the transmission of infective disease within families, farms and villages.
+
+
+== Research and content ==
+Epidemiology in Country Practice contains Pickles's observational studies and a number of articles previously published in medical journals, including the detailed observational studies of the 1928 epidemic of jaundice and the 1929 epidemic of Bornholm disease.  The book has been described as more of an essay on epidemiology than a book filled with masses of data.
+Most of the research was done between 1929 and 1939. From 1937, in order to work on the book, Pickles kept evening surgeries "to a minimum and often there were no patients at all". He methodically reported patterns of prevalent diseases in his area; however, his data collection and publications lacked the consent processes now considered necessary to avoid identification of individuals afflicted by epidemics, particularly in small communities where recognition of persons is deemed easier. Pickles was well acquainted with the eight villages he looked after, and once, as he looked down upon Wensleydale from the top of a hill, realised that he knew everyone in the village and most on first-name basis.
+The book begins with a personal appeal by Pickles for GPs to consider the importance of observations, followed by eight chapters that cover cases such as "influenza, measles, scarlet fever, whooping-cough, and mumps", as a well as jaundice and myalgia. One story is that of a "gypsy" who accompanied her sick husband into the village in a caravan. Her husband was suffering from typhoid and Pickles was able to trace the source of the disease to a faulty water pump that the wife used to wash her laundry. In the book, he compares the case to the work of one of his heroes, William Budd, who carried out similar observations.
+The book also describes an epidemic of catarrhal jaundice that resulted in 250 cases out of a population of almost 6,000, many of which were children. The exact incubation period was not known and ranged from 3 to 40 days. After two years of keeping records and with assistance from the Ministry of Health, Pickles was able to show that the incubation period was 26–35 days. He cross-referenced the evidence with smaller studies in neighbouring villages and in one case was able to trace 13 infections to a single country maid who was determined to attend a fete despite Pickles attending to her in her sickbed the same morning. One of the cases was another young woman and her male friend who, according to his (the man's) sister, often went "in the back door in the evenings, and helps her wash up", causing Pickles to observe that "studies in epidemiology sometimes reveal romances."
+
+
+== Publication history ==
+The book was first published by John Wright & Sons of Bristol in 1939. It had a preface by Major Greenwood, professor of epidemiology and vital statistics at the University of London. In April 1941, during the Second World War, the entire stock of the book, unbound sheets and the type were completely destroyed by enemy action but such was the demand for the book that in 1949 it was reissued in virtually identical form.
+In 1970, a limited edition was published with profits going to the Royal College of General Practitioners (RCGP) appeal. The book was subsequently reprinted by Devonshire Press of Torquay in 1972 and in later editions by the RCGP (1984: ISBN 0-85084-097-X).
+
+
+== Reception and legacy ==
+The book was described by John Horder in 1969 as a "classic", that "makes it all sound too easy and one wonders why no one had thought of it all before". Pickles's obituary in the British Medical Journal in 1969 declared that it had "received excellent notices" and in 2004, J.A. Reid portrayed it as "a seminal  book  that  has  been  read and assessed during past decades by  many  public  health  students and  practitioners". Later, RCGP president Denis Pereira Gray described it as "a masterpiece recognised throughout the world" and that practice-based research should be modelled on Pickles's thorough and accurate recording.
+The book facilitated the link between research and primary care, resulting in the modern expansion of surveillance practices for improvements in public health. In addition, it revealed that general practitioners could carry out "world class research" in the community.
+
+
+== References ==
+
+
+== Further reading ==
+Pickles, WN (1930). "Epidemic Catarrhal Jaundice: An Outbreak in Yorkshire". Br Med J. 1 (3620): 944–6. doi:10.1136/bmj.1.3620.944. PMC 2313304. PMID 20775468.
+Pickles, WN (1933). ""Bornholm" Disease: Account of a Yorkshire Outbreak". Br Med J. 2 (3800): 817–8. doi:10.1136/bmj.2.3800.817. PMC 2369562. PMID 20777871.
+Pemberton, John. (1970) Will Pickles of Wensleydale: The life of a country doctor. London: Bles. ISBN 0713802790
+
+
+== External links ==
+"Epidemiology in Country Practice". Rooke Books. Archived from the original on 26 June 2018. Retrieved 1 May 2018. Bookseller's site including several images of the book

data/en.wikipedia.org/wiki/Epidemiology_in_Relation_to_Air_Travel-0.md

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+---
+title: "Epidemiology in Relation to Air Travel"
+chunk: 1/1
+source: "https://en.wikipedia.org/wiki/Epidemiology_in_Relation_to_Air_Travel"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T08:47:48.910523+00:00"
+instance: "kb-cron"
+---
+
+Epidemiology in Relation to Air Travel is a book by Arthur Massey, the medical officer of health of Coventry, published by H. K. Lewis & Co. in 1933. By comparing the travel times of journeys by ship to those of travelling by air, he demonstrated how the quarantinable diseases plague, cholera, yellow fever and smallpox, could arrive in the UK in the early 1930s.
+Massey noted that travelling by aeroplane, from countries where major infectious diseases were common, to countries where those diseases were rare or non-existent, risked spreading those diseases during the incubation period.
+It was noted by Air Commodore H. E. Whittingham and in The Indian Medical Gazette to be one of the earliest works of its kind.
+
+
+== Publication ==
+Epidemiology in Relation to Air Travel was written by the Coventry-based medical officer of health Arthur Massey, and published by H. K. Lewis and Co. Ltd. in 1933, when the topic was relatively new, and in the year after the International Sanitary Convention for Aerial Navigation was drawn up. It has 59 pages and five maps.
+
+
+== Synopsis ==
+The book deals briefly with the danger of spreading infectious disease via aircraft as flight times in the 1930s brought West Africa and India within a few days' travel of England and Europe, and the United States more speedily reached from Central and South America. Massey noted that travelling by aeroplane, from countries where major infectious diseases were common, to countries where those diseases were rare or non-existent, risked spreading those diseases during the incubation period. It was aimed at informing health authorities and offered solutions for prevention. By comparing the travel times of travelling by ship to those of travelling by air, he demonstrated how particularly four quarantinable diseases (plague, cholera, yellow fever and smallpox), could arrive in the UK in the early 1930s. He made particular note of mosquitoes and the risk of transferring yellow fever. In the preface, he wrote:
+
+Speedier transport is equivalent to a reduction of distance. This was shown when steamships superseded sailing vessels. It is demonstrated more forcibly today by the events of civil aviation. Among the momentous advantages, fraternal and commercial, born of this development, there is the disadvantage that countries affected by certain major infectious diseases are brought nearer to countries which ordinarily enjoy freedom therefrom.
+The book addresses disinfection and sanitation in aircraft, and the prevention of aircraft transmitting plague, cholera, malaria, relapsing fever and smallpox. How to dispose of excrement and implement procedures to avoid carrying disease bearing insects are included in the book.
+
+
+== Response ==
+It was noted by Air Commodore H. E. Whittingham, to be one of the earliest works of its kind, along with that of Air Commodore David Munro, who wrote on the subject in 1925. The Indian Medical Gazette also noted it to be a new field, but disagreed with some of the maps showing plague and cholera distribution in Asia and noted some minor errors in the text.
+
+
+== References ==

data/en.wikipedia.org/wiki/Etiology,_Concept_and_Prophylaxis_of_Childbed_Fever-0.md

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+---
+title: "Etiology, Concept and Prophylaxis of Childbed Fever"
+chunk: 1/1
+source: "https://en.wikipedia.org/wiki/Etiology,_Concept_and_Prophylaxis_of_Childbed_Fever"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T08:47:50.066960+00:00"
+instance: "kb-cron"
+---
+
+Etiology, Concept and Prophylaxis of Childbed Fever (German: Die Ätiologie, der Begriff und die Prophylaxis des Kindbettfiebers) is a pioneering medical book written by Ignaz Semmelweis and published in 1861, which explains how hygiene in hospitals can drastically reduce unnecessary deaths. The book and concept saved millions of mothers from a preventable streptococcal infection.
+The book is 524 pages long and includes studies in hospitals conducted in Vienna in 1847. It is claimed to be one of the most comprehensive medical studies ever published. It was translated into English in 1983 by Dr. K. Codell Carter.
+Semmelweis's findings challenged conventional ideas about  the incidence of puerperal fever (also known as postpartum infections or childbed fever), finding that it could be drastically reduced by requiring hand disinfection in obstetrical clinics. He also cites bed hygiene by washing linens after each patient.
+Puerperal fever was a deadly infection, common in mid-19th-century hospitals. Semmelweis proposed the practice of washing hands with chlorinated lime solutions in 1847 while working in Vienna General Hospital's First Obstetrical Clinic, where doctors' wards had three times the mortality of midwives' wards.
+Semmelweis had his life ruined at the time of publication because his ideas, though now proved and trusted, seemed impossible. The book contains a 100-page section purely dedicated to disproving many of the claims his critics had made about his research and ideas. Due to said critique, Semmelweis's personal life fell apart, leading to behavioral issues and his eventual death.
+Despite this, in today's world Semmelweis is described as the "saviour of mothers."
+
+
+== References ==
+
+
+=== Works cited ===
+
+
+== External links ==
+New York Times
+Google books

data/en.wikipedia.org/wiki/Feminine_Forever-0.md

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+---
+title: "Feminine Forever"
+chunk: 1/1
+source: "https://en.wikipedia.org/wiki/Feminine_Forever"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T08:47:52.361242+00:00"
+instance: "kb-cron"
+---
+
+Feminine Forever is a 1966 book written by American gynecologist Robert A. Wilson. The book characterized menopause and associated symptoms as a serious disease state and strongly advocated the use of estrogen-based menopausal hormone therapy to alleviate it, maintain femininity and well-being, and improve quality of life and health. Wilson's claims were criticized as not being based on adequate research and evidence. Nonetheless, Wilson's book was marketed directly to women and was a best-seller, with it having been implicated in causing a rapid and large rise in prescriptions of menopausal hormone therapy. Subsequently, trials such as the Women's Health Initiative (WHI) contradicted Wilson's claims and showed that menopausal hormone therapy could have significant medical risks, such as venous thromboembolism and breast cancer, and that its benefits were not as great as once believed.
+Decades after the book's publication, it was revealed that the manufacturer of the estrogen drug Premarin had secretly paid Wilson to promote its use by menopausal women.
+
+
+== References ==

data/en.wikipedia.org/wiki/Fixing_Sex-0.md

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+---
+title: "Fixing Sex"
+chunk: 1/1
+source: "https://en.wikipedia.org/wiki/Fixing_Sex"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T08:47:53.573873+00:00"
+instance: "kb-cron"
+---
+
+Fixing Sex: Intersex, Medical Authority, and Lived Experience, a book by Stanford anthropologist and bioethicist Katrina Karkazis, was published in 2008. Described as "thoughtful", "meticulous", and an "authoritative treatise on intersex", the book examines the perspectives of intersex people, their families, and clinicians to offer compassionate look at the treatment of people born with atypical sex characteristics.
+
+
+== Synopsis ==
+In a scholarly work, Karkazis draws heavily on interviews with intersex adults, parents, and physicians to explore how intersex is understood and treated. In part 1, she reviews the history of treatment for intersex traits, highlighting the work of John Money and the introduction of the, then new, terms "gender", "gender role" and "gender identity". She explores the events following publication of Milton Diamond's study of the David Reimer or "John/Joan" case, and the ways in which public opinion impacted on medical treatment. In part 2, Karkazis presents an analysis of current medical approaches to intersex, and the risks involved, in the wake of a 2006 "consensus statement on the management of intersex disorders". She also reviews the methods utilised to assign a sex of rearing to intersex infants, such as genitals and penis size, chromosomes, fertility, "sexing of the brain", and parental wishes; these impact upon determination whether or not to proceed with early genital surgery. Part 3 interviews parents of children with complete androgen insensitivity syndrome and congenital adrenal hyperplasia, and adults with intersex experiences. Part 3 also looks at activism by intersex organizations.
+
+
+== Reception ==
+The book has been well received by both clinicians and intersex groups. Gary Berkovitz, writing in the New England Journal of Medicine states that Karkazis's analysis is fair, compelling, and eloquent; "Current consensus guidelines recommend early separation of the vagina and urethra for female subjects with abnormalities in the formation of the sex organs... Karkazis presents a compelling argument for the deferment of subsequent surgery until the patient is able to decide." Elizabeth Reis, reviewing the book in the American Journal of Bioethics, states that the book identifies risk of incontinence, fistulas, scarring and lack of physical sensation arising from surgical intervention, and the psychological harm caused by the knowledge that "one's genitals are 'wrong,' requiring constant medical scrutiny and 'fixing'. It "masterfully examines the concerns and fears of all those with a stake in the intersex debate: physicians, parents, intersex adults, and activists. ... Karkazis’s honest, multi-pronged approach poses critical questions." Mijeon in the American Journal of Human Genetics writes that the "conclusion is quite fitting", "the history of thinking about the body ... can be highly politicized and controversial". Kenneth Copeland, former president of the Lawson Wilkins Pediatric Endocrine Society, describes the book as "Masterfully balancing all aspects of one of the most polarizing, contentious topics in medicine... the most recent authoritative treatise on intersex."
+Gayle Rubin describes the book as "meticulous, sensitive, and brilliantly executed". Arlene Baratz (Accord Alliance) describes the book as "a velvet-gloved punch to the gut", "astonishing, a tale told straight from the mouths of affected adults, parents, and physicians in tender and lyrical prose." Intersex community organization Organisation Intersex International Australia regards the book as "approachable," "compelling and recommended reading".
+The book was referenced by Involuntary or coerced sterilisation of intersex people in Australia, a 2013 report of a committee of the Senate of Australia in 2013.
+
+
+== Awards and recognition ==
+The book was nominated for the Margaret Mead Award, 2010, and a finalist for the Lambda Literary Award, 2009.
+
+
+== References ==
+
+
+== External links ==
+Official site

data/en.wikipedia.org/wiki/Flexner_Report-0.md

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+---
+title: "Flexner Report"
+chunk: 1/4
+source: "https://en.wikipedia.org/wiki/Flexner_Report"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T08:47:54.714737+00:00"
+instance: "kb-cron"
+---
+
+The Flexner Report is a book-length landmark report of medical education in the United States and Canada, written by Abraham Flexner and published in 1910 under the aegis of the Carnegie Foundation. Flexner not only described the state of medical education in North America, but he also gave detailed descriptions of the medical schools that were operating at the time. He provided both criticisms and recommendations for improvements of medical education in the United States.
+While it had many positive effects on American medical education, the Flexner report has been accused of introducing policies that encouraged systemic racism and sexism.
+The Report, also called Carnegie Foundation Bulletin Number Four, called on American medical schools to enact higher admission and graduation standards, and to adhere strictly to the protocols of mainstream science principles in their teaching and research. The report talked about the need for revamping and centralizing medical institutions. Many American medical schools fell short of the standard advocated in the Flexner Report and, subsequent to its publication, nearly half of such schools merged or were closed outright.
+Colleges for the education of the various forms of alternative medicine, such as electrotherapy, were closed. Homeopathy, traditional osteopathy, eclectic medicine, and physiomedicalism (botanical therapies that had not been tested scientifically) were derided.
+The Report also concluded that there were too many medical schools in the United States, and that too many doctors were being trained. A repercussion of the Flexner Report, resulting from the closure or consolidation of university training, was the closure of all but two black medical schools and the reversion of American universities to male-only admittance programs to accommodate a smaller admission pool.
+In Chapter 11, Flexner stressed that the success of medical education reform and the professionalization of medicine relied heavily on the effective legal and ethical functioning of state medical boards. However, he noted that these boards were failing in their mission, stalling progress, and allowing substandard medical practices to continue, thereby jeopardizing public health. This problem persists as a significant issue in the current practice of medicine in the United States.
+
+== Background ==
+
+During the nineteenth century, American medicine was neither economically supported nor regulated by the government. Few state licensing laws existed, and when they did exist, they were weakly enforced. There were numerous medical schools, all varying in the type and quality of the education they provided.
+In 1904, the American Medical Association (AMA) created the Council on Medical Education (CME), whose objective was to restructure American medical education. At its first annual meeting, the CME adopted two standards: one laid down the minimum prior education required for admission to a medical school; the other defined a medical education as consisting of two years training in human anatomy and physiology followed by two years of clinical work in a teaching hospital. Generally speaking, the council strove to improve the quality of medical students, looking to draw from the society of upper-class, educated students.
+In 1908, seeking to advance its reformist agenda and hasten the elimination of schools that failed to meet its standards, the CME contracted with the Carnegie Foundation for the Advancement of Teaching to survey American medical education. Henry Pritchett, president of the Carnegie Foundation and a staunch advocate of medical school reform, chose Abraham Flexner to conduct the survey. Neither a physician, a scientist, nor a medical educator, Flexner held a Bachelor of Arts degree and operated a for-profit school in Louisville, Kentucky. He visited every one of the 155 North American medical schools that were in operation at the time, all of which differed greatly in their curricula, methods of assessment, and requirements for admission and graduation. Summarizing his findings, he wrote:
+
+"Each day students were subjected to interminable lectures and recitations. After a long morning of dissection or a series of quiz sections, they might sit wearily in the afternoon through three or four or even five lectures delivered in methodical fashion by part-time teachers. Evenings were given over to reading and preparation for recitations. If fortunate enough to gain entrance to a hospital, they observed more than participated."
+The Report became notorious for its harsh description of certain establishments. For example, Flexner described Chicago's fourteen medical schools as "a disgrace to the State whose laws permit its existence ... indescribably foul ... the plague spot of the nation." Nevertheless, several schools received praise for excellent performance, including Western Reserve (now Case Western Reserve), Michigan, Wake Forest, McGill, Toronto, and particularly Johns Hopkins, which was described as the 'model for medical education'.
+The Report ultimately produced many unintended consequences, and many of the repercussions of the Report are still seen in American medicine today. Minority groups, such as African Americans and women, faced fewer opportunities as a result of the publishing of the Flexner Report. Additionally, many medical schools for alternative medicine and osteopathic medicine eventually closed as a result of the Report.

data/en.wikipedia.org/wiki/Flexner_Report-1.md

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+---
+title: "Flexner Report"
+chunk: 2/4
+source: "https://en.wikipedia.org/wiki/Flexner_Report"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T08:47:54.714737+00:00"
+instance: "kb-cron"
+---
+
+== Recommended changes ==
+To help with the transition and change the minds of other doctors and scientists, John D. Rockefeller gave many millions to colleges, hospitals and founded a philanthropic group called "General Education Board" (GEB).
+In the nineteenth century, it was relatively easy to not only receive a medical education, but also to start a medical school. When Flexner researched his report, many American medical schools were small "proprietary" trade schools owned by one or more doctors, unaffiliated with a college or university, and run to make a profit. A degree was typically awarded after only two years of study with laboratory work and dissection optional. Many of the instructors were local doctors teaching part-time. There were very few full-time professors, dedicated to medical education. Medical schools did not receive funding, and their only money came from the students' tuitions. Regulation of the medical profession by state governments was minimal or nonexistent. American doctors varied enormously in their scientific understanding of human physiology, and the word "quack" was in common use.
+Flexner carefully examined the situation. Using the Johns Hopkins School of Medicine as the ideal medical school, he issued the following recommendations:
+
+Reduce both the number of medical schools (from 155 to 31) and the number of poorly trained physicians;
+Increase the prerequisites to enter medical training;
+Train physicians to practice in a scientific manner and engage medical faculty in research;
+Give medical schools control of clinical instruction in hospitals;
+Hire trained, full-time staff for medical education;
+Grant medical schools increased funding;
+Strengthen state regulation of medical licensure
+Flexner expressed that he found Hopkins to be a "small but ideal medical school, embodying in a novel way, adapted to American conditions, the best features of medical education in England, France, and Germany." To Flexner, Hopkins incorporated the high standards of German medical education, while keeping the American standard of high respect for patients by physicians. In his efforts to ensure that Hopkins was the standard to which all other medical schools in the United States were compared, Flexner went on to claim that all the other medical schools were subordinate in relation to this "one bright spot." In addition to Johns Hopkins School of Medicine, Flexner also considered the medical schools at Harvard, University of Michigan, and the University of Pennsylvania to be strong schools. He said that medical schools that did not meet these high standards must change their approach to medical education or close their doors.
+Flexner also believed that admission to a medical school should require, at minimum, a high school diploma and at least two years of college or university study, primarily devoted to basic science. When Flexner researched his report, in the nineteenth century, only 16 out of 155 medical schools in the United States and Canada required applicants to have completed two or more years of university education. By 1920, 92 percent of U.S. medical schools required this prerequisite of applicants. Flexner also argued that the length of medical education should be four years, and its content should be what the CME agreed to in 1905. Flexner recommended that the proprietary medical schools should either close or be incorporated into existing universities. Furthermore, he stated that medical schools needed to be part of a larger university since a proper stand-alone medical school would have to charge too much in order to break even financially.
+Less known is Flexner's recommendation that medical schools appoint full-time clinical professors. During the research of his report, Flexner noted a lack of dedicated, full-time professors. American medical education needed committed professors to teach the next generations of physicians. Holders of these appointments would become "true university teachers, barred from all but charity practice, in the interest of teaching." Flexner pursued this objective for years, despite widespread opposition from existing medical faculty.
+Flexner was the child of German immigrants, and he had studied and traveled in Europe extensively. He was well aware that one could not practice medicine in continental Europe without having undergone an extensive specialized university education. There were many aspects of German medical education that Flexner, along with other medical educators and physicians who had traveled to Germany, admired, such as their national standards for students and universities, academic freedom, and the expectation of postgraduate training. Furthermore, many physicians who traveled to Europe to receive postgraduate training were impressed with the German dedication to research, innovation, and teaching. In effect, Flexner demanded that American medical education conform to prevailing practice in continental Europe.
+By and large, medical schools in Canada and the United States followed many of Flexner's recommendations. However, schools have increased their emphasis on matters of public health.

data/en.wikipedia.org/wiki/Flexner_Report-2.md

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+---
+title: "Flexner Report"
+chunk: 3/4
+source: "https://en.wikipedia.org/wiki/Flexner_Report"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T08:47:54.714737+00:00"
+instance: "kb-cron"
+---
+
+=== Strengthening state regulation of medical licensure ===
+Chapter 11 of the Flexner Report, "The State Boards," offers a scathing critique of the medical regulatory landscape at the time, particularly focusing on the inefficacy and inconsistency of state medical boards. Flexner identifies the critical role these boards were intended to play in upholding medical education standards, both legally and ethically, but argues that they had largely failed in this responsibility."In 1906, the worst of the Chicago schools a school with no entrance requirement, no laboratory teaching, no hospital connections made before state boards the best record attained by any Chicago school in that year. This school, essentially the same now as then, has only recently been declared "not in good standing" with the state board of Illinois. Everywhere in Canada and the United States wretched institutions refute criticism by pointing to their successful state board records."Flexner's broader reform plan, which aimed to elevate medical education in the United States, was fundamentally dependent on state medical boards functioning as effective gatekeepers to the profession. He insisted that state boards must rigorously ensure that only those who completed proper, standardized training could enter medical practice. From a legal standpoint, state boards were to have the authority to license practitioners, while ethically, they were responsible for maintaining the integrity of the profession by enforcing these standards."The power that validates the diploma with its license must have the strength to protect its issues against either debasement or infringement." However, Flexner's report critiques the widespread corruption and lack of uniformity among state boards, which allowed substandard medical schools to continue operating. The boards were often controlled by political forces rather than by educational or professional considerations, leading to inconsistency in their enforcement of licensing standards. Some states maintained high standards, while others allowed almost anyone with minimal training to practice medicine."In many states appointments are regarded as political spoils; quite generally teachers are ineligible for appointment. It happens, therefore, that the boards are sometimes weak, and either unwilling to antagonize the schools or legally incapable of so doing; again, well meaning but incompetent; in some cases unquestionably neither weak nor well meaning, but cunning, powerful, and closely aligned with selfish and harmful political interests." Flexner lamented that this patchwork regulatory system undermined his vision for a unified, scientific, and ethical medical profession across the U.S. His plan relied on the boards acting as ethical watchdogs for public health and safety, but the failures of these boards to fulfill their role were highlighted as a significant barrier to achieving widespread reform.
+
+== Impact of the report ==
+Many aspects of the medical profession in North America changed following the Flexner Report. Medical training adhered more closely to the scientific method and became grounded in human physiology and biochemistry. Medical research aligned more fully with the protocols of scientific research. Average physician quality significantly increased.
+
+=== Medical school closings ===
+Flexner wanted to improve both the admissions standards of medical school and the quality of medical education itself. He recognized that many of the medical schools had inadequate admissions requirements and a lack of adequate education. Consequently, Flexner sought to reduce the number of medical schools in the United States. A majority of American institutions granting MD or DO degrees as of the date of the Report (1910) closed within two to three decades. (In Canada, only the medical school at Western University was deemed inadequate, but none was closed or merged subsequent to the Report.) In 1904, before the Report, there were 160 MD-granting institutions with more than 28,000 students. By 1920, after the Report, there were only 85 MD-granting institutions, educating only 13,800 students. By 1935, there were only 66 medical schools operating in the United States.
+Between 1910 and 1935, more than half of all American medical schools merged or closed. The dramatic decline was in some part due to the implementation of the Report's recommendation that all "proprietary" schools be closed and that medical schools should henceforth all be connected to universities. Of the 66 surviving MD-granting institutions in 1935, 57 were part of a university. An important factor driving the mergers and closures of medical schools was the national regulation and enforcement of medical school criteria: All state medical boards gradually adopted and enforced the Report 's recommendations. In response to the Flexner Report, some schools fired senior faculty members as part of a process of reform and renewal.
+
+=== Impact on the role of physician ===
+The vision for medical education described in the Flexner Report narrowed medical schools' interests to disease, moving away from an interest on the system of health care or society's health beyond disease. Preventive medicine and population health were not considered a responsibility of physicians, bifurcating "health" into two separate fields: scientific medicine and public health.
+
+=== Impact on African-American doctors and patients ===
+The Flexner Report has been criticized for introducing policies that encouraged systemic racism .
+Flexner advocated for the closing of all but two of the historically black medical schools. As a result, only Howard University College of Medicine and Meharry Medical College were left open, while five other schools were closed. Flexner emphasized his view that black doctors should treat only black patients and should play roles subservient to those of white physicians. Flexner promoted the idea that African American medical students should be trained in "hygiene rather than surgery" and be employed as "sanitarians," with a primary role to protect white Americans from disease. Flexner stated in the Report:
+
+"A well-taught negro sanitarian will be immensely useful; an essentially untrained negro wearing an M.D. degree is dangerous."
+Furthermore, along with his adherence to germ theory, Flexner argued that, if not properly trained and treated, African-Americans posed a health threat to middle and upper-class whites. Flexner argued that African American physicians should be educated in order to stop the transmission of diseases among African Americans and to prevent the contamination of white people from those same diseases.

data/en.wikipedia.org/wiki/Flexner_Report-3.md

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+---
+title: "Flexner Report"
+chunk: 4/4
+source: "https://en.wikipedia.org/wiki/Flexner_Report"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T08:47:54.714737+00:00"
+instance: "kb-cron"
+---
+
+"The practice of the Negro doctor will be limited to his own race, which in its turn will be cared for better by good Negro physicians than by poor white ones. But the physical well-being of the Negro is not only of moment to the Negro himself. Ten million of them live in close contact with sixty million whites. Not only does the Negro himself suffer from hookworm and tuberculosis; he communicates them to his white neighbors, precisely as the ignorant and unfortunate white contaminates him. Self-protection not less than humanity offers weighty counsel in this matter; self- interest seconds philanthropy. The Negro must be educated not only for his sake, but for ours. He is, as far as the human eye can see, a permanent factor in the nation."
+Flexner's findings also restricted opportunities for African-American physicians in the medical sphere. Even the Howard and Meharry schools struggled to stay open following the Flexner Report, having to meet the institutional requirements of white medical schools, reflecting a divide in access to health care between white and African-Americans. Following the Flexner Report, African-American students sued universities, challenging the precedent set by Plessy v. Ferguson. However, those students were met by opposition from schools that remained committed to segregated medical education. It was not until 15 years after Brown v. Board of Education in 1954 that the AAMC ensured access to medical education for African-Americans and minorities by supporting the diversification of medical schools.
+The closure of the five schools, and the fact that black students were not admitted to many U.S. medical schools for the 50 years following the Flexner Report, has contributed to the low numbers of American-born physicians of color as the ramifications are still felt, more than a century later. Tens of thousands of African American physicians disappeared as a result of the Flexner Report. In relation to the national Census, physicians belonging to minority groups, including African Americans, remain underrepresented in medicine.
+In response to the racist writings of the Flexner Report, the AAMC decided to rename the prestigious Abraham Flexner award in 2020.  David Acosta, M.D., the chief diversity and inclusion officer of AAMC, stated, "We must not ignore medicine's racist history and make every effort toward reparation when this history is identified." However, the view that Flexner and the Report were detrimental to black medical schools is resisted by Thomas N. Bonner, who contended that Flexner worked to save the two black medical schools that were graduating most of the black physicians at that time.
+
+=== Impact on women ===
+The Flexner Report has also been criticized for introducing policies that encouraged sexism, resulting in "the near elimination of women in the physician workforce between 1910 and 1970."  Before the publication of the Flexner Report, in the mid-to-latter part of the nineteenth century, universities had just begun opening and expanding female admissions as part of both women's and co-educational facilities with the founding of co-educational Oberlin College in 1833 and private all-women's colleges such as Vassar College and Pembroke College. Furthermore, many women opened their own medical schools for women as a response to other medical schools refusing to admit them.
+In the Report, Flexner noted that there were few women in medical education. Flexner believed that the small numbers of female medical students and female physicians was not due to a lack of opportunity because, as he saw it, there were ample opportunities for women to be educated in medicine. Thus, he believed that the low numbers were due to a decreased desire and tendency to enter medical school.
+
+“Now that women are freely admitted to the medical profession, it is clear that they show a decreasing inclination to enter it. More schools in all sections are open to them; fewer attend and fewer graduate.”
+Flexner also emphasized women's particular role in medicine throughout the Report, stating that "[w]oman has so apparent a function in certain medical specialties". While some people thought that women were the intellectual equals of men and could be proficient in any field, the majority assumed that women were naturally nurturing and loving, and if they were going to pursue a medical career, they should do so in child health, occupational health, or maternal health. Today, it is speculated that the Report may have been a factor in encouraging female physicians to specialize in pediatrics, obstetrics and gynecology rather than other disciplines.
+
+=== Impact on alternative medicine ===
+When Flexner researched his report, "modern" medicine faced vigorous competition from several quarters, including osteopathic medicine, chiropractic medicine, electrotherapy, eclectic medicine, naturopathy, and homeopathy. Flexner clearly doubted the scientific validity of all forms of medicine other than that based on scientific research, deeming any approach to medicine that did not advocate the use of treatments such as vaccines to prevent and cure illness as tantamount to quackery and charlatanism. Medical schools that offered training in various disciplines including electromagnetic field therapy, phototherapy, eclectic medicine, physiomedicalism, naturopathy, and homeopathy, were told either to drop these courses from their curriculum or lose their accreditation and underwriting support. A few schools resisted for a time, but eventually most schools for alternative medicine complied with the Report or shut their doors.
+
+=== Impact on osteopathic medicine ===
+While almost all the alternative medical schools listed in the Flexner Report were closed, the American Osteopathic Association (AOA) brought a number of osteopathic medical schools into compliance with Flexner's recommendations to produce an evidence-based approach and practice. Today, the curricula of DO- and MD-awarding medical schools are now nearly identical, the chief difference being the additional instruction in osteopathic schools of osteopathic manipulative medicine.
+
+== See also ==
+Committee of Ten
+African American student access to medical schools
+
+== References ==
+
+== Further reading ==
+Beck, Andrew H. (May 5, 2004). "The Flexner report and the standardization of American medical education" (PDF). The Journal of the American Medical Association. 291 (17): 2139–40. doi:10.1001/jama.291.17.2139. PMID 15126445. Retrieved November 24, 2012.
+Bonner, Thomas Neville, 2002. Iconoclast: Abraham Flexner and a Life in Learning. Johns Hopkins Univ. Press. ISBN 0-8018-7124-7.
+Flexner, Abraham; Pritchett, Henry (1910). "The Flexner Report" (PDF).(PDF) from the Carnegie Foundation for the Advancement of Teaching
+Gevitz, Norman, and Grant, U. S., 2004. The D.O.s (2nd ed.). Baltimore: The Johns Hopkins University Press. ISBN 0-8018-7834-9.
+Starr, Paul, 1982. The Social Transformation of American Medicine. Basic Books. ISBN 0-465-07935-0.
+Wheatley, S. C., 1989. The Politics of Philanthropy: Abraham Flexner and Medical Education. University of Wisconsin Press. ISBN 0-299-11750-2, ISBN 0-299-11754-5.
+
+== External links ==
+"Flexner Report Transformed Med Schools", All Things Considered, August 16, 2008.
+The Flexner Report ― 100 Years Later (September 2011)
+ The Flexner Report public domain audiobook at LibriVox

data/en.wikipedia.org/wiki/Full_Catastrophe_Living-0.md

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+---
+title: "Full Catastrophe Living"
+chunk: 1/3
+source: "https://en.wikipedia.org/wiki/Full_Catastrophe_Living"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T08:47:55.897257+00:00"
+instance: "kb-cron"
+---
+
+Full Catastrophe Living: Using the Wisdom of Your Body and Mind to Face Stress, Pain, and Illness is a book by Jon Kabat-Zinn, first published in 1990, revised in 2013, which describes the mindfulness-based stress reduction (MBSR) program developed at the University of Massachusetts Medical Center's Stress Reduction Clinic. In addition to describing the content and background of MBSR, Kabat-Zinn describes scientific research showing the medical benefits of mindfulness-based interventions (MBIs), and lays out an approach to mind-body medicine emphasizing the depth of the interconnections between physical and mental health. The book has been called "one of the great classics of mind/body medicine", and has been seen as a landmark in the development of the secular mindfulness movement in the United States and internationally.
+
+== Background ==
+
+Full Catastrophe Living grew out of the work of the University of Massachusetts Medical Center's Stress Reduction Clinic, founded in 1979 by Jon Kabat-Zinn. The purpose of the Clinic was to "serve as a referral service for physicians and other health providers, to which they could send medical patients with a wide range of diagnoses and conditions who were not responding completely to more traditional treatments, or who were 'falling through the cracks' in the health care system altogether and not feeling satisfied with their medical treatments and outcomes." The Clinic's Stress Reduction and Relaxation Program, later renamed mindfulness-based stress reduction (MBSR), aimed to help patients by providing  a relatively intensive training in mindfulness meditation and mindful hatha yoga. This was done through an eight-week course, which, in the words of Kabat-Zinn,
+
+was meant to serve as an educational (in the sense of inviting what is already present to come forth) vehicle through which people could assume a degree of responsibility for their own well-being and participate more fully in their own unique movement towards greater levels of health by cultivating and refining our innate capacity for paying attention and for a deep, penetrative seeing/sensing of the interconnectedness of apparently separate aspects of experience, many of which tend to hover beneath
+our ordinary level of awareness regarding both inner and outer experience.
+Kabat-Zinn composed Full Catastrophe Living with aim of capturing "the essence and spirit of the MBSR curriculum as it unfolds for our patients", while at the same time articulating "the dharma that underlies the curriculum, but without ever using the word 'Dharma' or invoking Buddhist thought or authority, since for obvious reasons, we do not teach MBSR in that way."
+Kabat-Zinn recalls his desire for the book to "embody ... the dharma essence of the Buddha's teachings" in a way that was "accessible to mainstream Americans", and to avoid "as much as possible the risk of it being seen as Buddhist, 'New Age,' 'Eastern Mysticism' or just plain 'flakey.'" In this connection, Kabat-Zinn experienced internal conflict over whether to include a letter of endorsement from Thich Nhat Hanh in the book's first edition, which was published in 1990. Kabat-Zinn felt that the letter "spoke deeply and directly to the essence of the original vision and intention of MBSR", but was also mindful that it "used the very foreign word dharma not once, but four times". Nhat Hanh's letter read as follows:
+
+This very readable and practical book will be helpful in many ways. I believe many people will profit from it. Reading it, you will see that meditation is something that deals with our daily life. The book can be described as a door opening both on the dharma (from the side of the world) and on the world (from the side of the dharma). When the dharma is really taking care of the problems of life, it is true dharma. And this is what I appreciate most about the book. I thank the author for having written it.
+Eventually, Kabat-Zinn decided to include the letter in his book as a preface, judging that by 1990 "there was no longer as big a risk of our work being identified with a 'lunatic fringe'", due to the scientific evidence that had already emerged for MBSR's efficacy, as well as the accelerating interpenetration of the so-called "counter-culture" with America's mainstream culture.
+
+== Publication ==
+Full Catastrophe Living was first published in 1990 and went through numerous reprintings, before eventually being reissued in a revised second edition in 2013. The second edition refines the meditation instructions and descriptions of mindfulness-based approaches found in the first edition, and also reflects the "exponential" growth of scientific research into mindfulness and its clinical applications in the two decades after the book was first published.
+
+== Title ==
+The title Full Catastrophe Living is derived from the film Zorba the Greek, in which the title character says, in response to being asked whether he has ever married, "Am I not a man? Of course I've been married. Wife, house, kids ... the full catastrophe". According to Kabat-Zinn:
+
+Zorba's response embodies a supreme appreciation for the richness of life and the inevitability of all its dilemmas, sorrows, traumas, tragedies, and ironies. His way is to "dance" in the gale of the full catastrophe, to celebrate life, to laugh with it and at himself, even in the face of personal failure and defeat. In doing so, he is never weighed down for long, never ultimately defeated either by the world or by his own considerable folly.
+Kabat-Zinn has written that his editor for the first edition of the book was concerned that including the word "catastrophe" in the title might "repel potential readers right from the start." However, Kabat-Zinn found that the phrase Full Catastrophe Living "just kept coming back", as it seemed to touch on "something very special that lies within us, our capacity for embracing the actuality of things, often when it seems utterly impossible, in ways that are healing and transforming, even in the face of the full catastrophe of the human condition."
+
+== Summary ==

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+title: "Full Catastrophe Living"
+chunk: 2/3
+source: "https://en.wikipedia.org/wiki/Full_Catastrophe_Living"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T08:47:55.897257+00:00"
+instance: "kb-cron"
+---
+
+=== Introduction ===
+In the introduction to the revised edition of 2013, Kabat-Zinn defines mindfulness, reflects on the massive growth of  MBSR and other mindfulness-based practices since the publication of the first edition in 1990, and lays out the findings of relevant scientific studies. He defines mindfulness operationally as "the awareness that arises by paying attention on purpose, in the present moment, and non-judgmentally", while noting that "when we speak of mindfulness, it is important to keep in mind that we equally mean heartfulness ... It is a more-than-conceptual knowing. It is more akin to wisdom, and to the freedom a wisdom perspective provides." He emphasizes that mindfulness involves accessing within ourselves capacities that we in fact already possess, "finding, recognizing, and making use of that in us which is already okay, already beautiful, already whole by virtue of our being human—and drawing upon it to live our lives as if it really mattered how we stand in relationship to what arises, whatever it is." While stressing that "mindfulness has its own internal logic and poetry", he suggests that scientific research showing its beneficial effects for health and well-being may provide extra incentive to follow the MBSR curriculum. He highlights, among other research, studies using fMRI technology to show significant beneficial changes in the brain subsequent to MBSR training.
+
+=== Part I: The Practice of Mindfulness ===
+Kabat-Zinn begins this section by laying out what he sees as the foundational attitudes necessary for mindfulness practice. The attitudes Kabat-Zinn identifies – non-judging, patience, beginner's mind, trust, non-striving, acceptance, and letting go – reflect his grounding in Zen Buddhism. In particular, Kabat-Zinn emphasizes the non-instrumental nature of mindfulness practice, as in his explication of "non-striving":
+
+Almost everything we do we do for a purpose, to get something or somewhere. But in meditation this attitude can be a real obstacle. That is because meditation is different from all other human activities. Although it takes a lot of work and energy of a certain kind, ultimately meditation is a non-doing. It has no goal other than for you to be yourself. The irony is that you already are. This sounds paradoxical and a little crazy. Yet this paradox and craziness may be pointing you toward a new way of seeing yourself, one in which you are trying less and being more. This comes from intentionally cultivating the attitude of non-striving.
+Kabat-Zinn's Zen training is also evident in his emphasis on non-duality, as in his explication of "non-judging", in which he stresses the limitations of all mental categorizations and judgements.
+The remainder of the section is devoted to a detailed description of the various meditation practices taught in the MBSR course. These practices reflect a Theravada or vipassana influence, in that they emphasize the systematic investigation of various aspects of present-moment experience. Kabat-Zinn describes at length the practices of the body scan, mindfulness of breathing, and mindful hatha yoga, as well as other practices such as walking meditation and mindfulness of daily activities such as eating. He also narrates the stories of various MBSR participants and their experiences with the practices. For instance, he tells the story of "Mary", for whom the body scan precipitated a transformative encounter with physical tensions connected with traumatic experiences from childhood, and that of a young woman for whom the walking meditation proved to be the key to overcoming her extreme anxiety.
+
+=== Part II: The Paradigm ===
+In this section Kabat-Zinn lays out the theoretical basis for his approach to health and healing, emphasizing the concepts of "wholeness" and "interconnectedness". He summarizes this approach, which he associates with mind-body and integrative medicine, as follows:
+
+Perhaps the most fundamental development in medicine over the past decades is the recognition that we can no longer think about health as being solely a characteristic of the body or the mind, because body and mind are not two separate domains—they are intimately interconnected and completely integrated. The new perspective acknowledges the central importance of thinking in terms of wholeness and interconnectedness and the need to pay attention to the interactions of mind, body, and behavior in any comprehensive effort to understand and treat illness. This view emphasizes that science will never be able fully to describe a complex dynamical process such as health, or even a relatively simple chronic disease, without looking at the functioning of the whole organism, rather than restricting itself solely to an analysis of parts and components, no matter how important that domain may be as well.
+Kabat-Zinn goes on to lay out the extensive scientific evidence for the close interconnection between mental and physical processes, examining the impact that attitudes such as optimism or pessimism, self-efficacy, hardiness, sense of coherence, and anger can have on physical conditions including cancer and heart disease. He also extends the concept of wholeness to stress the intimate interconnectedness of all living and non-living phenomena, approvingly quoting a letter from Albert Einstein stating that the human sense of being "something separated from the rest" is "a kind of optical delusion of consciousness".
+
+=== Part III: Stress ===
+In this section Kabat-Zinn lays out a range of scientific evidence relating to the psychological and physiological effects of stress, then goes on to describe how mindfulness practice can alleviate these effects. Drawing on the work of Richard Lazarus and Susan Folkman, he defines psychological stress in terms of the relationship between a person and their environment, which in this case is perceived as taxing or threatening. Kabat-Zinn examines both the prevalence and the deleterious effects of chronic stress within modern societies, noting that many of the automatic stress reactions common to human beings are poorly adapted to the types of problems modern people most often face. He writes:

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+---
+title: "Full Catastrophe Living"
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+source: "https://en.wikipedia.org/wiki/Full_Catastrophe_Living"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T08:47:55.897257+00:00"
+instance: "kb-cron"
+---
+
+Health can be undermined by a lifetime of ingrained behavior patterns that compound and exacerbate the pressures of living we continually face. Ultimately, our habitual and automatic reactions to the stressors we encounter, particularly when we get in the habit of reacting maladaptively, determine in large measure how much stress we experience. Automatic reactions triggered out of unawareness—especially when the circumstances are not life-threatening but we take them that way all the same—can compound and exacerbate stress, making what might have remained basically simple problems into worse ones over time. They can prevent us from seeing clearly, from solving problems creatively, and from expressing our emotions effectively when we need to communicate with other people or even understand what is going on within ourselves. ... A lifetime of unconscious and unexamined habitual reactivity to challenges and perceived threats is likely to increase our risk of eventual breakdown and illness significantly.
+Habitual maladaptive reactions to stressors can include physical tensions, workaholism, addiction to various chemicals, drugs, or foods, and depressive rumination. Kabat-Zinn describes how mindfulness practice can help people to overcome such maladaptive reactions by bringing them into awareness, "allowing you to engage in and influence the flow of events and your relationship to them at those very moments when you are most likely to react automatically, and plunge into hyperarousal and maladaptive attempts to keep things under some degree of control." Mindful awareness, Kabat-Zinn writes, allows us to respond to stressors wisely rather than reacting automatically, helping us to deal with stressors more effectively while also bringing "the comfort of wisdom and inner trust, the comfort of being whole."
+
+=== Part IV: The Applications ===
+In this section Kabat-Zinn offers detailed advice for practicing mindfulness in the face of a range of specific stressors, including medical symptoms, emotional disturbance, time and work pressures, relationship issues, and stress relating to political or world events. Reflecting MBSR's origins in a medical clinic, significant space is devoted to considerations relevant to people suffering from chronic pain and other long-term health conditions. Kabat-Zinn notes that MBSR's approach to pain seems counter-intuitive to many people, as it does not involve trying to get rid of it or distracting the mind from it, but rather involves accepting and investigating the pain with compassionate attention. He writes:
+
+The way of mindfulness is to accept ourselves right now, as we are, symptoms or no symptoms, pain or no pain, fear or no fear. Instead of rejecting our experience as undesirable, we ask, "What is this symptom saying, what is it telling me about my body and my mind right now?" We allow ourselves, for a moment at least, to go right into the full-blown feeling of the symptom. This takes a certain amount of courage, especially if the symptom involves pain, a chronic illness, or fear of death. But the challenge here is can you at least "dip your toe in the water" by trying it just a little, say for ten seconds, just to move in a little closer for a clearer look? Can we metaphorically put out the welcome mat for what is here, simply because it is already here, and take a look, or even better, allow ourselves to feel our way into the full range of our experience in such moments?
+Kabat-Zinn describes how paying attention to pain in this way can help people to identify with it less – to see a headache as "just a headache" rather than "my headache" – and to overcome habitual maladaptive mental and physical reactions that, in the case of chronic pain in particular, can play a significant role in both the intensity and the salience of pain experiences. Kabat-Zinn describes various scientific studies showing the significant benefits of mindfulness practice for chronic pain sufferers, and illustrates these findings with the stories of MBSR patients.
+
+== Reception and influence ==
+
+After its publication, Full Catastrophe Living became a global bestseller. It has been described as a "landmark" and a "classic" in the fields of mind-body medicine and secular mindfulness, and has been cited in scholarly works and books over fifteen thousand times as of August 2023. The book is generally seen as the foundational text of the mindfulness-based stress reduction (MBSR) program, which is offered in more than 740 hospitals, clinics, and stand-alone programs worldwide. Full Catastrophe Living has also been credited with an important role in inspiring the development of other mindfulness-based interventions (MBIs), including mindfulness-based cognitive therapy (MBCT) and mindfulness-based pain management (MBPM).
+
+== See also ==
+Jon Kabat-Zinn
+Mindfulness-based stress reduction (MBSR)
+
+== References ==

data/en.wikipedia.org/wiki/Galileo's_Middle_Finger-0.md

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+---
+title: "Galileo's Middle Finger"
+chunk: 1/1
+source: "https://en.wikipedia.org/wiki/Galileo's_Middle_Finger"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T08:47:57.079400+00:00"
+instance: "kb-cron"
+---
+
+Galileo's Middle Finger is a 2015 book about the ethics of medical research by Alice Dreger, an American bioethicist and author. Dreger explores the relationship between science and social justice by discussing a number of scientific controversies. These include the debates surrounding intersex genital surgery, autogynephilia, and anthropologist Napoleon Chagnon's work.
+
+
+== Synopsis ==
+The first part of Galileo's Middle Finger recounts Dreger's activism against surgical "correction" of intersex individuals' genitalia. Some surgeons called this "total urogenital mobilization" which is "...ripping out everything that didn't seem right to the doctor and rebuilding a girl's genitals from scratch using Frankenstein stitches..." Based on her interactions with the intersex community as well as her own research, she advocated that genital surgery for intersex children be postponed until the individual is old enough to make an informed decision, in the absence of any evidence that the benefits of such surgery outweighed its already reported risks.
+The second section provides her analysis of the controversy surrounding The Man Who Would Be Queen (2003), by sex researcher and psychologist J. Michael Bailey. In that book, Bailey summarized research on Blanchard's transsexualism typology in a way that Dreger says is scientifically accurate, well-intended, and sympathetic, but insensitive to its political implications. Dreger writes that "Bailey made the mistake of thinking that openly accepting and promoting the truth about people's identities would be understood as the same as accepting them and helping them, as he felt he was". Instead, many activists in the trans community objected to the contention that their transition was sexually motivated.
+Bailey's book was based on the academic publications of psychologist Ray Blanchard, which Bailey interpreted for a lay audience. The larger audience and potential to influence public beliefs about transgenderism led a prominent transgender activist, Lynn Conway, to campaign against Bailey.  Dreger concludes that the accusations levied against Bailey by Conway and others did not hold up to scrutiny. "Conway developed what became an enormous Web site hosted by the University of Michigan for the purpose of taking down Bailey and his ideas [and] that largely enabled me to figure out what she had really done and how Bailey had essentially been set up in an effort to shut him up about autogynephilia". Dreger wrote that some activists had turned their horror at Bailey's findings into a very public vendetta against him and his family, including thinly veiled allegations that he sexually abused his children. After researching the allegations against Bailey, she concluded that they were false.  Moreover, Dreger observed that "the most interesting mail, from my perspective, came from trans women who wrote to tell me that, though they weren't thrilled with Bailey's oversimplifications of their lives, they also had been harassed and intimidated by Andrea James for daring to speak anything other than the politically popular 'I was always just a woman trapped in a man's body' story. They thanked me for standing up to a bully."
+Dreger also investigates the controversy surrounding biologist Randy Thornhill and anthropologist Craig T. Palmer's A Natural History of Rape (2000) and accusations by Patrick Tierney in his book Darkness in El Dorado (2000) that anthropologist Napoleon Chagnon seriously abused the Yanomamo. She returns to the issue of intersex in an examination of geneticist Maria New's research in prenatal dexamethasone use in cases of congenital adrenal hyperplasia.
+
+
+== Reception ==
+The New York Times described the book as "a rant, a manifesto, a treasury of evocative new terms (sissyphobia, autogynephilia, Phall-O-Meter) and an account of the author's transformation" from activist to scientist and back again. Salon describes the book as "highly readable" with an important message: "Science and social justice require each other to be healthy and both are critically important to human freedom." The book was also discussed by Tom Bartlett in the Chronicle of Higher Education. Kirkus Reviews named it one of the best non-fiction books of 2015.
+The book was at first selected as 2016 finalist for a Lambda Literary Award in the LGBTQ nonfiction category, but the foundation rescinded this nomination on March 22, 2016, describing the book as "inconsistent with its mission of affirming LGBTQ lives." Brynn Tannehill, writing for The Advocate, compared arguments made in the book to the arguments made by anti-transgender groups like the Family Research Council. She wrote that the book promoted a theory that trans people are "just self-hating homosexual men who believe they could have guilt-free sex if they were female and heterosexual men with an out-of-control fetish (autogynephilia)".
+
+
+== References ==
+
+
+== External links ==
+Official site on Penguin Random House

data/en.wikipedia.org/wiki/Homeopathy_and_Its_Kindred_Delusions-0.md

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+---
+title: "Homeopathy and Its Kindred Delusions"
+chunk: 1/1
+source: "https://en.wikipedia.org/wiki/Homeopathy_and_Its_Kindred_Delusions"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T08:47:59.420677+00:00"
+instance: "kb-cron"
+---
+
+Homœopathy and Its Kindred Delusions is a work by Oliver Wendell Holmes Sr., based upon two lectures he gave in 1842, Medical Delusions and Homœopathy. The work criticizes homeopathy, which he considered to be akin to "astrology, palmistry and other methods of getting a living out of the weakness and credulity of mankind and womankind". It is considered to be a classic text, one of Holmes' most important works, as well as one of the earliest criticisms of homeopathy.
+
+
+== Synopsis ==
+Homeopathy and Its Kindred Delusions is composed of two parts. In the first, Holmes explains how the placebo effect can produce false positives, and describes numerous forms of popular but ineffective quackery (including the royal touch, the tractors of Elisha Perkins, and the powder of sympathy), to demonstrate that positive anecdotal evidence is not necessarily indicative of an effective medical therapy. He also describes how Perkins claimed the healing powers of the tractors were due to their being made of a special alloy, but how they declined in popularity after it was discovered that the tractors had the same effect no matter what they were made of. In the second, he criticizes the basis of homeopathy itself, such as its theory of dilutions. Another issue is that of homeopathic provings (the practice of taking a substance to see what symptoms it causes). Holmes claims that during provings, subjects consider even the slightest discomfort (such as itching) to be the result of the substance, and that this method does not demonstrate symptom causality.
+In the work Holmes also expressed a belief that "real advances were made only after years of work by highly trained men who cared little for fame and money".
+
+
+== Reception ==
+Homeopathy and Its Kindred Delusions received both praise and criticism after its release. In a series of letters titled Some Remarks on Dr. O. W. Holmes's Lectures on Homeopathy and Its Kindred Delusions; Communicated to a Friend, Robert Wesselhoeft negatively compared Holmes' work to writers that "made sport of their fellow man" and considered the work to be representative of "Old School medicine's continued scorn for reform". In contrast, Eric W. Boyle wrote in his 2013 book Quack Medicine that Holmes' work was "the most thoroughly explicated attack on homeopathy as a dangerous and deadly error".
+
+
+== References ==

data/en.wikipedia.org/wiki/How_Doctors_Think-0.md

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+---
+title: "How Doctors Think"
+chunk: 1/2
+source: "https://en.wikipedia.org/wiki/How_Doctors_Think"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T08:48:00.599302+00:00"
+instance: "kb-cron"
+---
+
+How Doctors Think is a book released in March 2007 by Jerome Groopman, the Dina and Raphael Recanati Chair of Medicine at Harvard Medical School, chief of experimental medicine at Beth Israel Deaconess Medical Center in Boston, and staff writer for The New Yorker magazine.
+The book opens with a discussion of a woman in her thirties who suffered daily stomach cramps and serious weight loss, and who visited some 30 doctors over a period of 15 years.  Several misdiagnoses were made before she was finally found to have celiac disease. Groopman explains that no one can expect a physician to be infallible, as medicine is an uncertain science, and every doctor sometimes makes mistakes in diagnosis and treatment.  But the frequency and seriousness of those mistakes can be reduced by "understanding how a doctor thinks and how he or she can think better".
+The book includes Groopman's own experiences both as an oncologist and as a patient, as well as interviews by Groopman of prominent physicians in the medical community. Notably, he describes his difficulties with a number of orthopedic surgeons as he sought treatment for a debilitating ligament laxity he developed in his right hand, which over several years had led to the formation of cysts in the bones of his wrist.
+
+== Salem's challenge ==
+Groopman spends a great deal of the book discussing the challenge posed to him by Dr. Deeb Salem, chairman of the Department of Internal Medicine at Tufts-New England Medical Center, during a presentation the author made at their hospital grand rounds. During the presentation, Groopman was discussing the importance of compassion and communication in providing medical care when Salem posed the following question:
+
+There are primary care physicians in every hospital who speak with great sensitivity and concern, and their longtime patients love them, but clinically they are incompetent--how is a patient to know this?
+At the time of the presentation, Groopman was unable to provide a satisfactory response. Salem's question reminded Groopman of his experiences with physicians at the Phillips House of the world-renowned Massachusetts General Hospital, where he trained as a resident in the 1970s. Per his account:
+
+A few of [the physicians at Philips House] were highly skilled, but several were, at best, marginal in their clinical acumen. Nonetheless, their patients were devoted to them. It was the job of the residents to plug the holes in these marginal doctors' care. Just as a physician has to be wary of his first impression of a patient's condition, as a patient you have to be careful of your first impression of a physician...Thankfully, fewer students are admitted to medical school now because of social standing and family connections than at the time of my training. America has become more of a meritocracy in the professions. Medical school admissions committees no longer accept a record of gentlemen's C's at an Ivy League college.
+
+At best, I said to Salem, a layman should inquire of friends and, if possible, other physicians as well as nurses about the clinical qualities of a doctor beyond his personality. His credentials can be found on the Internet or by contacting a local medical board...Salem's query required a much more comprehensive answer, which I hope this book will help provide.
+
+== The availability heuristic ==
+Early in the work, Groopman discusses the work of Amos Tversky and Nobel laureate Daniel Kahneman, psychologists from Hebrew University in Jerusalem. Specifically, he explores their development in the early 1980s of a concept known as the availability heuristic.
+In the theory, "availability" is defined as the tendency to judge the likelihood of explanation for an event by the ease with which relevant examples come to mind. In a clinical situation a diagnosis may be made because the physician often sees similar cases in their practice — for example, the misclassification of aspirin toxicity as a viral pneumonia, or the improper recognition of an essential tremor as delirium tremens due to alcohol withdrawal in an indigent urban setting. Groopman argues that clinicians will misattribute a general symptom as specific to a certain disease based on the frequency they encounter that disease in their practice.
+Kahneman won the Nobel Prize in economics in 2002 for his work on heuristics, an honor that Groopman believes Tversky would have shared had he not died in 1996.
+
+== Lack of recognition for gatekeepers ==
+Groopman also serves as an advocate for primary care physicians in his book. He argues that gatekeeper physicians are underreimbursed for their work, believing this to be a legacy of the period earlier this century when surgeons headed the medical societies that negotiated with insurers about what a 'customary' payment for services was to be.
+He suggests that the poor reimbursement and lack of recognition for primary care physicians is fundamentally flawed. He quotes Dr. Eric J. Cassell's book, Doctoring: The Nature of Primary Care Medicine, to defend his assertion:
+
+A common error in thinking about primary care is to see it as entry-level medicine...and, because of this, rudimentary medicine...This is a false notion. One should not confuse highly technical, even complicated, medical knowledge--special practical knowledge about an unusual disease, treatment, condition, or technology--with the complex, many-sided worldly-wise knowledge we expect of the best physicians.

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+---
+title: "How Doctors Think"
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+category: "reference"
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+date_saved: "2026-05-05T08:48:00.599302+00:00"
+instance: "kb-cron"
+---
+
+The narrowest subspecialist, the reasoning goes, should also be able to provide this [broad] range of medical services. This naive idea arises, as do so many other wrong beliefs about primary care, because of the concept that doctors take care of diseases. Diseases, the idea goes on, form a hierarchy from simple to difficult. Specialists take care of difficult diseases, so, of course, they will naturally do a good job on simple diseases. Wrong. Doctors take care of people, some of whom have diseases and all of whom have some problem. People used to doing complicated things usually do complicated things in simple situations--for example, ordering tests or x-rays when waiting a few days might suffice--thus overtreating people with simple illnesses and overlooking the clues about other problems that might have brought the patient to the doctor.
+
+== The fallacy of logic ==
+In a later chapter Groopman reports a frank discussion with Dr. James E. Lock, chief of cardiology at Boston Children's Hospital. During their conversation, Groopman asks the world-renowned cardiologist about the times in his career when he made mistakes in patient treatment.
+To the query, Lock gives the cryptic response, "All my mistakes have the same things in common."
+Lock then elaborates, discussing recommendations he made to repair specific heart defects in neonates that ultimately led to worse clinical outcomes and potentially avoidable deaths. The recommendations he made were based on a purely logical understanding of cardiac physiology. The crucial point of Lock's discussion came with his confession:
+
+Impeccable logic doesn't always suffice. My mistake was that I reasoned from first principles when there was no prior experience. I turned out to be wrong because there are variables that you can't factor in until you actually do it. And you make the wrong recommendation, and the patient doesn't survive. I didn't leave enough room for what seems  [sic] like minor effects--the small fluctuations in oxygen levels, which might amount to one or two or three percent but actually can signal major problems in the heart....[The proposed treatment] is very sound logic. But it's wrong...These children developed right heart failure and clinically they became worse. There are aspects to human biology and human physiology that you just can't predict. Deductive reasoning doesn't work for every case. Sherlock Holmes is a model detective, but human biology is not a theft or a murder where all the cues can add up neatly.
+Groopman goes on to write, "Lock averted his gaze and his face fell; to be wrong about a child is a form of suffering unique to his profession [as a pediatrician]."
+
+== Disregard of uncertainty ==
+Groopman also discusses the work of Renee Fox, a physician and occupational sociologist who observed residents and attendings in a hospital ward setting, noting their various ways of coping with the uncertainties of medical treatment. The mechanisms to cope that Fox observed included, for example, black humor, making bets about who would be right about a patient's prognosis, and engaging in magical thinking to maintain a sense of poise and competence in front of patients while performing circumspect procedures.
+Jay Katz, a clinical instructor at Yale Law School has since termed these coping mechanisms under the rubric 'disregard of uncertainty', which he believes physicians develop to deal with the anxiety of shifting from the certainty of theoretical discussions of medicine early in their training to its more happenstance practical application.
+Groopman recalls that in situations where he had been hesitant to take clinical action based on incomplete data, it had been wisest at times to follow the advice of his mentor Dr. Linda A. Lewis: "Don't just do something, stand there." Groopman asserts that there exist situations in which inaction may be the wisest course of action.
+
+== Suggestions for patients ==
+Groopman closes with an epilogue giving advice for patients. He gives the following tools that patients can use to help reduce or rectify cognitive errors:
+
+Ask What else could it be?, combating satisfaction of search bias and leading the doctor to consider a broader range of possibilities.
+Ask Is there anything that doesn't fit?, combatting confirmation bias and again leading the doctor to think broadly.
+Ask Is it possible I have more than one problem?, because multiple simultaneous disorders do exist and frequently cause confusing symptoms.
+Tell what you are most worried about, opening discussion and leading either to reassurance (if the worry is unlikely) or careful analysis (if the worry is plausible).
+Retell the story from the beginning. Details that were omitted in the initial telling may be recalled, or different wording or the different context may make clues more salient. (This is most appropriate when the condition has not responded to treatment or there is other reason to believe that a misdiagnosis is possible.)
+
+== See also ==
+Availability heuristic
+Diagnosis
+Medical ethics
+The Deadly Dinner Party
+Fatal Care: Survive in the U.S. Health System
+To Err is Human
+
+== References ==

data/en.wikipedia.org/wiki/Kaitai_Shinsho-0.md

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+---
+title: "Kaitai Shinsho"
+chunk: 1/2
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+date_saved: "2026-05-05T08:48:04.089453+00:00"
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+---
+
+Kaitai Shinsho (解体新書; Kyūjitai: 解體新書, roughly meaning "New Text on Anatomy") is a medical text translated into Japanese during the Edo period. It was written by Sugita Genpaku, and was published by Suharaya Ichibee (須原屋市兵衛) in 1774, the third year of An'ei. The body comprises four volumes, the illustrations, one. The contents are written kanbun-style. It is based on a translation of the Dutch Ontleedkundige Tafelen, often known in Japan as Tafel Anatomie (ターヘル・アナトミア, Tāheru Anatomia), of Johann Adam Kulmus’ Latin Tabulae Anatomicae, published before 1722 (exact year is unknown) in Gdańsk, Polish–Lithuanian Commonwealth. As a full-blown translation from a Western language, it was the first of its kind in Japan.
+
+== Background ==
+On 4 March 1771, the eighth year of Meiwa, the students of Rangaku medicine Sugita Genpaku, Maeno Ryōtaku, Nakagawa Jun'an, et al., by studying performing autopsies on criminals executed at the Kozukappara execution grounds (now, there is a possibility that Katsuragawa Hoshū was at this facility as well, but from the description in Rangaku Koto Hajime (蘭学事始), it seems more likely that he was not). Both Sugita and Maeno had the book Ontleedkundige Tafelen, imported from Holland. Sugita, marveling at the accuracy of the work while comparing it by eye with his autopsies, proposed to Maeno that it be translated. For some time, Sugita had a desire to translate something from Dutch; now he would get approval for this. He met with Maeno the very next day (5 March) and began translation. The one who recommended Kaitai Shinsho to the shōgun was Katsuragawa Hosan.
+At first, Sugita and Nakagawa could not actually read Dutch; even with Maeno who could, their Dutch vocabulary was inadequate. It would have been difficult for them to consult with the Dutch translations and translators (Tsūji) in Nagasaki, and naturally there were no dictionaries at the time. A translation from any other Western language would have been out of the question, as the government of the time did not allow contact with any other Western nation. Therefore, in a process comparable to cryptanalysis, they progressed with translation work. In his later years, Sugita would detail the process in Rangaku Koto Hajime.
+In the second year of An'ei (1773), as they arrived at a translation goal, in order to ascertain society's and above all the authorities' response, they released the "Anatomical Diagrams" (解体約図, Kaitai Yakuzu), a five-page flyer.
+In 1774, Kaitai Shinsho was published.
+
+== Influences ==
+Maeno Ryōtaku was at the center of the translation work, but his name is only mentioned in the dedication written by the famous interpreter Yoshio Kōsaku. By one account, Maeno was on the way to study at Nagasaki; when he prayed at a Tenman-gū for the fulfillment of his studies, he vowed not to study in order to raise his own name, so he abstained from submitting it. By another account, since he knew that the completed works were not completely perfect, the academic Maeno could not submit his name in good conscience.  Sugita Genpaku said, "I am sickly and numbered in years as well. I do not know when I will die." While he knew the translation was imperfect in places, he rushed to publish. The publication of "Anatomic Illustrations" was also Sugita's design; in regard to this, Maeno is said to have had shown dislike for it. However, the man would actually go on to live an extremely long life for the time (he lived to the age of eighty-five). Unsure of when he would die and unsure of whether the government would approve the distribution of the Western ideas, it could be said this was a risky but important move.
+Nakagawa Jun'an, after Kaitai Shinsho’s publication, also continued his study of Dutch, along with Katsuragawa Hoshū, and took on the natural history of Sweden according to Thunberg.  Katsuragawa Hosan was a same-generation friend of Sugita's. With his status as a hōgen, he served as a court physician to the shōgun. He was not a direct influence on the translation work itself, though his son Hoshū did participate. Also, he provided for the  supplementary materials that amounted to three volumes of Dutch medical texts. Upon the publishing of Kaitai Shinsho, since there was a possibility that it encroached on the Bakufu's taboos, Katsuragawa was the one who ran it by the Ōoku.  Katsuragawa Hoshū was the son of the hōgen Katsuragawa Hosan, and would become a hōgen himself later on. He is said to have been involved with the translation work from early on. Afterwards, he would serve to develop rangaku along with Ōtsuki Gentaku.
+There are others that had to do with the translation work, like Ishikawa Genjō, whose name appears in the opening pages, Toriyama Shōen,  Kiriyama Shōtetsu, and Mine Shuntai (among others) whose names appear in Rangaku Koto Hajime.  Yoshio Kōgyū (posthumously Yoshio Nagaaki) was a Dutch tsūji. He wrote the preface to Kaitai Shinsho, and admired what he felt to be Sugita and Maeno's masterpiece.  Hiraga Gennai, on Shōgatsu of the third year of An'ei, visited the home of Sugita Genpaku. The translation of Kaitai Shinsho’s text was nearly complete, and he was informed that they were looking for an artist for the dissection figures.  Odano Naotake was a bushi from Kakunodate in the Akita Domain, and the artist. By Hiraga Gennai's referral, he got to drawing Kaitai Shinsho's figures off the original pictures. Until Kaitai Shinsho's first edition, it took the short time of half a year. It was his first time working in Edo, and yet it was historical record-setting work for Japanese science.
+
+== Content ==

data/en.wikipedia.org/wiki/Kaitai_Shinsho-1.md

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+---
+title: "Kaitai Shinsho"
+chunk: 2/2
+source: "https://en.wikipedia.org/wiki/Kaitai_Shinsho"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T08:48:04.089453+00:00"
+instance: "kb-cron"
+---
+
+Kaitai Shinsho is generally said to be a translation of Ontleedkundige Tafelen. However, other than the work itself, Bartholini's, Blankaart's, Schamberger’s, Koyter’s, Veslingius', Palfijn's,  and others' works were also consulted; the cover is based on Valuerda's. Of course, Asian sources and opinions also had an influence.
+The book is not a mere translation; the translation was done mostly by Maeno Ryōtaku and then transponed into classical Chinese by Sugita. There are notes in various places left by Sugita, as leftovers from the work. All those lengthy footnotes that cover more than 50% of Kulmus' book were left out.
+The contents are split into four volumes:
+
+Volume I
+General remarks; forms and names; parts of the body; skeletal structure: general remarks about joints; skeletal structure: detailed exposition about joints.
+Volume II
+The head; the mouth; the brain and nerves; the eyes; the ears; the nose; the tongue.
+Volume III
+The chest and the diaphragm; the lungs; the heart; arteries; veins; the portal vein; the abdomen; the bowels and stomach; the mesentery and lacteals; the pancreas.
+Volume IV
+The spleen; the liver and gall bladder; the kidneys and the bladder; the genitalia; pregnancy; the muscles.
+The illustrations only comprise one volume.
+
+== Effect afterwards ==
+After the publication of the Kaitai Shinsho, there was besides the development in medical science, the progress of the comprehension of the Dutch language. Also, it is important to note that Japan, even under its extreme isolationist policies, still had some foundation to understand the products of Western culture. It also helped to give a chance for promotion for such talents as those of Ōtsuki Gentaku.
+In translation, some words had to be coined (that is, there were no Japanese words that existed for them prior to the work). Some of them, such as the terms for "nerve" (神経, shinkei), "cartilage" (軟骨, nankotsu), and "artery" (動脈, dōmyaku) are still used to this day as a result. A great number of anatomical terms were transliterated using Chinese characters. They disappeared quickly during the following decades.
+The fact that this was a first translation means that misunderstandings were practically unavoidable. There are many mistranslations in the Kaitai Shinsho; later on, Ōtsuki Gentaku retranslated it and released the Authoritative and Revised New Text on Anatomy (重訂解体新書, Chōtei Kaitai Shinsho) in the ninth year of Bunsei (1826).
+In his last years, Sugita Genpaku would write about the work on Kaitai Shinsho in The Beginnings of Rangaku (蘭学事始, Rangaku Koto Hajime). This text had a great influence on writings about the modernization of Japanese medicine.
+
+== See also ==
+Sugita Genpaku
+Nakagawa Jun'an
+Satake Shozan
+Hiraga Gennai
+Kaitai-Shin Show (an educational program on NHK)
+
+== References ==
+
+Screech, Timon and Carl Peter Thunberg. Japan Extolled and Decried: Carl Peter Thunberg and the Shogun's Realm, 2005. ISBN 0-7007-1719-6.
+Takashina Shūji, Yōrō Takeshi, Haga Tōru, et al. Present Day in the middle of Edo – Akita Dutch Pictures and "Kaitai Shinsho", 1996. ISBN 4-480-85729-X.
+
+== External links ==
+
+Johann Adam Kulmus.  Kaitai shinsho. Illustrations from the original text.  Historical Anatomies on the Web, National Library of Medicine.
+(in Japanese) Kaitai Shinsho

data/en.wikipedia.org/wiki/Libellus_de_Medicinalibus_Indorum_Herbis-0.md

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+---
+title: "Libellus de Medicinalibus Indorum Herbis"
+chunk: 1/1
+source: "https://en.wikipedia.org/wiki/Libellus_de_Medicinalibus_Indorum_Herbis"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T08:48:06.360253+00:00"
+instance: "kb-cron"
+---
+
+The Libellus de Medicinalibus Indorum Herbis (Latin for "Little Book of the Medicinal Herbs of the Indians") is an Aztec herbal manuscript, describing the medicinal properties of 250 plants used by the Aztecs. It was translated into Latin by Juan Badiano, from a Nahuatl original composed in the Colegio de Santa Cruz de Tlatelolco in 1552 by Martín de la Cruz that is no longer existant. The Libellus is also known as the Badianus Manuscript, after the translator; the Codex de la Cruz-Badiano, after both the original author and translator; and the Codex Barberini, after Cardinal Francesco Barberini, who had possession of the manuscript in the early 17th century.
+The Badianus Manuscript of 1552 is the first illustrated and descriptive scientific text of Nahua medicine and botany produced in the Americas. It is a significant text in the history of botany and the history of medicine.
+
+
+== History ==
+In 1552 Jacobo de Grado, the friar in charge of the Convent of Tlatelolco and the College of Santa Cruz, had the herbal created and translated for Don Francisco de Mendoza, son of Don Antonio de Mendoza, the viceroy of New Spain. Mendoza sent the Latin manuscript to Spain, where it was deposited into the royal library. There it presumably remained until the early 17th century, when it somehow came into the possession of Diego de Cortavila y Sanabria, pharmacist to King Philip IV. From Cortavila it travelled to the Italian Cardinal Francesco Barberini, possibly via intermediate owners. The manuscript remained in the Barberini library until 1902, when the Barberini library became part of the Vatican Library, and the manuscript along with it. Finally, in 1990 — over four centuries after it was sent to Spain — Pope John Paul II returned the Libellus to Mexico, and it is now in the library of the National Institute of Anthropology and History in Mexico City.
+A copy was made in the 17th century by Cassiano dal Pozzo, the secretary of Cardinal Barberini. Dal Pozzo's collection, called his Museo Cartaceo ("Papers Museum"), was sold by his heirs to Pope Clement XI, who sold it to his nephew, Cardinal Alessandro Albani, who himself sold it to King George III in 1762. Dal Pozzo's copy is now part of the Royal Library, Windsor. Another copy may have been made by Francesco de' Stelluti, but is now lost. Dal Pozzo and de' Stelluti were both members of the Accademia dei Lincei.
+There are several published editions of the manuscript, beginning with the one by William E. Gates in 1939, now reissued in an inexpensive edition by Dover Books. Gates acquired photographs of the manuscript in Latin and water color renderings of the botanical drawings. He published both the original Latin manuscript as well as his translation to English. The reissued edition of Gates's manuscript has a very useful introduction by Bruce Byland, recounting the publication history of the manuscript and subsequent scholarship.
+At the same time Gates was working on this publication, another was being prepared for publication by Emily Walcott Emmart.  This resulted in a full-color facsimile publication, transcription, and translation to English, with notes and commentary.  In 1964, an edition of the manuscript was published in full-color facsimile, with a translation of the Latin to Spanish.
+The manuscript has been mainly studied by scholars interested in history of medicine and history of botany. In history of medicine, there has been some focus on the extent to which the manuscript might be incorporating aspects of European humoral theories of medicine or whether text is purely from the Nahua viewpoint. According to a study by Bernard R. Ortiz de Montellano, the Badianus herbal was prepared for the king of Spain to demonstrate the intellectual sophistication of the Nahuas which might have skewed the manuscript to emulating aspects of European culture.
+The botanical aspects of the manuscript are significant, showing that the Nahuas had a classification system that was indeed highly sophisticated. As with Book 11, "The Earthly Things" of the Florentine Codex by Franciscan Bernardino de Sahagún, the Badianus manuscript gives the Nahuatl names of plants, an illustration of the example, and the uses for the plant. However, unlike the Florentine Codex, there is little emphasis on supernatural healing characteristics of the plants. The examples in the Badianus manuscript deal solely with the medical conditions and curative aspects of the plants. For example, in the Gates translation, subject headings for plants' curative powers include "Against stupidity of the mind," [against] "Goaty armpits of sick people," "Against lassitude," "Medicine to take away foul and fetid breath."  For scholars interested in women's health, the Badianus manuscript has a whole chapter on "remedies for recent parturition, the menses, lotion of the internal parts, childbirth, tubercules of the breasts, [and] medicine for increasing milk flow." Various plants listed in the Badianus manuscript have psychoactive properties, examined by anthropologist Peter Furst.
+
+
+== Modern editions ==
+Several modern editions of the Libellus have been published since the 20th century. An English translation by William Gates appeared in 1939, followed by others including Emily Walcott Emmart and Henry E. Sigerist. A critical edition and Spanish translation by Francisco Guerra was published in Mexico in 2000.
+In 2021, the Instituto Nacional de Antropología e Historia (INAH) published a digitized and annotated edition of the Libellus, including a paleographic transcription, Spanish translation, and scholarly commentary.
+A fully edited print version of the same project was released in 2023 by INAH in Mexico City, under the title Libellus de medicinalibus indorum herbis / Códice De la Cruz-Badiano.
+
+
+== Proposed connection with the Voynich Manuscript ==
+In 2014, Arthur Tucker and Rexford Talbert published a paper claiming that some of the plant illustrations in the Voynich Manuscript match plant illustrations from the Libellus de Medicinalibus Indorum Herbis, suggesting that the Voynich Manuscript originated in the New World. This analysis has been criticized by noted Voynich Manuscript researchers, who suggest it is just a coincidence, as any large set of fictitious plant illustrations is bound to have several that resemble real plants.
+
+
+== Translations ==
+
+
+== See also ==
+Aztec entheogenic complex
+
+
+== References ==
+
+
+== External links ==
+ Media related to Codex de la Cruz-Badiano at Wikimedia Commons
+PDF of William Gates' English translation

data/en.wikipedia.org/wiki/Medical_Visions-0.md

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+---
+title: "Medical Visions"
+chunk: 1/1
+source: "https://en.wikipedia.org/wiki/Medical_Visions"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T08:48:07.505430+00:00"
+instance: "kb-cron"
+---
+
+Medical Visions: Producing the Patient through Film, Television, and Imaging Technologies is a non-fiction book by Kirsten Ostherr. It was published in 2013 by Oxford University Press.
+
+
+== General references ==
+Guy, Mary (2015-07-28). "Medical Visions: Producing the Patient Through Film, Television, and Imaging Technologies". Medical Law Review fwv033. doi:10.1093/medlaw/fwv033. ISSN 0967-0742.
+Jordanova, Ludmilla (2014). "Medical Visions: Producing the Patient through Film, Television, and Imaging Technologies by Kirsten Ostherr (review)". Literature and Medicine. 32 (1): 224–227. ISSN 1080-6571.
+Willis, Martin (July 2016). "Book Review: Medical Visions: Producing the Patient Through Film, Television, and Imaging Technologies". Critical Studies in Television: The International Journal of Television Studies. 11 (2): 257–260. doi:10.1177/1749602016642932. ISSN 1749-6020.

data/en.wikipedia.org/wiki/Prime_Obsession-0.md

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+---
+title: "Prime Obsession"
+chunk: 1/1
+source: "https://en.wikipedia.org/wiki/Prime_Obsession"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T08:46:28.637361+00:00"
+instance: "kb-cron"
+---
+
+Prime Obsession: Bernhard Riemann and the Greatest Unsolved Problem in Mathematics (2003) is a historical book on mathematics by John Derbyshire, detailing the history of the Riemann hypothesis, named for Bernhard Riemann, and some of its applications. 
+The book was awarded the Mathematical Association of America's inaugural Euler Book Prize in 2007.
+
+
+== Overview ==
+The book is written such that even-numbered chapters present historical elements related to the development of the conjecture, and odd-numbered chapters deal with the mathematical and technical aspects. Despite the title, the book provides biographical information on many iconic mathematicians including Euler, Gauss, and Lagrange.
+In chapter 1, "Card Trick", Derbyshire introduces the idea of an infinite series and the ideas of convergence and divergence of these series. He imagines that there is a deck of cards stacked neatly together, and that one pulls off the top card so that it overhangs from the deck. Explaining that it can overhang only as far as the center of gravity allows, the card is pulled so that exactly half of it is overhanging. Then, without moving the top card, he slides the second card so that it is overhanging too at equilibrium. As he does this more and more, the fractional amount of overhanging cards as they accumulate becomes less and less. He explores various types of series such as the harmonic series.
+In chapter 2, Bernhard Riemann is introduced and a brief historical account of Eastern Europe in the 18th Century is discussed.
+In chapter 3, the Prime Number Theorem (PNT) is introduced. The function which mathematicians use to describe the number of primes in N numbers, π(N), is shown to behave in a logarithmic manner, as so:
+
+  
+    
+      
+        π
+        (
+        N
+        )
+        ≈
+        
+          
+            N
+            
+              log
+              ⁡
+              (
+              N
+              )
+            
+          
+        
+      
+    
+    {\displaystyle \pi (N)\approx {\frac {N}{\log(N)}}}
+  
+
+where log is the natural logarithm.
+In chapter 4, Derbyshire gives a short biographical history of Carl Friedrich Gauss and Leonard Euler, setting up their involvement in the Prime Number Theorem.
+In chapter 5, the Riemann Zeta Function is introduced:
+
+  
+    
+      
+        ζ
+        (
+        s
+        )
+        =
+        1
+        +
+        
+          
+            1
+            
+              2
+              
+                s
+              
+            
+          
+        
+        +
+        
+          
+            1
+            
+              3
+              
+                s
+              
+            
+          
+        
+        +
+        
+          
+            1
+            
+              4
+              
+                s
+              
+            
+          
+        
+        +
+        ⋯
+        =
+        
+          ∑
+          
+            n
+            =
+            1
+          
+          
+            ∞
+          
+        
+        
+          
+            1
+            
+              n
+              
+                s
+              
+            
+          
+        
+      
+    
+    {\displaystyle \zeta (s)=1+{\frac {1}{2^{s}}}+{\frac {1}{3^{s}}}+{\frac {1}{4^{s}}}+\cdots =\sum _{n=1}^{\infty }{\frac {1}{n^{s}}}}
+  
+
+In chapter 7, the sieve of Eratosthenes is shown to be able to be simulated using the Zeta function. With this, the following statement which becomes the pillar stone of the book is asserted:
+
+  
+    
+      
+        ζ
+        (
+        s
+        )
+        =
+        
+          ∏
+          
+            p
+             
+            
+              p
+              r
+              i
+              m
+              e
+            
+          
+        
+        
+          
+            1
+            
+              1
+              −
+              
+                
+                  p
+                  
+                    −
+                    s
+                  
+                
+              
+            
+          
+        
+      
+    
+    {\displaystyle \zeta (s)=\prod _{p\ \mathrm {prime} }{\frac {1}{1-{p^{-s}}}}}
+  
+
+Following the derivation of this finding, the book delves into how this is manipulated to expose the PNT's nature.
+
+
+== Audience and reception ==
+According to reviewer S. W. Graham, the book is written at a level that is suitable for advanced undergraduate students of mathematics. In contrast, James V. Rauff recommends it to "anyone interested in the history and mathematics of the Riemann hypothesis".
+Reviewer Don Redmond writes that, while the even-numbered chapters explain the history well, the odd-numbered chapters present the mathematics too informally to be useful, failing to provide insight to readers who do not already understand the mathematics, and failing even to explain the importance of the Riemann hypothesis. Graham adds that the level of mathematics is inconsistent, with detailed explanations of basics and sketchier explanations of material that is more advanced. But for those who do already understand the mathematics, he calls the book "a familiar story entertainingly told".
+
+
+== Notes ==
+
+
+== External links ==
+Publisher's web site

data/en.wikipedia.org/wiki/Proofs_and_Refutations-0.md

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 source: "https://en.wikipedia.org/wiki/Proofs_and_Refutations"
 category: "reference"
 tags: "science, encyclopedia"
-date_saved: "2026-05-05T07:08:23.745480+00:00"
+date_saved: "2026-05-05T08:46:32.102198+00:00"
 instance: "kb-cron"
 ---
 

data/en.wikipedia.org/wiki/Proofs_from_THE_BOOK-0.md

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+---
+title: "Proofs from THE BOOK"
+chunk: 1/1
+source: "https://en.wikipedia.org/wiki/Proofs_from_THE_BOOK"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T08:46:33.272504+00:00"
+instance: "kb-cron"
+---
+
+Proofs from THE BOOK is a book of mathematical proofs by Martin Aigner and Günter M. Ziegler, first published in 1998. The book is inspired by and named after an expression used by the mathematician Paul Erdős, who often referred to "The Book" in which God kept the best proof of each mathematical theorem. During a lecture in 1985, Erdős said, "You don't have to believe in God, but you should believe in The Book." The greatest praise Erdős gave to mathematical work was to proclaim it "straight from the Book".
+Aigner and Zeigler proposed to Erdős a real book that would be "a first (and very modest) approximation to 'The Book'". Erdős had many suggestions for proofs that should be included, and would have been a co-author except that he died in 1996. Proofs from THE BOOK is instead dedicated to his memory.
+Including its original publication, Proofs from THE BOOK has had six editions in English, and has been translated into Persian, French, German, Hungarian, Italian, Japanese, Chinese, Polish, Portuguese, Korean, Turkish, Russian, Spanish and Greek.
+The American Mathematical Society awarded the 2018 Leroy P. Steele Prize for Mathematical Exposition to Aigner and Ziegler for this book.
+
+
+== Content ==
+In its most recent sixth edition, Proofs from THE BOOK contains 45 chapters grouped into five parts: number theory, geometry, analysis, combinatorics and graph theory. In most cases, each chapter is devoted to a particular theorem, sometimes with multiple proofs and related results. In a few cases, a chapter explores proofs related to a particular theme.
+Aigner and Ziegler stated that they had no definite criteria for what counted as a proof from "The Book", but selected only those that would be accessible to someone with knowledge of basic undergraduate mathematics. Nevertheless some background in algebra, analysis, and topology is required to understand certain parts. Ziegler accepted that different proofs would be "perfect" for different readers.
+There are differences between the various editions of the book. These are mostly additions of chapters, but some involved adding new results or new proofs for already-present results, and there was one complete deletion of a chapter. The first edition included John Leech's proof that it is impossible for thirteen unit spheres to touch a given sphere. It was removed for later editions because Aigner and Ziegler could not fill in details in a way that was "brief and elegant".
+Because the book concerns beauty in mathematics, Aigner and Ziegler thought that it should have a correspondingly attractive appearance, and thus devoted a lot of time to the text and typography, and to selecting appropriate photographs and other illustrations.
+The book is illustrated with drawings by Karl H. Hofmann.
+
+
+== Outline ==
+The outline below relates to the sixth edition. Previous editions contained fewer chapters, in some cases differently arranged.
+
+
+=== Number theory ===
+Chapter 1: Six proofs of the infinity of the primes, including Euclid's and Furstenberg's.
+Chapter 2: Paul Erdős's 1932 proof of Bertrand's postulate.
+Chapter 3: Binomial coefficients are almost never powers.
+Chapter 4: Fermat's theorem on sums of two squares.
+Chapter 5: Two proofs of the law of quadratic reciprocity.
+Chapter 6: Proof of Wedderburn's little theorem asserting that every finite division ring is a field.
+Chapter 7: The spectral theorem, Hadamard's maximal determinant problem and Hadamard's inequality.
+Chapter 8: Some irrational numbers, including Ivan Niven's proof that 
+  
+    
+      
+        π
+      
+    
+    {\displaystyle \pi }
+  
+ (pi) is irrational.
+Chapter 9: Four proofs of the solution to Basel problem, namely that 
+  
+    
+      
+        
+          ∑
+          
+            n
+            ≥
+            1
+          
+          
+            ∞
+          
+        
+        
+          
+            1
+            
+              n
+              
+                2
+              
+            
+          
+        
+        =
+        
+          
+            
+              π
+              
+                2
+              
+            
+            6
+          
+        
+      
+    
+    {\displaystyle \sum _{n\geq 1}^{\infty }{\frac {1}{n^{2}}}={\frac {\pi ^{2}}{6}}}
+  
+.
+
+
+=== Geometry ===
+Chapter 10: Hilbert's third problem.
+Chapter 11: Lines in the plane, including the Sylvester–Gallai theorem and the De Bruijn–Erdős theorem.
+Chapter 12: The slope problem.
+Chapter 13: Applications of Euler's formula.
+Chapter 14: Cauchy's rigidity theorem.
+Chapter 15: The non-existence of the Borromean rings.
+Chapter 16: Touching simplices.
+Chapter 17: Large angles in point sets.
+Chapter 18: Borsuk's conjecture.
+Chapter 19: The Schröder–Bernstein theorem and Wetzel's problem on families of analytic functions with few distinct values.
+
+
+=== Analysis ===
+Chapter 21: The fundamental theorem of algebra.
+Chapter 22: Monsky's theorem.
+Chapter 23: A theorem of George Pólya on polynomials.
+Chapter 24: Van der Waerden's conjecture.
+Chapter 25: Littlewood–Offord lemma.
+Chapter 26: The cotangent and Herglotz's trick.
+Chapter 27: Buffon's needle problem.
+
+
+=== Combinatorics ===
+Chapter 28: Pigeonhole principle and double counting, Sperner's lemma.
+Chapter 29: Results on tiling rectangles due to Nicolaas Govert de Bruijn and Max Dehn.
+Chapter 30: Sperner's theorem, Erdős–Ko–Rado theorem and Hall's theorem
+Chapter 31: Shuffling cards.
+Chapter 32: Lattice paths and determinants, including Lindström–Gessel–Viennot lemma and the Cauchy–Binet formula.
+Chapter 33: Four proofs of Cayley's formula.
+Chapter 34: Identities versus bijections.
+Chapter 35: Kakeya sets in vector spaces over finite fields.
+
+
+=== Graph Theory ===
+Chapter 37: The Bregman–Minc inequality.
+Chapter 38: The Dinitz problem.
+Chapter 39: The five color theorem.
+Chapter 40: Steve Fisk's proof of the art gallery theorem.
+Chapter 41: Five proofs of Turán's theorem.
+Chapter 42: Shannon capacity and Lovász number.
+Chapter 43: Chromatic number of Kneser graphs.
+Chapter 44: Friendship theorem.
+Chapter 45: Some proofs using the probabilistic method.
+
+
+== Notes ==
+
+
+== References ==
+Aigner, Martin; Ziegler, Günter M. (2018). Proofs from THE BOOK (6th ed.). Springer. ISBN 978-3-662-57264-1.
+1st edition: Proofs from THE BOOK. Springer. 1998. ISBN 978-3-662-22345-1.
+2nd edition: Proofs from THE BOOK. Springer. 2002. ISBN 978-3-540-67865-6.
+3rd edition: Proofs from THE BOOK. Springer. 2004. ISBN 978-3-540-40460-6.
+4th edition: Proofs from THE BOOK. Springer. 2010. ISBN 978-3-642-00855-9.
+5th edition: Proofs from THE BOOK. Springer. 2014. ISBN 978-3-662-44204-3.
+[The AMS secretary] (2018). "2018 Leroy P. Steele Prizes" (PDF). Notices of the American Mathematical Society. 65 (4): 455–458.
+Cain, Alan J. (2024). Form & Number: A History of Mathematical Beauty. Lisbon: Ebook.
+Hoffman, Paul (1999). The Man Who Loved Only Numbers: The Story of Paul Erdős and the Search for Mathematical Truth. London: Fourth Estate. ISBN 978-1-85702-829-4.
+Klarreich, Erica (2018-03-19). "In Search of God's Perfect Proofs". Quanta Magazine. Archived from the original on 2018-05-30. Retrieved 2022-07-12.
+Shepherd, Mary (2002-08-15). "Review of Proofs from THE BOOK". MAA Reviews. Mathematical Association of America. Archived from the original on 2024-05-27.
+
+
+== External links ==
+Günter M. Ziegler's homepage (archived), including a list of editions and translations.

data/en.wikipedia.org/wiki/Pythagorean_Triangles-0.md

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+---
+title: "Pythagorean Triangles"
+chunk: 1/1
+source: "https://en.wikipedia.org/wiki/Pythagorean_Triangles"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T08:46:35.563939+00:00"
+instance: "kb-cron"
+---
+
+Pythagorean Triangles is a book on right triangles, the Pythagorean theorem, and Pythagorean triples. It was originally written in the Polish language by Wacław Sierpiński (titled Trójkąty pitagorejskie), and published in Warsaw in 1954. Indian mathematician Ambikeshwar Sharma translated it into English, with some added material from Sierpiński, and published it in the Scripta Mathematica Studies series of Yeshiva University (volume 9 of the series) in 1962. Dover Books republished the translation in a paperback edition in 2003. There is also a Russian translation of the 1954 edition.
+
+
+== Topics ==
+As a brief summary of the book's contents, reviewer Brian Hopkins quotes The Pirates of Penzance: "With many cheerful facts about the square of the hypotenuse."
+The book is divided into 15 chapters (or 16, if one counts the added material as a separate chapter). The first three of these define the primitive Pythagorean triples (the ones in which the two sides and hypotenuse have no common factor), derive the standard formula for generating all primitive Pythagorean triples, compute the inradius of Pythagorean triangles, and construct all triangles with sides of length at most 100.
+Chapter 4 considers special classes of Pythagorean triangles, including those with sides in arithmetic progression, nearly-isosceles triangles, and the relation between nearly-isosceles triangles and square triangular numbers. The next two chapters characterize the numbers that can appear in Pythagorean triples, and chapters 7–9 find sets of many Pythagorean triangles with the same side, the same hypotenuse, the same perimeter, the same area, or the same inradius.
+Chapter 10 describes Pythagorean triangles with a side or area that is a square or cube, connecting this problem to Fermat's Last Theorem. After a chapter on Heronian triangles, Chapter 12 returns to this theme, discussing triangles whose hypotenuse and sum of sides are squares. Chapter 13 relates Pythagorean triangles to rational points on a unit circle, Chapter 14 discusses right triangles whose sides are unit fractions rather than integers, and Chapter 15 is about the Euler brick problem, a three-dimensional generalization of Pythagorean triangles, and related problems on integer-sided tetrahedra. Sadly, in giving an example of a Heronian tetrahedron found by E. P. Starke, the book repeats a mistake of Starke in calculating its volume.
+
+
+== Audience and reception ==
+The book is aimed at mathematics teachers, in order to inspire their interest in this subject, despite complaining that some of its proofs are overly complicated, reviewer Donald Vestal also suggests this as a "fun book for a mostly general audience".
+Reviewer Brian Hopkins suggests that some of the book's material could be simplified using modular notation and linear algebra, and that the book could benefit by updating it to include a bibliography, index, more than its one illustration, and pointers to recent research in this area such as the Boolean Pythagorean triples problem. Nevertheless, he highly recommends it to mathematics teachers and readers interested in "thorough and elegant proofs". Reviewer Eric Stephen Barnes rates Sharma's translation as "very readable". The editors of zbMATH write of the Dover edition that "It is a pleasure to have this classic text available again".
+
+
+== References ==

data/en.wikipedia.org/wiki/Quasicrystals_and_Geometry-0.md

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+---
+title: "Quasicrystals and Geometry"
+chunk: 1/1
+source: "https://en.wikipedia.org/wiki/Quasicrystals_and_Geometry"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T08:46:36.726659+00:00"
+instance: "kb-cron"
+---
+
+Quasicrystals and Geometry is a book on quasicrystals and aperiodic tiling by Marjorie Senechal, published in 1995 by Cambridge University Press (ISBN 0-521-37259-3).
+One of the main themes of the book is to understand how the mathematical properties of aperiodic tilings such as the Penrose tiling, and in particular the existence of arbitrarily large patches of five-way rotational symmetry throughout these tilings, correspond to the properties of quasicrystals including the five-way symmetry of their Bragg peaks. Neither kind of symmetry is possible for a traditional periodic tiling or periodic crystal structure, and the interplay between these topics led from the 1960s into the 1990s to new developments and new fundamental definitions in both mathematics and crystallography.
+
+
+== Topics ==
+The book is divided into two parts. The first part covers the history of crystallography, the use of X-ray diffraction to study crystal structures through the Bragg peaks formed on their diffraction patterns, and the discovery in the early 1980s of quasicrystals, materials that form Bragg peaks in patterns with five-way symmetry, impossible for a repeating crystal structure. It models the arrangement of atoms in a substance by a Delone set, a set of points in the plane or in Euclidean space that are neither too closely spaced nor too far apart, and it discusses the mathematical and computational issues in X-ray diffraction and the construction of the diffraction spectrum from a Delone set.
+Finally, it discusses a method for constructing Delone sets that have Bragg peaks by projecting bounded subsets of higher-dimensional lattices into lower-dimensional spaces.
+This material also has strong connections to spectral theory and ergodic theory, deep topics in pure mathematics, but these were omitted in order to make the book accessible to non-specialists in those topics.
+Another method for the construction of Delone sets that have Bragg peaks is to choose as points the vertices of certain aperiodic tilings such as the Penrose tiling. (There also exist other aperiodic tilings, such as the pinwheel tiling, for which the existence of discrete peaks in the diffraction pattern is less clear.) The second part of the book discusses methods for generating these tilings, including projections of higher-dimensional lattices as well as recursive constructions with hierarchical structure, and it discusses the long-range patterns that can be shown to exist in tilings constructed in these ways.
+Included in the book are software for generating diffraction patterns and Penrose tilings, and a "pictorial atlas" of the diffraction patterns of known aperiodic tilings.
+
+
+== Audience ==
+Although the discovery of quasicrystals immediately set off a rush for applications in materials capable of withstanding high temperature, providing non-stick surfaces, or having other useful material properties, this book is more abstract and mathematical, and concerns mathematical models of quasicrystals rather than physical materials. Nevertheless, chemist István Hargittai writes that it can be read with interest by "students and researchers in mathematics, physics, materials science, and crystallography".
+
+
+== References ==
+
+
+== External links ==
+Quasicrystals and Geometry on the Internet Archive

data/en.wikipedia.org/wiki/Rabdology-0.md

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+---
+title: "Rabdology"
+chunk: 1/1
+source: "https://en.wikipedia.org/wiki/Rabdology"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T08:46:37.868793+00:00"
+instance: "kb-cron"
+---
+
+In 1617 a treatise in Latin titled Rabdologiæ and written by John Napier was published in Edinburgh. Printed three years after his treatise on the discovery of logarithms and in the same year as his death, it describes three devices to aid arithmetic calculations.
+The devices themselves don't use logarithms, rather they are tools to reduce multiplication and division of natural numbers to simple addition and subtraction operations.
+The first device, which by then was already popularly used and known as Napier's bones, was a set of rods inscribed with the multiplication table. Napier coined the word rabdology (from Greek ῥάβδος [rhabdos], rod and λόγoς [logos] calculation or reckoning) to describe this technique. The rods were used to multiply, divide and even find the square roots and cube roots of numbers.
+The second device was a promptuary (Latin promptuarium meaning storehouse) and consisted of a large set of strips that could multiply multidigit numbers more easily than the bones. In combination with a table of reciprocals, it could also divide numbers.
+The third device used a checkerboard like grid and counters moving on the board to perform binary arithmetic. Napier termed this technique location arithmetic from the way in which the locations of the counters on the board represented and computed numbers. Once a number is converted into a binary form, simple movements of counters on the grid could multiply, divide and even find square roots of numbers.
+Of these devices, Napier's bones were the most popular and widely known. In fact, part of his motivation to publish the treatise was to establish credit for his invention of the technique. The bones were easy to manufacture and simple to use, and several variations on them were published and used for many years.
+The promptuary was never widely used, perhaps because it was more complex to manufacture, and it took nearly as much time to lay out the strips to find the product of numbers as to find the answer with pen and paper.
+Location arithmetic was an elegant insight into the simplicity of binary arithmetic, but remained a curiosity probably because it was never clear that the effort to convert numbers in and out of binary form was worth the trouble.
+An interesting tidbit is this treatise contains the earliest written reference to the decimal point (though its usage would not come into general use for another century).
+The computing devices in Rabdology were overshadowed by Napier's seminal work on logarithms as they proved more useful and more widely applicable. Nevertheless, these devices (as indeed are logarithms) are examples of Napier's ingenious attempts to discover easier ways to multiply, divide and find roots of numbers. Location arithmetic in particular foreshadowed the ease of and power of mechanizing binary arithmetic, but was never fully appreciated.
+
+
+== References ==
+John Napier (1990) [1617]. Rabdologiæ [Rabdology] (in Latin). Translated by William Frank Richardson. Introduction by Robin E. Rider. MIT Press. ISBN 0-262-14046-2.
+John Napier (1617). Rabdologiæ (in Latin). Andro Hart.

data/en.wikipedia.org/wiki/Regular_Figures-0.md

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+---
+title: "Regular Figures"
+chunk: 1/1
+source: "https://en.wikipedia.org/wiki/Regular_Figures"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T08:46:38.980218+00:00"
+instance: "kb-cron"
+---
+
+Regular Figures is a book on polyhedra and symmetric patterns, by Hungarian geometer László Fejes Tóth. It was published in 1964 by Pergamon in London and Macmillan in New York.
+
+
+== Topics ==
+Regular Figures is divided into two parts, "Systematology of the Regular Figures" and "Genetics of the Regular Figures", each in five chapters. Although the first part represents older and standard material, much of the second part is based on a large collection of research works by Fejes Tóth, published over the course of approximately 25 years, and on his previous exposition of this material in a 1953 German-language text.
+The first part of the book covers many of the same topics as a previously published book, Regular Polytopes (1947), by H. S. M. Coxeter, but with a greater emphasis on group theory and the classification of symmetry groups. Its first three chapters describe the symmetries that two-dimensional geometric objects can have: the 17 wallpaper groups of the Euclidean plane in the first chapter, with the first English-language presentation of the proof of their classification by Evgraf Fedorov, the regular spherical tilings in chapter two, and the uniform tilings of the hyperbolic plane in chapter three. Also mentioned is the Voderberg tiling by non-convex enneagons, as an example of a systematically constructed tiling that lacks all symmetry (prefiguring the discovery of aperiodic tilings). The fourth chapter describes symmetric polyhedra, including the five Platonic solids, the 13 Archimedean solids, and the five parallelohedra also enumerated by Federov, which come from the discrete translational symmetries of Euclidean space. The fifth and final chapter of this section of the book extends this investigation into higher dimensions and the regular polytopes.
+The second part of the book concerns the principle that many of these symmetric patterns and shapes can be generated as the solutions to optimization problems, such as the Tammes problem of arranging a given number of points on a sphere so as to maximize the minimum distance between pairs of points. Isometric inequalities for polyhedra and problems of packing density and covering density of sphere packings and coverings are also included, and the proofs make frequent use of Jensen's inequality. This part is organized into chapters in the same order as the first part of the book: Euclidean, spherical, and hyperbolic plane geometry, solid geometry, and higher-dimensional geometry.
+The book is heavily illustrated, including examples of ornamental patterns with the symmetries described, and twelve two-color stereoscopic images. Applications of its material, touched on in the book, include art and decoration, crystallography, urban planning, and the study of plant growth.
+
+
+== Audience and reception ==
+Reviewer W. L. Edge writes that the book's exposition combines "lightness of touch and conciseness of exposition in a quite delightful way", and H. S. M. Coxeter similarly writes that the book has "everything that could be desired in a mathematical monograph: a pleasant style, careful explanation ..., [and] a great variety of topics with a single unifying idea".
+C. A. Rogers finds some of the proofs in the second part unconvincing and incomplete. Patrick du Val complains that the level of difficulty is uneven, with the second part of the book being significantly more technical than the first, but nevertheless recommends it "to specialists in this field", while Michael Goldberg calls the book "an excellent reference work". Although calling the content of the book excellent, J. A. Todd complains that its production is marred by poor typographic quality.
+
+
+== See also ==
+List of books about polyhedra
+
+
+== References ==
+
+
+== Further reading ==
+Florian, A., "Review of Regular Figures", zbMATH (in German), Zbl 0134.15705

data/en.wikipedia.org/wiki/Regular_Polytopes_(book)-0.md

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+---
+title: "Regular Polytopes (book)"
+chunk: 1/1
+source: "https://en.wikipedia.org/wiki/Regular_Polytopes_(book)"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T08:46:40.134422+00:00"
+instance: "kb-cron"
+---
+
+Regular Polytopes is a geometry book on regular polytopes written by Harold Scott MacDonald Coxeter. It was originally published by Methuen in 1947 and by Pitman Publishing in 1948, with a second edition published by Macmillan in 1963 and a third edition by Dover Publications in 1973.
+The Basic Library List Committee of the Mathematical Association of America has recommended that it be included in undergraduate mathematics libraries.
+
+
+== Overview ==
+The main topics of the book are the Platonic solids (regular convex polyhedra), related polyhedra, and their higher-dimensional generalizations. It has 14 chapters, along with multiple appendices, providing a more complete treatment of the subject than any earlier work, and incorporating material from 18 of Coxeter's own previous papers. It includes many figures (both photographs of models by Paul Donchian and drawings), tables of numerical values, and historical remarks on the subject.
+The first chapter discusses regular polygons, regular polyhedra, basic concepts of graph theory, and the Euler characteristic. Using the Euler characteristic, Coxeter derives a Diophantine equation whose integer solutions describe and classify the regular polyhedra. The second chapter uses combinations of regular polyhedra and their duals to generate related polyhedra, including the semiregular polyhedra, and discusses zonohedra and Petrie polygons. Here and throughout the book, the shapes it discusses are identified and classified by their Schläfli symbols. 
+Chapters 3 through 5 describe the symmetries of polyhedra, first as permutation groups and later, in the most innovative part of the book, as the Coxeter groups, groups generated by reflections and described by the angles between their reflection planes. This part of the book also describes the regular tessellations of the Euclidean plane and the sphere, and the regular honeycombs of Euclidean space. Chapter 6 discusses the star polyhedra including the Kepler–Poinsot polyhedra.
+The remaining chapters cover higher-dimensional generalizations of these topics, including two chapters on the enumeration and construction of the regular polytopes, two chapters on higher-dimensional Euler characteristics and background on quadratic forms, two chapters on higher-dimensional Coxeter groups, a chapter on cross-sections and projections of polytopes, and a chapter on star polytopes and polytope compounds.
+
+
+== Later editions ==
+The second edition was published in paperback; it adds some more recent research of Robert Steinberg on Petrie polygons and the order of Coxeter groups, appends a new definition of polytopes at the end of the book, and makes minor corrections throughout. The photographic plates were also enlarged for this printing, and some figures were redrawn. The nomenclature of these editions was occasionally cumbersome, and was modernized in the third edition. The third edition also included a new preface with added material on polyhedra in nature, found by the electron microscope.
+
+
+== Reception ==
+The book only assumes a high-school understanding of algebra, geometry, and trigonometry, but it is primarily aimed at professionals in this area, and some steps in the book's reasoning which a professional could take for granted might be too much for less-advanced readers. Nevertheless, reviewer J. C. P. Miller recommends it to "anyone interested in the subject, whether from recreational, educational, or other aspects", and (despite complaining about the omission of regular skew polyhedra) reviewer H. E. Wolfe suggests more strongly that every mathematician should own a copy. Geologist A. J. Frueh Jr., describing the book as a textbook rather than a monograph, suggests that the parts of the book on the symmetries of space would likely be of great interest to crystallographers; however, Frueh complains of the lack of rigor in its proofs and the lack of clarity in its descriptions.
+Already in its first edition the book was described as "long awaited", and "what is, and what will probably be for many years, the only organized treatment of the subject". In a review of the second edition, Michael Goldberg (who also reviewed the first edition) called it "the most extensive and authoritative summary" of its area of mathematics. By the time of Tricia Muldoon Brown's 2016 review, she described it as "occasionally out-of-date, although not frustratingly so", for instance in its discussion of the four color theorem, proved after its last update. However, she still evaluated it as "well-written and comprehensive".
+
+
+== See also ==
+List of books about polyhedra
+
+
+== References ==

data/en.wikipedia.org/wiki/Revolutions_in_Mathematics-0.md

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+---
+title: "Revolutions in Mathematics"
+chunk: 1/1
+source: "https://en.wikipedia.org/wiki/Revolutions_in_Mathematics"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T08:46:42.514232+00:00"
+instance: "kb-cron"
+---
+
+Revolutions in Mathematics is a 1992 collection of essays in the history and philosophy of mathematics.
+
+
+== Contents ==
+Michael J. Crowe, Ten "laws" concerning patterns of change in the history of mathematics (1975) (15–20);
+Herbert Mehrtens, T. S. Kuhn's theories and mathematics: a discussion paper on the "new historiography" of mathematics (1976) (21–41);
+Herbert Mehrtens, Appendix (1992): revolutions reconsidered (42–48);
+Joseph Dauben, Conceptual revolutions and the history of mathematics: two studies in the growth of knowledge (1984) (49–71);
+Joseph Dauben, Appendix (1992): revolutions revisited (72–82);
+Paolo Mancosu, Descartes's Géométrie and revolutions in mathematics (83–116);
+Emily Grosholz, Was Leibniz a mathematical revolutionary? (117–133);
+Giulio Giorello, The "fine structure" of mathematical revolutions: metaphysics, legitimacy, and rigour. The case of the calculus from Newton to Berkeley and Maclaurin (134–168);
+Yu Xin Zheng, Non-Euclidean geometry and revolutions in mathematics (169–182);
+Luciano Boi, The "revolution" in the geometrical vision of space in the nineteenth century, and the hermeneutical epistemology of mathematics (183–208);
+Caroline Dunmore, Meta-level revolutions in mathematics (209–225);
+Jeremy Gray, The nineteenth-century revolution in mathematical ontology (226–248);
+Herbert Breger, A restoration that failed: Paul Finsler's theory of sets (249–264);
+Donald A. Gillies, The Fregean revolution in logic (265–305);
+Michael Crowe, Afterword (1992): a revolution in the historiography of mathematics? (306–316).
+
+
+== Reviews ==
+The book was reviewed by Pierre Kerszberg for Mathematical Reviews and by Michael S. Mahoney for American Mathematical Monthly. Mahoney says "The title should have a question mark." He sets the context by referring to paradigm shifts that characterize scientific revolutions as described by Thomas Kuhn in his book The Structure of Scientific Revolutions. According to Michael Crowe in chapter one, revolutions never occur in mathematics. Mahoney explains how mathematics grows upon itself and does not discard earlier gains in understanding with new ones, such as happens in biology, physics, or other sciences.  A nuanced version of revolution in mathematics is described by Caroline Dunmore who sees change at the level of "meta-mathematical values of the community that define the telos and methods of the subject, and encapsulate general beliefs about its value." On the other hand, reaction to innovation in mathematics is noted, resulting in "clashes of intellectual and social values".
+
+
+== Editions ==
+Gillies, Donald (1992) Revolutions in Mathematics, Oxford Science Publications, The Clarendon Press, Oxford University Press.
+
+
+== References ==
+Pierre Kerszberg (1994, 2009) Review of Revolutions in Mathematics in Mathematical Reviews.
+Michael S. Mahoney (1994) "Review of Revolutions in Mathematics", American Mathematical Monthly 101(3):283–7.

data/en.wikipedia.org/wiki/Sacred_Mathematics-0.md

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+---
+title: "Sacred Mathematics"
+chunk: 1/1
+source: "https://en.wikipedia.org/wiki/Sacred_Mathematics"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T08:46:44.766570+00:00"
+instance: "kb-cron"
+---
+
+Sacred Mathematics: Japanese Temple Geometry is a book on Sangaku, geometry problems presented on wooden tablets as temple offerings in the Edo period of Japan. It was written by Fukagawa Hidetoshi and Tony Rothman, and published in 2008 by the Princeton University Press. It won the PROSE Award of the Association of American Publishers in 2008 as the best book in mathematics for that year.
+
+
+== Topics ==
+The book begins with an introduction to Japanese culture and how this culture led to the production of Sangaku tablets, depicting geometry problems, their presentation as votive offerings at temples, and their display at the temples. It also includes a chapter on the Chinese origins of Japanese mathematics, and a chapter on biographies of Japanese mathematicians from the time.
+The Sangaku tablets illustrate theorems in Euclidean geometry, typically involving circles or ellipses, often with a brief textual explanation. They are presented as puzzles for the viewer to prove, and in many cases the proofs require advanced mathematics. In some cases, booklets providing a solution were included separately, but in many cases the original solution has been lost or was never provided. The book's main content is the depiction, explanation, and solution of over 100 of these Sangaku puzzles, ranked by their difficulty, selected from over 1800 catalogued Sangaku and over 800 surviving examples. The solutions given use modern mathematical techniques where appropriate rather than attempting to model how the problems would originally have been solved.
+Also included is a translation of the travel diary of Japanese mathematician Yamaguchi Kanzan (or Kazu), who visited many of the temples where these tablets were displayed and in doing so built a collection of problems from them. The final three chapters provide a scholarly appraisal of precedence in mathematical discoveries between Japan and the west, and an explanation of the techniques that would have been available to Japanese problem-solvers of the time, in particular discussing how they would have solved problems that in western mathematics would have been solved using calculus or inversive geometry.
+
+
+== Audience and reception ==
+Sacred Geometry can be read by historians of mathematics, professional mathematicians, "people who are simply interested in geometry", and "anyone who likes mathematics", and the puzzles it presents also span a wide range of expertise. Readers are not expected to already have a background in Japanese culture and history. The book is heavily illustrated, with many color photographs, also making it suitable as a mathematical coffee table book despite the depth of the mathematics it discusses.
+Reviewer Paul J. Campbell calls this book "the most thorough account of Japanese temple geometry available", reviewer Jean-Claude Martzloff calls it "exquisite, artfull, well-thought, and particularly well-documented",, reviewer Frank J. Swetz calls it "a well-crafted work that combines mathematics, history, and cultural considerations into an intriguing narrative", and reviewer Noel J. Pinnington calls it "excellent and well-thought-out". However, Pinnington points out that it lacks the citations and bibliography that would be necessary in a work of serious historical scholarship. Reviewer Peter Lu also criticizes the book's review of Japanese culture as superficial and romanticized, based on the oversimplification that the culture was born out of Japan's isolation and uninfluenced by the later mathematics of the west.
+
+
+== Related works ==
+This is the third English-language book on Japanese mathematics from Fukagawa; the first two were Japanese Temple Geometry Problems (with Daniel Pedoe, 1989) and Traditional Japanese Mathematics Problems from the 18th and 19th Centuries (with John Rigby, 2002). Sacred Mathematics expands on a 1998 article on Sangaku by Fukagawa and Rothman in Scientific American.
+
+
+== References ==

data/en.wikipedia.org/wiki/Sequences_(book)-0.md

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+---
+title: "Sequences (book)"
+chunk: 1/1
+source: "https://en.wikipedia.org/wiki/Sequences_(book)"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T08:46:45.913883+00:00"
+instance: "kb-cron"
+---
+
+Sequences is a mathematical monograph on integer sequences. It was written by Heini Halberstam and Klaus Roth, published in 1966 by the Clarendon Press, and republished in 1983 with minor corrections by Springer-Verlag. Although planned to be part of a two-volume set, the second volume was never published.
+
+
+== Topics ==
+The book has five chapters, each largely self-contained and loosely organized around different techniques used to solve problems in this area, with an appendix on the background material in number theory needed for reading the book. Rather than being concerned with specific sequences such as the prime numbers or square numbers, its topic is the mathematical theory of sequences in general.
+The first chapter considers the natural density of sequences, and related concepts such as the Schnirelmann density. It proves theorems on the density of sumsets of sequences, including Mann's theorem that the Schnirelmann density of a sumset is at least the sum of the Schnirelmann densities and Kneser's theorem on the structure of sequences whose lower asymptotic density is subadditive. It studies essential components, sequences that when added to another sequence of Schnirelmann density between zero and one, increase their density, proves that additive bases are essential components, and gives examples of essential components that are not additive bases.
+The second chapter concerns the number of representations of the integers as sums of a given number of elements from a given sequence, and includes the Erdős–Fuchs theorem according to which this number of representations cannot be close to a linear function. The third chapter continues the study of numbers of representations, using the probabilistic method; it includes the theorem that there exists an additive basis of order two whose number of representations is logarithmic, later strengthened to all orders in the Erdős–Tetali theorem.
+After a chapter on sieve theory and the large sieve (unfortunately missing significant developments that happened soon after the book's publication), the final chapter concerns primitive sequences of integers, sequences like the prime numbers in which no element is divisible by another. It includes Behrend's theorem that such a sequence must have logarithmic density zero, and the seemingly-contradictory construction by Abram Samoilovitch Besicovitch of primitive sequences with natural density close to 1/2. It also discusses the sequences that contain all integer multiples of their members, the Davenport–Erdős theorem according to which the lower natural and logarithmic density exist and are equal for such sequences, and a related construction of Besicovitch of a sequence of multiples that has no natural density.
+
+
+== Audience and reception ==
+This book is aimed at other mathematicians and students of mathematics; it is not suitable for a general audience. However, reviewer J. W. S. Cassels suggests that it could be accessible to advanced undergraduates in mathematics.
+Reviewer E. M. Wright notes the book's "accurate scholarship", "most readable exposition", and "fascinating topics". Reviewer Marvin Knopp describes the book as "masterly", and as the first book to overview additive combinatorics. Similarly, although Cassels notes the existence of material on additive combinatorics in the books Additive Zahlentheorie (Ostmann, 1956) and Addition Theorems (Mann, 1965), he calls this "the first connected account" of the area, and reviewer Harold Stark notes that much of material covered by the book is "unique in book form". Knopp also praises the book for, in many cases, correcting errors or deficiencies in the original sources that it surveys. Reviewer Harold Stark writes that the book "should be a standard reference in this area for years to come".
+
+
+== References ==

data/en.wikipedia.org/wiki/Shuli_jingyun-0.md

@@ -0,0 +1,29 @@
+---
+title: "Shuli jingyun"
+chunk: 1/1
+source: "https://en.wikipedia.org/wiki/Shuli_jingyun"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T08:46:47.061966+00:00"
+instance: "kb-cron"
+---
+
+The Shuli jingyun (數理精蘊), known in English as the Collected Essential Principles of Mathematics, is a 53-volume mathematical encyclopedia, part of the Siku Quanshu collection, on musical tuning, calculation, and the calendar. It includes three treatises on astronomy, mathematics, and music, compiled under imperial order during the Kangxi reign. The book was completed in 1723.
+
+
+== Production and distribution ==
+The encyclopedia was commissioned by the Kangxi Emperor in 1713 and involved over one hundred scholars studying under the Emperor and Jesuit experts. The compilation of this book was supervised by Prince Yūnlu, with He Guozong (d. 1767) and Mei Gucheng (1681-1746) as main compilers. The book began its creation in 1713 and was finished by 1723. In 1724, the first copy was published by the imperial printing shop. The encyclopedia was intended to be used as an imperial textbook in China. Upon its publication, it has been imported to different countries such as Korea in 1729.
+The Shuli jingyun is included in the Siku Quanshu collection, commissioned by the Qianlong Emperor. This collection, compiled between 1773 and 1782, includes 3,461 titles and is divided into four treasuries.
+
+
+== Contents ==
+
+The Shuli jingyun has two parts and an appendix with tables in 8 juan. The first part covers the theory and foundations of Chinese mathematics, while the second part includes five chapters on different mathematical concepts like lines, areas, and volumes.
+
+
+=== Tables ===
+The original Shuli jingyun consists of eight volumes (juan) of tables. The first two volumes contain trigonometric function tables calculated every 10 seconds of the quadrant (540 pages). The next two include prime number factors up to 100,000 (702 pages). The next two provide logarithms for numbers up to 100,000 (1,000 pages). The last two offer logarithms of trigonometric functions every 10 seconds of the quadrant (540 pages).
+The tables of logarithms were directly taken from the Arithmetica logarithmica and Trigonometria artificialis, both works by Adriaan Vlacq.
+
+
+== References ==

data/en.wikipedia.org/wiki/Significant_Figures_(book)-0.md

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+---
+title: "Significant Figures (book)"
+chunk: 1/1
+source: "https://en.wikipedia.org/wiki/Significant_Figures_(book)"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T08:46:48.244917+00:00"
+instance: "kb-cron"
+---
+
+Significant Figures: The Lives and Work of Great Mathematicians is a 2017 nonfiction book by British mathematician  Ian Stewart , published by Basic Books. In the work, Stewart discusses the lives and contributions of 25 figures who are prominent in the history of mathematics. The 25 mathematicians selected are: Archimedes, Liu Hui, Muḥammad ibn Mūsā al-Khwārizmī, Madhava of Sangamagrama, Gerolamo Cardano, Pierre de Fermat, Isaac Newton, Euler, Fourier, Gauss, Lobachevsky, Galois, Ada Lovelace, Boole, Riemann, Cantor, Sofia Kovalevskaia, Poincaré, Hilbert, Emmy Noether, Ramanujan, Gödel, Turing, Mandelbrot, and Thurston.
+
+
+== Reception ==
+In Kirkus Reviews, it was written that "even a popularizer as skilled and prolific as Stewart cannot expect general readers to fully digest his highly distilled explanations of what these significant figures did to resolve ever more complex conundrums as math advanced." However, the reviewer praised Stewart's sketches of the lives and times of the innovators. The book was described as "a text for teachers, precocious students, and intellectually curious readers unafraid to tread unfamiliar territory".
+
+
+== See also ==
+In Pursuit of the Unknown: 17 Equations That Changed the World
+
+
+== References ==

data/en.wikipedia.org/wiki/Solving_the_Riddle_of_Phyllotaxis-0.md

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+---
+title: "Solving the Riddle of Phyllotaxis"
+chunk: 1/1
+source: "https://en.wikipedia.org/wiki/Solving_the_Riddle_of_Phyllotaxis"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T08:46:49.465367+00:00"
+instance: "kb-cron"
+---
+
+Solving the Riddle of Phyllotaxis: Why the Fibonacci Numbers and the Golden Ratio Occur in Plants is a book on the mathematics of plant structure, and in particular on phyllotaxis, the arrangement of leaves on plant stems. It was written by Irving Adler, and published in 2012 by World Scientific. The Basic Library List Committee of the Mathematical Association of America has suggested its inclusion in undergraduate mathematics libraries.
+
+
+== Background ==
+Irving Adler (1913–2012) was known as a peace protester, schoolteacher, and children's science book author before, in 1961, earning a doctorate in abstract algebra. Even later in his life, Adler began working on phyllotaxis, the mathematical structure of leaves on plant stems. This book, which collects several of his papers on the subject previously published in journals and edited volumes, is the last of his 85 books to be published before his death.
+
+
+== Topics ==
+Different plants arrange their leaves differently, for instance on alternating sides of the plant stem, or rotated from each other by other fractions of a full rotation between consecutive leaves. In these patterns, rotations by 1/2 of an angle, 1/3 of an angle, 3/8 of an angle, or 5/8 of an angle are common, and it does not appear to be coincidental that the numerators and denominators of these fractions are all Fibonacci numbers. Higher Fibonacci numbers often appear in the number of spiral arms in the spiraling patterns of sunflower seed heads, or the helical patterns of pineapple cells. The theme of Adler's work in this area, in the papers reproduced in this volume, was to find  a mathematical model for plant development that would explain these patterns and the occurrence of the Fibonacci numbers and the golden ratio within them.
+The papers are arranged chronologically; they include four journal papers from the 1970s, another from the late 1990s, and a preface and book chapter also from the 1990s. Among them, the first is the longest, and reviewer Adhemar Bultheel calls it "the most fundamental"; it uses the idea of "contact pressure" to cause plant parts to maximize their distance from each other and maintain a consistent angle of divergence from each other, and makes connections with the mathematical theories of circle packing and space-filling curves. Subsequent papers refine this theory, make additional connections for instance to the theory of continued fractions, and provide a more general overview.
+Interspersed with the theoretical results in this area are historical asides discussing, among others, the work on phyllotaxis of Theophrastus (the first to study phyllotaxis), Leonardo da Vinci (the first to apply mathematics to phyllotaxis), Johannes Kepler (the first to recognize the importance of the Fibonacci numbers to phyllotaxis), and later naturalists and mathematicians.
+
+
+== Audience and reception ==
+Reviewer Peter Ruane found the book gripping, writing that it can be read by a mathematically inclined reader with no background knowledge in phyllotaxis. He suggests, however, that it might be easier to read the papers in the reverse of their chronological order, as the broader overview papers were written later in this sequence. And Yuri V. Rogovchenko calls its publication "a thoughtful tribute to Dr. Adler’s multi-faceted career as a researcher, educator, political activist, and author".
+
+
+== References ==

data/en.wikipedia.org/wiki/Sphere_Packings,_Lattices_and_Groups-0.md

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+---
+title: "Sphere Packings, Lattices and Groups"
+chunk: 1/1
+source: "https://en.wikipedia.org/wiki/Sphere_Packings,_Lattices_and_Groups"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T08:46:50.644463+00:00"
+instance: "kb-cron"
+---
+
+Sphere Packings, Lattices and Groups is a book about geometry and group theory by John Conway and Neil Sloane, with contributions by other mathematicians, first published in 1988.
+H. S. M. Coxeter noted, "Much of the book is inspired by the Leech lattice." The book covers many results that, as Richard K. Guy phrased it, "appear little short of miraculous", such as how the Leech lattice, a set of points in 24-dimensional space, is related via special relativity to stacking cannonballs. The interrelated topics featured in the book include Golay codes, Mathieu groups and Monstrous Moonshine. Many of the chapters are updates of papers that had been published in journals previously. Portions of the text were coauthored by Eiichi Bannai, Richard Borcherds, John Leech, Simon Norton, Andrew M. Odlyzko, Richard A. Parker, Larissa Queen and B. B. Venkov.
+Francis Fung called it "monumental", and Nick Lord described it as "epochal". Gian-Carlo Rota wrote:
+
+This is the best survey of the best work in the best fields of combinatorics written by the best people. It will make the best reading by the best students interested in the best mathematics that is now going on.
+
+
+== Editions ==
+The book is volume 290 in Springer's Grundlehren der mathematischen Wissenschaften series.
+
+Sphere Packings, Lattices and Groups (1st ed.). Springer-Verlag. 1988. ISBN 0-387-96617-X. MR 0920369.
+Sphere Packings, Lattices and Groups (2nd ed.). Springer-Verlag. 1993. ISBN 9780387979120.
+Sphere Packings, Lattices and Groups (3rd ed.). Springer-Verlag. 1998. doi:10.1007/978-1-4757-6568-7. ISBN 9780387985855.
+Russian translation, by S. N. Litsyn, M. A. Tsfasman and G. B. Shabat; Mir Publishers, Moscow, 1990. Volume 1: ISBN 9785030023687 MR 1148591; volume 2: ISBN 9785030023694 MR 1148592.
+
+
+== References ==
+
+Coxeter, H. S. M. (June–July 1989). The American Mathematical Monthly. 96 (6): 538–544. JSTOR 2323992.{{cite journal}}:  CS1 maint: untitled periodical (link)
+Guy, Richard K. (July 1989). "Review". Bulletin of the American Mathematical Society. 21 (1): 142–147. doi:10.1090/S0273-0979-1989-15795-9.
+Rota, Gian-Carlo (November 1990). Advances in Mathematics. 84 (1): 136. doi:10.1016/0001-8708(90)90041-K.{{cite journal}}:  CS1 maint: untitled periodical (link)
+Lord, Nick (July 2004). The Mathematical Gazette. 88 (512): 357–358. doi:10.1017/S0025557200175461. JSTOR 3620888.{{cite journal}}:  CS1 maint: untitled periodical (link)
+Fung, Francis (2009-11-03). "From Error-Correcting Codes Through Sphere Packings to Simple Groups". MAA Reviews. Mathematical Association of America.
+Ryba, Alex; et al. (August 2022). "John Horton Conway (1937–2020)". Notices of the American Mathematical Society. 69 (7): 1171–1187. doi:10.1090/noti2514.
+
+
+== External links ==
+SPLAG at Neil Sloane's web site

data/en.wikipedia.org/wiki/Sumario_Compendioso-0.md

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+---
+title: "Sumario Compendioso"
+chunk: 1/1
+source: "https://en.wikipedia.org/wiki/Sumario_Compendioso"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T08:46:52.962788+00:00"
+instance: "kb-cron"
+---
+
+The Sumario Compendioso was the first mathematics book published in the New World. The book was published in Mexico City in 1556 by a clergyman Juan Diez.
+
+
+== Availability ==
+The book has been digitized and is available on the Internet.
+Before the Digital Age the only four known surviving copies were preserved at the Huntington Library, San Marino, California, the British Library, London, Duke University Library, and the University of Salamanca in Spain.
+
+
+== Excerpts ==
+In his book The Math Book, Clifford A. Pickover provided the following information about Sumario Compendioso:
+
+The Sumario Compendioso, published in Mexico City in 1556, is the first work on mathematics printed in the Americas. The publication of Sumario Compendioso in the New World preceded by many decades the emigration of the Puritans to North America and the settlement in Jamestown, Virginia. The author, Brother Juan Diez, was a companion of Hernando Cortes, the Spanish conquistador, during Cortes's conquests of the Aztec Empire.
+
+
+== References ==
+
+
+== External links ==
+Open Library
+HathiTrust
+JSTOR
+Archive.org

data/en.wikipedia.org/wiki/Symmetry_aspects_of_M._C._Escher's_periodic_drawings-0.md

@@ -0,0 +1,43 @@
+---
+title: "Symmetry aspects of M. C. Escher's periodic drawings"
+chunk: 1/1
+source: "https://en.wikipedia.org/wiki/Symmetry_aspects_of_M._C._Escher's_periodic_drawings"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T08:46:55.237869+00:00"
+instance: "kb-cron"
+---
+
+Symmetry aspects of M. C. Escher's periodic drawings is a book by crystallographer Caroline H. MacGillavry published for the International Union of Crystallography (IUCr) by Oosthoek in 1965. The book analyzes the  symmetry of M. C. Escher's colored periodic drawings using the international crystallographic notation.
+In 1959, MacGillavry  met Escher. His work, the regular tiling of the plane, showed obvious links with the symmetry principles of crystallography. After seeking approval from the organisers (Joseph and Gabrielle Donnay), MacGillavry asked Escher to exhibit his lithographic works at the IUCr Congress in Cambridge, U.K. in 1960. The exhibition was a success, and as a consequence the IUCr commissioned MacGillavry to write the book under its auspices.
+
+
+== Structure and topics ==
+The book has three chapters. In the first chapter, entitled Patterns with Classical Symmetry, the author introduces the concepts of motif, symmetry operations, lattice and unit cell, and uses these to analyze the symmetry of 13 of Escher's tiling designs.
+In the second chapter, Patterns with Black-white Symmetry, the antisymmetry operation (indicated by a prime ') is introduced.  The chapter analyzes 22 of Escher's design in terms of black-white symmetry and assigns each a symbol in the international notation describing its symmetries.
+In the third chapter, Patterns with Polychromatic Symmetry, the analysis is extended to 7 of Escher's design possessing three or more colors. The book is printed in full color to facilitate the recognition of color symmetries in the images.
+
+
+== Audience ==
+The publication of the book was sponsored by the IUCr and the original target audience was crystallography students learning the principles of symmetry, particularly color symmetry. In the introduction to the book the author states "Although the book is meant primarily for undergraduate students, I hope that many people who are simply amused and intrigued by Escher's designs will be interested to see how they illustrate the laws of symmetry".
+
+
+== Reception and influence ==
+The reception of the book was positive. Robert M. Mengel in Scientific American wrote "[the author] has organized this unique and beautiful book from the corpus of marvelous spacefilling periodic drawings made over two decades by the artist Maurits C. Escher. Adding a few specially drawn for this work, Escher has here given us the classical crystal groups in the plane, and a good many more that exploit the latest extensions to color symmetry, foreseen by the artist before mathematicians had officially recognized and classified them."
+F. I. G. Rawlins in Acta Crystallographica wrote "Under [the author's] sure guidance the reader is skilfully conducted through such regions of the theory of symmetry as are necessary for a tolerable grasp of the full significance of these patterns, several of them produced in full colour."
+J. Bohm reviewed the book in Kristall Und Technik. Bohm acknowledged the special value of Escher's art as crystallographic teaching material. He praised the author for preparing the material in a detailed, crystallographically valid and didactically appealing way. Overall he stated that the book was a successful collaboration between the artist, author, publisher and the IUCr.
+In 1976 an announcement in the IUCr's journals stated that the book was "extremely popular" and this had a necessitated a reprint in both the Netherlands and the U.S.A. In an obituary of the author it is stated that the publication of the book helped to popularise M. C. Escher's work in the U.S.A. MacGillavry's book inspired further work on the symmetry analysis of M. C. Escher's work, particularly by Doris Schattschneider in M. C. Escher: Visions of Symmetry.
+
+
+== Editions ==
+First edition published for International Union of Crystallography by Oosthoek in 1965
+Second edition published for International Union of Crystallography by Bohn, Scheltema & Holkema in 1976
+Reprint edition with the title Fantasy & symmetry: the periodic drawings of M. C. Escher published by Harry N. Abrams in 1976
+Third edition published by International Union of Crystallography in 2017
+
+
+== References ==
+
+
+== External links ==
+MacGillavry, Caroline H. (1976). Fantasy & symmetry: the periodic drawings of M. C. Escher. H. N. Abrams. ISBN 978-0-8109-0850-5. at the Internet Archive

data/en.wikipedia.org/wiki/Symmetry_in_Science_and_Art-0.md

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+---
+title: "Symmetry in Science and Art"
+chunk: 1/1
+source: "https://en.wikipedia.org/wiki/Symmetry_in_Science_and_Art"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T08:46:56.409275+00:00"
+instance: "kb-cron"
+---
+
+Symmetry in Science and Art is a book by A.V. Shubnikov and V.A. Koptsik published by Plenum Press in 1974. The book is a translation of Simmetrija v nauke i iskusstve (Russian: Симметрия в науке и искусстве) published by Nauka in 1972. The book was notable because it gave English-language speakers access to Russian work in the fields of  dichromatic and polychromatic symmetry.
+
+
+== Structure and topics ==
+The book is divided into two parts. The first part is an updated version of A.V. Shubnikov's 1940 book Symmetry: laws of symmetry and their application in science, technology and applied arts (Russian: Симметрия : законы симметрии и их применение в науке, технике и прикладном искусстве). The following types of classical (one-color) and dichromatic (two-color) symmetries are covered in the first part of the book: one-sided rosettes, figures with a singular point, one-sided bands, two-sided bands, rods, network patterns, layers and space groups.
+The second part consists of three new chapters written by V.A. Koptsik covering the following subjects: group theory, crystallographic groups, antisymmetry, colored symmetry, symmetry in science and art, and conservation laws.
+
+
+== Audience ==
+The book is written for crystallographers, mathematicians and physicists who are interested in the application of color symmetry to crystal structure analysis and physics experiments involving magnetic or ferroelectric materials. Werner Nowacki in his review of the book for Science stated: "This is an extraordinary book, dealing with symmetry in all its aspects and written for the nonspecialist as well as the specialist (crystallographer and physicist) in this domain of natural sciences."
+
+
+== Reception ==
+The book had a mixed reception from contemporary reviewers.  Marc H. Bornstein in a review for Leonardo praised the book: "Shubnikov and Koptsik, I find, should stand beside Weyl's classic treatise, Symmetry". Werner Nowacki wrote a positive review: "This clearly written, beautifully illustrated book will become a standard work for all who are interested in unifying branches of natural sciences and of art, and we must be grateful to the translator, the editor, and the publisher for having produced such a precious publication."
+However, Herbert Callen in American Scientist, criticised the book:"The book remains as it was in its original edition - an exhaustive classification of symmetry groups for systems with particular types of symmetry operations, now updated by Koptsik. The larger philosophical and aesthetic extensions, however, do not meet Western standards of critical accuracy, rigour, or precision of statement; they are not pursued in any depth, and they draw on no currents of thought outside the Soviet Union."
+
+
+== Influence ==
+Tony Crilly, when reviewing Jaswon and Rose's Crystal symmetry, theory of colour crystallography in The Mathematical Gazette in 1984 commented: "The beginning student would find Symmetry in Science and Art (by A. V. Shubnikov and V. A. Koptsick, 1974) a stimulating introduction to the ideas worked out in technical detail by Jaswon and Rose." István and Magdolna Hargittai in the preface to their book Symmetry through the eyes of a chemist remarked: "We would like especially to note here two classics in the literature of symmetry which have strongly influenced us: Weyl's Symmetry and Shubnikov and Koptsik's Symmetry in Science and Art".
+In later reviews of the literature by R.L.E. Schwarzenberger and by Branko Grünbaum and G.C. Shephard in their book Tilings and patterns the work of the Russian color symmetry school led by A.V. Shubnikov and N.V. Belov was put into its proper historical context. Schwarzenberger, and Grünbaum and Shephard, give credit to Shubnikov and Belov for relaunching the field of color symmetry after the work of Heinrich Heesch and H.J. Woods in the 1930s was largely ignored. However, they criticise Shubnikov and Koptsik for taking a crystallographic rather than a group-theoretic approach, and for continuing to use their own confusing notation rather than adopting the international standard Hermann–Mauguin notation for crystallographic symmetry elements.
+
+
+== References ==
+
+
+== External links ==
+Symmetry in Science and Art. Plenum Press. 1974. ISBN 978-0-306-30759-1. at the Internet Archive

data/en.wikipedia.org/wiki/Synopsis_of_Pure_Mathematics-0.md

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+---
+title: "Synopsis of Pure Mathematics"
+chunk: 1/1
+source: "https://en.wikipedia.org/wiki/Synopsis_of_Pure_Mathematics"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T08:46:57.582639+00:00"
+instance: "kb-cron"
+---
+
+Synopsis of Pure Mathematics is a book by G. S. Carr, written in 1886. The book attempted to summarize the state of most of the basic mathematics known at the time.
+The book is noteworthy because it was a major source of information for the legendary and self-taught mathematician Srinivasa Ramanujan who managed to obtain a library loaned copy from a friend in 1903. Ramanujan reportedly studied the contents of the book in detail. The book is generally acknowledged as a key element in awakening the genius of Ramanujan.
+Carr acknowledged the main sources of his book in its preface:
+
+... In the Algebra, Theory of Equations, and Trigonometry sections, I am largely indebted to Todhunter's well-known treatises ...
+In the section entitled Elementary Geometry, I have added to simpler propositions a selection of theorems from Townsend's Modern Geometry and Salmon's Conic Sections.
+In Geometric Conics, the line of demonstration followed agrees, in the main, with that adopted in Drew's treatise on the subject. ...
+The account of the C. G. S. system given in the preliminary section, has been compiled from a valuable contribution on the subject by Professor Everett, of Belfast, published by the Physical Society of London.
+
+In addition to the authors already named, the following treatises have been consulted—Algebras, by Wood, Bourdon, and Lefebvre de Fourey; Snowball's Trigonometry; Salmon's Higher Algebra; the geometrical exercises in Pott's Euclid; and Geometrical Conics by Taylor, Jackson, and Renshaw.
+
+
+== Bibliography ==
+Carr, George Shoobridge (1886), A synopsis of elementary results in pure mathematics containing propositions, formulae, and methods of analysis, with abridged demonstrations., Reprinted by Chelsea, 1970, London. Fr. Hodgson. Cambridge. Macmillan and Bowes, ISBN 978-0-8284-0239-2 {{citation}}: ISBN / Date incompatibility (help)
+
+
+== References ==
+
+
+== External links ==
+Carr, George Shoobridge (1886), A synopsis of elementary results in pure mathematics containing propositions, formulae, and methods of analysis, with abridged demonstrations., London. Fr. Hodgson. Cambridge. Macmillan and Bowes - archive.org
+Carr, George Shoobridge (1886), A synopsis of elementary results in pure mathematics containing propositions, formulae, and methods of analysis, with abridged demonstrations., London. Fr. Hodgson. Cambridge. Macmillan and Bowes - archive.org
+Carr, George Shoobridge (1886), A synopsis of elementary results in pure mathematics containing propositions, formulae, and methods of analysis, with abridged demonstrations. (PDF), London. Fr. Hodgson. Cambridge. Macmillan and Bowes - rarebooksocietyofindia.org

data/en.wikipedia.org/wiki/The_Deadly_Dinner_Party-0.md

@@ -0,0 +1,32 @@
+---
+title: "The Deadly Dinner Party"
+chunk: 1/1
+source: "https://en.wikipedia.org/wiki/The_Deadly_Dinner_Party"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T08:47:37.245785+00:00"
+instance: "kb-cron"
+---
+
+The Deadly Dinner Party and Other Medical Detective Stories (2009, ISBN 978-0-300-12558-0) is a nonfiction book by Jonathan A. Edlow, MD about medical mysteries. 
+The book contains fifteen real-life stories of everyday people caught up in medical crises that take deduction and detective work to solve, and to determine a correct diagnosis. The book has been compared to the "medical mystery" books of Berton Roueché. The book is published by Yale University Press.
+
+
+== Reception ==
+In a review for New Scientist, Druin Burch wrote that the "collection of bite-sized essays about obscure infections, poisons and diseases […] make an enjoyable and interesting book. The stories don’t flow, but they do add up to more than a list of anecdotes […]."
+In The New York Review of Books, Jerome Groopman described how Edlow wrote in "clear and fluid prose" about unusual diagnoses and the ultimate need for a "discerning doctor".
+
+
+== See also ==
+Diagnosis
+Medical ethics
+How Doctors Think
+Fatal Care: Survive in the U.S. Health System
+
+
+== References ==
+
+
+== External links ==
+Review of book in The New York Review of Books (November 5, 2009)
+Review in New Scientist (October 11, 2009)

data/en.wikipedia.org/wiki/The_Desideratum-0.md

@@ -0,0 +1,22 @@
+---
+title: "The Desideratum; or, Electricity Made Plain and Useful"
+chunk: 1/1
+source: "https://en.wikipedia.org/wiki/The_Desideratum;_or,_Electricity_Made_Plain_and_Useful"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T08:47:38.416207+00:00"
+instance: "kb-cron"
+---
+
+The Desideratum; or, Electricity Made Plain and Useful - By a Lover of Mankind, and of Common Sense is a 1760 book by John Wesley advocating the use of electric shock therapy. Wesley collected the accounts of other researchers with "electrifying machines", and to them added observations from his own experiments in public clinics.
+
+
+== Legacy ==
+The 72-page book has led Wesley to be mentioned alongside his contemporaries Richard Lovett and Jean Paul Marat as a pioneer advocate of the medical uses of electroconvulsive therapy, despite the fact that Wesley's tests and results are not considered scientific by modern standards.
+
+
+== References ==
+
+
+== External links ==
+Digital copy of an 1871 reprint at Archive.org

data/en.wikipedia.org/wiki/The_Doctor_in_War-0.md

@@ -0,0 +1,28 @@
+---
+title: "The Doctor in War"
+chunk: 1/1
+source: "https://en.wikipedia.org/wiki/The_Doctor_in_War"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T08:47:43.085159+00:00"
+instance: "kb-cron"
+---
+
+The Doctor in War is a book published in November 1918 by Woods Hutchinson, an American physician who travelled throughout Europe from 15 January to 24 December 1917 visiting hospitals, ambulance trains, and other locations to offer his services to the war effort during World War I.
+
+
+== Background ==
+As Hutchinson believed that "the doctor and the sanitarian would play an important part" in the World War, he offered to help the British Army medical staff but was told in order to serve he would have to swear allegiance and in turn lose his American citizenship.  With the help of Secretary of War Newton Diehl Baker and Colonel Roosevelt he was able to travel to Europe and see everything that had "any value or interest from a medical and public health point of view."
+
+
+== Summary ==
+Hutchinson emphasizes the importance that doctors played in the war.  One of the major things they have contributed is the decrease in deaths due to disease. In the American Civil War the ratio was five deaths to disease for every one in battle, however during 'The Great War' the ratio was changed to ten deaths in battle for every one to disease. Hutchinson believes that three major points contribute to this protection against infectious disease: inoculations and sanitary measures; surgical skill and hospital organization increasing recovery rate; and the better food provided to soldiers.
+
+
+== References ==
+"The Doctor in War". Journal of the American Medical Association. 72 (1): 64. 4 January 1919. doi:10.1001/jama.1919.02610010070026.
+"Reviews". British Medical Journal. 1 (3046): 612. 17 May 1919. doi:10.1136/bmj.1.3046.612. S2CID 220033816.
+
+
+== Further reading ==
+Hutchinson, Woods (1918). The Doctor In War. Boston, New York: Houghton Mifflin Company.

data/en.wikipedia.org/wiki/The_Green_Book_(immunisation_guide)-0.md

@@ -0,0 +1,52 @@
+---
+title: "The Green Book (immunisation guide)"
+chunk: 1/1
+source: "https://en.wikipedia.org/wiki/The_Green_Book_(immunisation_guide)"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T08:47:58.214179+00:00"
+instance: "kb-cron"
+---
+
+Immunisation against infectious disease, popularly known as The Green Book, provides information on vaccines for vaccine-preventable diseases. It acts as a guide to the UK's vaccination schedule for health professionals and health departments that give vaccines in the United Kingdom.
+The first two editions were published in 1992 and 1996. A third edition in 2006, was the last to appear in print. Updates have since been added by its clinical editors through advice and recommendations from the Joint Committee on Vaccination and Immunisation (JCVI) and appear only online as individual chapters via the immunisation section of the GOV.UK website. As of 2021 it includes updates on COVID-19.
+
+
+== Purpose ==
+Immunisation against infectious disease is popularly known as The Green Book, to provide information on the UK's vaccination schedule and vaccines for vaccine preventable infectious diseases. It is a guide for health professionals and health departments that give vaccines in the UK. Updates are added by its clinical editors through advice and recommendations from the Joint Committee on Vaccination and Immunisation (JCVI), as accepted by the Secretaries of State. Larger updates may also need consultations with UK health departments and public health bodies, MHRA, vaccine manufacturers, NHS England, National Travel Health Network and Centre (NaTHNaC), as well as the clinical editors.
+
+
+== Publication ==
+The first two editions were published by the HMSO in 1992 and 1996. The third edition, published by The Stationery Office in 2006, replaced the 1996 edition and was the last to appear in print.
+
+
+== 2006 edition ==
+The 2006 edition of The Green book has 468 pages, divided generally into two parts, preceded by a contents page, acknowledgements and preface, and followed by two indexes, one of vaccines by proprietary name and the other of vaccines by common name.
+
+
+=== Part one: principles, practices and procedures ===
+Part one, titled "principles, practice and procedures", has 12 chapters which include how vaccines work, storage and distribution, vaccine safety and adverse events, immunisation schedule and immunisation of healthcare and laboratory staff. How to give a vaccine is described in chapter four, common side effects in chapter eight and how to fill in a yellow card in chapter nine (updated 2013).
+
+
+=== Part two: diseases, vaccinations and vaccines ===
+Diseases and their vaccines are listed in alphabetical order and include all vaccines recommended in the routine immunisation programme for all children in the UK. Vaccine requirements for travellers and for contacts of people with infectious disease are included. The 2006 edition incorporated the then new vaccines for meningococcal group C and pneumococcal infections, included the cessation of the school's BCG programme and the introduction of the Hib-MenC booster at 12 months of age.
+Diseases included:
+
+
+== Online version ==
+The online version was published in 2013. Updates appear only online as individual chapters via the immunisation section of the GOV.UK website. These have included respiratory syncytial virus and rotavirus in 2015, and human papillomavirus in 2019. As of 2021, the online version stays divided into two parts, in the same way as the 2006 edition, and includes updates on shingles and COVID-19.
+According to Andrew Pollard, The Green Book should be "bookmarked" in all child clinics and notes that similar information can be obtained from the US Centers for Disease Control and Prevention website. It is a recommended source by the Royal College of Paediatrics and Child Health.
+
+
+== Editors ==
+1996 - David Salisbury, Norman T. Begg
+2006 - David Salisbury, Mary Ramsay, Karen Noakes
+2021 - Mary Ramsay
+
+
+== References ==
+
+
+== External links ==
+"Immunisation against infectious disease". GOV.UK. pp. 28–29. Retrieved 29 December 2021.
+Department of Health (2006). Salisbury, David; Ramsay, Mary (eds.). Immunisation against infectious disease. The Stationery Office. ISBN 978-0-11-322528-6. Archived from the original on 2008-08-17. Retrieved 2021-12-29.

data/en.wikipedia.org/wiki/The_Human_Embryo-0.md

@@ -0,0 +1,14 @@
+---
+title: "The Human Embryo"
+chunk: 1/1
+source: "https://en.wikipedia.org/wiki/The_Human_Embryo"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T08:48:01.741856+00:00"
+instance: "kb-cron"
+---
+
+The Human Embryo: Aristotle and the Arabic and European Traditions is a book looking at the philosophy and religious viewpoints of human reproduction over the ages by the Reverend Canon G. R. Dunstan and published by University of Exeter Press in 1990. It specialises in the study of the human embryo both historically and from different cultural viewpoints. The largest section is devoted to the understanding of the embryo in the Middle Ages, with seven articles alone reinterpreting Dante's passages on the animation of the embryo.
+
+
+== References ==

data/en.wikipedia.org/wiki/The_Princeton_Companion_to_Mathematics-0.md

@@ -0,0 +1,52 @@
+---
+title: "The Princeton Companion to Mathematics"
+chunk: 1/1
+source: "https://en.wikipedia.org/wiki/The_Princeton_Companion_to_Mathematics"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T08:46:29.787993+00:00"
+instance: "kb-cron"
+---
+
+The Princeton Companion to Mathematics is a book providing an extensive overview of mathematics that was published in 2008 by Princeton University Press. Edited by Timothy Gowers with associate editors June Barrow-Green and Imre Leader, it has been noted for the high caliber of its contributors. The book was the 2011 winner of the Euler Book Prize of the Mathematical Association of America, given annually to "an outstanding book about mathematics".
+
+
+== Topics and organization ==
+The book concentrates primarily on modern pure mathematics rather than applied mathematics, although it does also cover both applications of mathematics and the mathematics that relates to those applications;
+it provides a broad overview of the significant ideas and developments in research mathematics. It is organized into eight parts:
+
+An introduction to mathematics, outlining the major areas of study, key definitions, and the goals and purposes of mathematical research.
+An overview of the history of mathematics, in seven chapters including the development of important concepts such as number, geometry, mathematical proof, and the axiomatic approach to the foundations of mathematics. A chronology of significant events in mathematical history is also provided later in the book.
+Three core sections, totalling approximately 600 pages. The first of these sections provides an alphabetized set of articles on 99 specific mathematical concepts such as the axiom of choice, expander graphs, and Hilbert space. The second core section includes long surveys of 26 branches of research mathematics such as algebraic geometry and combinatorial group theory. The third describes 38 important mathematical problems and theorems such as the four color theorem, the Birch and Swinnerton-Dyer conjecture, and the Halting problem.
+A collection of biographies of nearly 100 famous deceased mathematicians, arranged chronologically, also including a history of Nicolas Bourbaki's pseudonymous collaboration.
+Essays describing the influences and applications of mathematics in the sciences, technology, business, medicine, and the fine arts.
+A section of perspectives on the future of mathematics, problem solving techniques, the ubiquity of mathematics, and advice to young mathematicians.
+Despite its length, the range of topics included is selective rather than comprehensive: some important established topics such as diophantine approximation are omitted, transcendental number theory, differential geometry, and cohomology get short shrift, and the most recent frontiers of research are also generally not included.
+
+
+== Target audience ==
+The book's authors have attempted to keep their work accessible by forgoing abstraction and technical nomenclature as much as possible and by making heavy use of concrete examples and illustrations. Compared to the concise and factual coverage of mathematics in sources such as Wikipedia and MathWorld, the articles in the Princeton Companion are intended to be more reflective and discursive, and to convey the beauty and depth of modern mathematics. Quoting a passage from Bertrand Russell that "Pure Mathematics is the class of all propositions of the form p implies q", the editor of the Companion states that it "is about everything that Russell’s definition leaves out."
+The core sections of the Companion are aimed primarily at readers who are already familiar with mathematics at the undergraduate level. Much of the rest of the book, such as its collection of biographies, would be accessible to a mathematically inclined high school student, and there is enough depth of coverage in the book to interest even professional research mathematicians. Reviewer Jonathan Borwein summarizes the audience for this book broadly:
+
+Every research mathematician, every  university student of mathematics, and every serious amateur of mathematical science should own at least one copy of the Companion.
+
+
+== Contributors ==
+The contributors to The Princeton Companion to Mathematics consist of 133 of the world's best mathematicians. Timothy Gowers, its editor, is the recipient of the Fields Medal, considered to be the top honor in mathematics. Other contributors include Fields medalists Michael Atiyah, Alain Connes, Charles Fefferman, and Terence Tao, and well-known mathematicians Noga Alon, George Andrews, Béla Bollobás, John P. Burgess, Kevin Buzzard, Clifford Cocks, Ingrid Daubechies, Persi Diaconis, Jordan Ellenberg, Oded Goldreich, Andrew Granville, Jeremy Gray, Frank Kelly, Sergiu Klainerman, Jon Kleinberg, János Kollár, Peter Lax, Dusa McDuff, Barry Mazur, Carl Pomerance, Eleanor Robson, Peter Sarnak, Madhu Sudan, Clifford Taubes, and Avi Wigderson. Among the historians who contributed to it are Charles C. Gillispie, Ivor Grattan-Guinness, Jeremy Gray, Niccolò Guicciardini, Ulf Hashagen, Eberhard Knobloch, Karen Hunger Parshall, Eleanor Robson, and Erhard Scholz.
+
+
+== Awards ==
+Gowers and the Princeton Companion were the 2011 winners of the Euler Book Prize of the Mathematical Association of America, given annually to "an outstanding book about mathematics".
+The Princeton Companion was also listed as an outstanding title by Choice Magazine, a publication of the American Library Association, in 2009.
+
+
+== See also ==
+The Princeton Companion to Applied Mathematics, published 2015 and edited by Nicholas Higham
+
+
+== References ==
+
+
+== External links ==
+Book homepage at Princeton University Press; contains several sample chapters
+Princeton Companion To Mathematics category in Gowers's blog (which contains 3 erratas written by him)

data/en.wikipedia.org/wiki/The_Principles_of_Mathematics-0.md

@@ -0,0 +1,51 @@
+---
+title: "The Principles of Mathematics"
+chunk: 1/2
+source: "https://en.wikipedia.org/wiki/The_Principles_of_Mathematics"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T08:46:30.914036+00:00"
+instance: "kb-cron"
+---
+
+The Principles of Mathematics (PoM) is a 1903 book by Bertrand Russell, in which the author presented his famous paradox and argued his thesis that mathematics and logic are identical.
+The book presents a view of the foundations of mathematics and Meinongianism  and has become a classic reference. It reported on developments by Giuseppe Peano, Mario Pieri, Richard Dedekind, Georg Cantor, and others.
+In 1905 Louis Couturat published a partial French translation that expanded the book's readership. In 1937 Russell prepared a new introduction saying, "Such interest as the book now possesses is historical, and consists in the fact that it represents a certain stage in the development of its subject." Further editions were published in 1938, 1951, 1996, and 2009.
+
+== Contents ==
+The Principles of Mathematics consists of 59 chapters divided into seven parts: indefinables in mathematics, number, quantity, order, infinity and continuity, space, matter and motion.
+In chapter one, "Definition of Pure Mathematics", Russell asserts that: 
+
+The fact that all Mathematics is Symbolic Logic is one of the greatest discoveries of our age; and when this fact has been established, the remainder of the principles of mathematics consists in the analysis of Symbolic Logic itself.
+Russell deconstructs pure mathematics with relations, by positing them, their converses and complements as primitive notions. Combining the calculus of relations of DeMorgan, Pierce and Schroder, with the symbolic logic of Peano, he analyses orders using serial relations, and writes that the theorems of measurement have been generalized to order theory. He notes that Peano distinguished a term from the set containing it: the set membership relation versus subset. Epsilon (ε)  is used to show set membership, but Russell indicates trouble when 
+  
+    
+      
+        x
+        ϵ
+        x
+        .
+      
+    
+    {\displaystyle x\epsilon x.}
+  
+ Russell's paradox is  mentioned 15 times and chapter 10 "The Contradiction" explains it. Russell had written previously on foundations of geometry, denoting, and relativism of space and time, so those topics are  recounted. Elliptic geometry according  to Clifford, and the Cayley-Klein metric are mentioned to illustrate non-Euclidean geometry. There is an anticipation of relativity physics in the final part as the last three chapters consider Newton's laws of motion, absolute and relative motion, and Hertz's dynamics. However, Russell rejects what he calls "the relational theory", and says on page 489:
+
+For us, since absolute space and time have been admitted, there is no need to avoid absolute motion, and indeed no possibility of doing so.
+In his review, G. H. Hardy says "Mr. Russell is a firm believer in absolute position in space and time, a view as much out of fashion nowadays that Chapter [58: Absolute and Relative Motion] will be read with peculiar interest."
+
+== Early reviews ==
+Reviews were prepared by G. E. Moore and Charles Sanders Peirce, but Moore's was never published and that of Peirce was brief and somewhat dismissive. He indicated that he thought it unoriginal, saying that the book "can hardly be called literature" and "Whoever wishes a convenient introduction to the remarkable researches into the logic of mathematics that have been made during the last sixty years [...] will do well to take up this book."
+G. H. Hardy wrote a favorable review expecting the book to appeal more to philosophers than mathematicians. But he says:
+
+[I]n spite of its five hundred pages the book is much too short. Many chapters dealing with important questions are compressed into five or six pages, and in some places, especially in the most avowedly controversial parts, the argument is almost too condensed to follow. And the philosopher who attempts to read the book will be especially puzzled by the constant presupposition of a whole philosophical system utterly unlike any of those usually accepted.
+In 1904 another review appeared in Bulletin of the American Mathematical Society (11(2):74–93) written by Edwin Bidwell Wilson. He says "The delicacy of the question is such that even the greatest mathematicians and philosophers of to-day have made what seem to be substantial slips of judgement and have shown on occasions an astounding ignorance of the essence of the problem which they were discussing. ... all too frequently it has been the result of a wholly unpardonable disregard of the work already accomplished by others." Wilson recounts the developments of Peano that Russell reports, and takes the occasion to correct Henri Poincaré who had ascribed them to David Hilbert. In praise of Russell, Wilson says "Surely the present work is a monument to patience, perseverance, and thoroughness." (page 88)
+
+== Second edition ==
+In 1938 the book was re-issued with a new preface by Russell. This preface was interpreted as a retreat from the realism of the first edition and a turn toward nominalist philosophy of symbolic logic. James Feibleman, an admirer of the book, thought Russell's new preface went too far into nominalism so he wrote a rebuttal to this introduction. Feibleman says, "It is the first comprehensive treatise on symbolic logic to be written in English; and it gives to that system of logic a realistic interpretation."
+
+== Later reviews ==
+In 1959 Russell wrote My Philosophical Development, in which he recalled the impetus to write the Principles:
+
+It was at the International Congress of Philosophy in Paris in the year 1900 that I became aware of the importance of logical reform for the philosophy of mathematics. ... I was impressed by the fact that, in every discussion, [Peano] showed more precision and more logical rigour than was shown by anybody else. ... It was [Peano's works] that gave the impetus to my own views on the principles of mathematics.
+Recalling the book as it his later work, he provides this evaluation:

data/en.wikipedia.org/wiki/The_Principles_of_Mathematics-1.md

@@ -0,0 +1,39 @@
+---
+title: "The Principles of Mathematics"
+chunk: 2/2
+source: "https://en.wikipedia.org/wiki/The_Principles_of_Mathematics"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T08:46:30.914036+00:00"
+instance: "kb-cron"
+---
+
+The Principles of Mathematics, which I finished on 23 May 1902, turned out to be a crude and rather immature draft of the subsequent work [Principia Mathematica], from which, however, it differed in containing controversy with other philosophies of mathematics.
+Such self-deprecation from the author after half a century of philosophical growth is understandable. On the other hand, Jules Vuillemin wrote in 1968: 
+
+The Principles inaugurated contemporary philosophy. Other works have won and lost the title. Such is not the case with this one. It is serious, and its wealth perseveres. Furthermore, in relation to it, in a deliberate fashion or not, it locates itself again today in the eyes of all those that believe that contemporary science has modified our representation of the universe and through this representation, our relation to ourselves and to others.
+Moreover, in the same reflection, Russell also recounts the singular place the composition of the book had in his intellectual life. He recalls:
+
+I finished this first draft of The Principles of Mathematics on the last day of the nineteenth century—i.e. December 31, 1900. The months since the previous July had been an intellectual honeymoon such as I have never experienced before or since. Every day I found myself understanding something that I had not understood on the previous day. I thought all difficulties were solved and all problems were at an end. 
+When W. V. O. Quine penned his autobiography, he wrote:
+
+Peano's symbolic notation took Russell by storm in 1900, but Russell's Principles was still in unrelieved prose. I was inspired by its profundity [in 1928] and baffled by its frequent opacity. In part it was rough going because of the cumbersomeness of ordinary language as compared with the suppleness of a notation especially devised for these intricate themes. Rereading it years later, I discovered that it had been rough going also because matters were unclear in Russell's own mind in those pioneer days.
+The Principles was an early expression of analytic philosophy and thus has come under close examination. Peter Hylton wrote, "The book has an air of excitement and novelty to it ... The salient characteristic of Principles is ... the way in which the technical work is integrated into metaphysical argument."
+Ivor Grattan-Guinness made an in-depth study of Principles. First he published Dear Russell – Dear Jourdain (1977), which included correspondence with Philip Jourdain who promulgated some of the book's ideas. Then in 2000 Grattan-Guinness published The Search for Mathematical Roots 1870 – 1940, which considered the author's circumstances, the book's composition and its shortcomings.
+In 2006, Philip Ehrlich challenged the validity of Russell's analysis of infinitesimals in the Leibniz tradition.
+A recent study documents the non-sequiturs in Russell's critique of the infinitesimals of Gottfried Leibniz and Hermann Cohen.
+
+== See also ==
+Introduction to Mathematical Philosophy
+Russellian change
+
+== Notes ==
+
+== References ==
+Stefan Andersson (1994). In Quest of Certainty: Bertrand Russell's Search for Certainty in Religion and Mathematics Up to The Principles of Mathematics. Stockholm: Almquist & Wiksell. ISBN 91-22-01607-4.
+
+== External links ==
+The Principles of Mathematics – Free searchable full text versions in PDF, ePub and HTML formats
+The Principles of Mathematics – Online text (scan of original) on fair-use.org
+The Principles of Mathematics – Full text at the Internet Archive
+The Principles of Mathematics at PhilPapers

data/en.wikipedia.org/wiki/The_Strange_Logic_of_Random_Graphs-0.md

@@ -0,0 +1,198 @@
+---
+title: "The Strange Logic of Random Graphs"
+chunk: 1/1
+source: "https://en.wikipedia.org/wiki/The_Strange_Logic_of_Random_Graphs"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T08:46:51.781673+00:00"
+instance: "kb-cron"
+---
+
+The Strange Logic of Random Graphs is a book on zero-one laws for random graphs. It was written by Joel Spencer and published in 2001 by Springer-Verlag as volume 22 of their book series Algorithms and Combinatorics.
+
+
+== Topics ==
+The random graphs of the book are generated from the Erdős–Rényi–Gilbert model 
+  
+    
+      
+        G
+        (
+        n
+        ,
+        p
+        )
+      
+    
+    {\displaystyle G(n,p)}
+  
+ in which 
+  
+    
+      
+        n
+      
+    
+    {\displaystyle n}
+  
+ vertices are given and a random choice is made whether to connect each pair of vertices by an edge, independently for each pair, with probability 
+  
+    
+      
+        p
+      
+    
+    {\displaystyle p}
+  
+ of making a connection. A zero-one law is a theorem stating that, for certain properties of graphs, and for certain choices of 
+  
+    
+      
+        p
+      
+    
+    {\displaystyle p}
+  
+,
+the probability of generating a graph with the property tends to zero or one in the limit as 
+  
+    
+      
+        n
+      
+    
+    {\displaystyle n}
+  
+ goes to infinity.
+A fundamental result in this area, proved independently by Glebskiĭ et al. and by Ronald Fagin, is that there is a zero-one law for 
+  
+    
+      
+        G
+        (
+        n
+        ,
+        1
+        
+          /
+        
+        2
+        )
+      
+    
+    {\displaystyle G(n,1/2)}
+  
+ for every property that can be described in the first-order logic of graphs. Moreover, the limiting probability is one if and only if the infinite Rado graph has the property. For instance, a random graph in this model contains a triangle with probability tending to one; it contains a universal vertex with probability tending to zero. For other choices of 
+  
+    
+      
+        p
+      
+    
+    {\displaystyle p}
+  
+, other outcomes can occur.
+For instance, the limiting probability of containing a triangle is between 0 and 1 when 
+  
+    
+      
+        p
+        =
+        c
+        
+          /
+        
+        n
+      
+    
+    {\displaystyle p=c/n}
+  
+ for a constant 
+  
+    
+      
+        c
+      
+    
+    {\displaystyle c}
+  
+; it tends to 0 for smaller choices of 
+  
+    
+      
+        p
+      
+    
+    {\displaystyle p}
+  
+ and to 1 for larger choices. The function 
+  
+    
+      
+        1
+        
+          /
+        
+        n
+      
+    
+    {\displaystyle 1/n}
+  
+ is said to be a threshold for the property of containing a triangle, meaning that it separates the values of 
+  
+    
+      
+        p
+      
+    
+    {\displaystyle p}
+  
+ with limiting probability 0 from the values with limiting probability 1.
+The main result of the book (proved by Spencer with Saharon Shelah) is that irrational powers of 
+  
+    
+      
+        n
+      
+    
+    {\displaystyle n}
+  
+ are never threshold functions. That is, whenever 
+  
+    
+      
+        a
+        >
+        0
+      
+    
+    {\displaystyle a>0}
+  
+ is an irrational number, there is a zero-one law for the first-order properties of the random graphs 
+  
+    
+      
+        G
+        (
+        n
+        ,
+        
+          n
+          
+            −
+            a
+          
+        
+        )
+      
+    
+    {\displaystyle G(n,n^{-a})}
+  
+. A key tool in the proof is the Ehrenfeucht–Fraïssé game.
+
+
+== Audience and reception ==
+Although it is essentially the proof of a single theorem, aimed at specialists in the area, the book is written in a readable style that introduces the reader to many important topics in finite model theory and the theory of random graphs. Reviewer Valentin Kolchin, himself the author of another book on random graphs, writes that the book is "self-contained, easily read, and is distinguished by elegant writing", recommending it to probability theorists and logicians. Reviewer Alessandro Berarducci calls the book "beautifully written" and its subject "fascinating".
+
+
+== References ==

data/en.wikipedia.org/wiki/The_Tower_of_Hanoi_–_Myths_and_Maths-0.md

@@ -0,0 +1,30 @@
+---
+title: "The Tower of Hanoi – Myths and Maths"
+chunk: 1/1
+source: "https://en.wikipedia.org/wiki/The_Tower_of_Hanoi_–_Myths_and_Maths"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T08:47:03.324829+00:00"
+instance: "kb-cron"
+---
+
+The Tower of Hanoi – Myths and Maths is a book in recreational mathematics, on the tower of Hanoi, baguenaudier, and related puzzles. It was written by Andreas M. Hinz, Sandi Klavžar, Uroš Milutinović, and Ciril Petr, and published in 2013 by Birkhäuser, with an expanded second edition in 2018. The Basic Library List Committee of the Mathematical Association of America has suggested its inclusion in undergraduate mathematics libraries.
+
+
+== Topics ==
+Although this book is in recreational mathematics, it takes its subject seriously, and brings in material from automata theory, computational complexity, the design and analysis of algorithms, graph theory, and group theory, topology, fractal geometry, chemical graph theory, and even psychology (where related puzzles have applications in psychological testing).
+The 1st edition of the book had 10 chapters, and the 2nd edition has 11. In both cases they begin with chapter zero, on the background and history of the Tower of Hanoi puzzle, covering its real-world invention by Édouard Lucas and in the mythical backstory he invented for it. Chapter one considers the Baguenaudier puzzle (or, as it is often called, the Chinese rings), related to the tower of Hanoi both in the structure of its state space and in the fact that it takes an exponential number of moves to solve, and likely the inspiration for Lucas. Chapter two introduces the main topic of the book, the tower of Hanoi, in its classical form in which one must move disks one-by-one between three towers, always keeping the disks on each tower sorted by size. It provides several different algorithms for solving the classical puzzle (in which the disks begin and end all on a single tower) in as few moves as possible, and for collecting all disks on a single tower when they begin in other configurations, again as quickly as possible. It introduces the Hanoi graphs describing the state space of the puzzle, and relates numbers of puzzle steps to distances within this graph. After a chapter on "irregular" puzzles in which the initial placement of disks on their towers is not sorted, chapter four discusses the "Sierpiński graphs" derived from the Sierpiński triangle; these are closely related to the three-tower Hanoi graphs but diverge from them for higher numbers of towers of Hanoi or higher-dimensional Sierpinski fractals.
+The next four chapters concern additional variants of the tower of Hanoi, in which more than three towers are used, the disks are only allowed to move between some of the towers or in restricted directions between the towers, or the rules for which disks can be placed on which are modified or relaxed. A particularly important case is the Reve's puzzle, in which the rules are unchanged except that there are four towers instead of three. An old conjecture concerning the minimum possible number of moves between two states with all disks on a single tower was finally proven in 2014, after the publication of the first edition of the book, and the second edition includes this material.
+Some of the definitions and proofs are extended into the book's many exercises. A new chapter in the second edition provides hints and partial solutions, and the final chapter collects open problems and (in the second edition) provides updates to previously-listed problems. Many color illustrations and photographs are included throughout the book.
+
+
+== Audience ==
+The book can be read both by mathematicians working on topics related to the tower of Hanoi puzzle, and by a general audience interested in recreational mathematics. Reviewer László Kozma describes the book as essential reading for the first type of audience and (despite occasional heavy notation and encyclopedic detail) accessible and interesting to the second type, even for readers with only a high school level background in mathematics. On the other hand, reviewer Cory Palmer cautions that "this book is not for a casual reader", adding that a good understanding of combinatorics is necessary to read it, and reviewer Charles Ashbacher suggests that it has enough depth of content to be the topic of an advanced undergraduate elective course.
+Although generally positive, reviewer S. V. Nagaraj complains about a "significant number of errors" in the book. Reviewer Andrew Percy calls it "an enjoyable adventure", "humorous, and very thorough". Reviewer Martin Klazar calls the book "wonderful", recommending it to anyone interested in recreational mathematics or mathematics more generally.
+
+
+== References ==
+
+
+== External links ==
+Home page

data/en.wikipedia.org/wiki/The_Whetstone_of_Witte-0.md

@@ -0,0 +1,46 @@
+---
+title: "The Whetstone of Witte"
+chunk: 1/1
+source: "https://en.wikipedia.org/wiki/The_Whetstone_of_Witte"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T08:47:18.369323+00:00"
+instance: "kb-cron"
+---
+
+The Whetstone of Witte is the shortened title of Robert Recorde's mathematics book published in 1557, the full title being The whetstone of witte, whiche is the seconde parte of Arithmetike: containyng thextraction of Rootes: The Coßike practise, with the rule of Equation: and the woorkes of Surde Nombers. The book covers topics including whole numbers, the extraction of roots and irrational numbers. The work is notable for containing the first recorded use of the equals sign and also for being the first book in English to use the plus and minus signs.
+Recordian notation for exponentiation, however, differed from the later Cartesian notation 
+  
+    
+      
+        
+          p
+          
+            q
+          
+        
+        =
+        p
+        ×
+        p
+        ×
+        p
+        ⋯
+        ×
+        p
+      
+    
+    {\displaystyle p^{q}=p\times p\times p\cdots \times p}
+  
+.  Recorde expressed indices and surds larger than 3 in a systematic form based on the prime factorization of the exponent: a factor of two he termed a zenzic, and a factor of three, a cubic. Recorde termed the larger prime numbers appearing in this factorization sursolids, distinguishing between them by use of ordinal numbers: that is, he defined 5 as the first sursolid, written as ʃz and 7 as the second sursolid, written as Bʃz.
+
+He also devised symbols for these factors: a zenzic was denoted by z, and a cubic by &.  For instance, he referred to p8=p2×2×2 as zzz (the zenzizenzizenzic), and q12=q2×2×3 as zz& (the zenzizenzicubic).Later in the book he includes a chart of exponents all the way up to p80=p2×2×2×2×5 written as zzzzʃz. There is an error in the chart, however, writing p69 as Sʃz, despite it not being a prime. It should be p3×23 or &Gʃz.
+Page images have been made available by Victor Katz and Frank Swetz through Convergence, a publication of Mathematical Association of America.
+
+
+== References ==
+
+
+== External links ==
+The Whetstone of Witte at The Internet Archive
+The Whetstone of Witte at The Library of Congres

data/en.wikipedia.org/wiki/Theory_of_Lie_groups-0.md

@@ -0,0 +1,20 @@
+---
+title: "Theory of Lie groups"
+chunk: 1/1
+source: "https://en.wikipedia.org/wiki/Theory_of_Lie_groups"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T08:46:59.850097+00:00"
+instance: "kb-cron"
+---
+
+In mathematics, Theory of Lie groups is a series of books on Lie groups by Claude Chevalley (1946, 1951, 1955). The first in the series was one of the earliest books on Lie groups to treat them from the global point of view, and for many years was the standard text on Lie groups. The second and third volumes, on algebraic groups and Lie algebras, were written in French, and later reprinted bound together as one volume. Apparently further volumes were planned but not published, though his lectures (Chevalley 2005) on the classification of semisimple algebraic groups could be considered as a continuation of the series.
+
+
+== References ==
+Chevalley, Claude (1946), Theory of Lie Groups. I, Princeton Mathematical Series, vol. 8, Princeton University Press, ISBN 978-0-691-04990-8, MR 0015396 {{citation}}: ISBN / Date incompatibility (help)
+Chevalley, Claude (1951), Théorie des groupes de Lie. Tome II. Groupes algébriques, Actualités Sci. Ind., vol. 1152, Hermann & Cie., Paris, MR 0051242
+Chevalley, Claude (1955), Théorie des groupes de Lie. Tome III. Théorèmes généraux sur les algèbres de Lie, Actualités Sci. Ind., vol. 1226, Hermann & Cie, Paris, MR 0068552
+Chevalley, Claude (1968), Théorie des groupes de Lie : Groupes algébriques, théorèmes généraux sur les algèbres de Lie (in French), vol. 8, Paris: Hermann, Reprint of volumes II and III bound as one volume
+Chevalley, Claude (2005) [1958], Cartier, P. (ed.), Classification des groupes algébriques semi-simples, Collected works., vol. 3, Berlin, New York: Springer-Verlag, ISBN 978-3-540-23031-1, MR 0106966
+Smith, P. A. (1947), "Review: Claude Chevalley, The theory of Lie groups, I", Bull. Amer. Math. Soc., 53 (9): 884–887, doi:10.1090/s0002-9904-1947-08876-5

data/en.wikipedia.org/wiki/Tilings_and_patterns-0.md

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+---
+title: "Tilings and patterns"
+chunk: 1/1
+source: "https://en.wikipedia.org/wiki/Tilings_and_patterns"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T08:47:01.029296+00:00"
+instance: "kb-cron"
+---
+
+Tilings and patterns is a book by mathematicians Branko Grünbaum and Geoffrey Colin Shephard published in 1987 by W.H. Freeman. The book was 10 years in development, and upon publication it was widely reviewed and highly acclaimed.
+
+
+== Structure and topics ==
+The book is concerned with tilings—a partition of the plane into regions (the tiles)—and patterns—repetitions of a motif in the plane in a regular manner.
+The book is divided into two parts. The first seven chapters define concepts and terminology, establish the general theory of tilings, survey tilings by regular polygons, review the theory of patterns, and discuss tilings in which all the tiles, or all the edges, or all the vertices, play the same role.
+The last five chapters survey a variety of advanced topics in tiling theory: colored patterns and tilings, polygonal tilings, aperiodic tilings, Wang tiles, and tilings with unusual kinds of tiles.
+Each chapter open with an introduction to the topic, this is followed by the detailed material of the chapter, much previously unpublished, which is always profusely illustrated, and normally includes examples and proofs. Chapters close with exercises, and a section of notes and references which detail the historical development of the topic. These notes sections are interesting and entertaining, as they discuss the efforts of the previous workers in the field and detail the good (and bad) approaches to the topic. The notes also identify unsolved problems, point out areas of potential application, and provide connections to other disciplines in mathematics, science, and the arts.
+The book has 700 pages, including a 40-page, 800-entry bibliography, and an index. The book is used as a source on numerous Wikipedia pages.
+
+
+== Audience ==
+In their preface the authors state "We have written this book with three main groups of readers in mind—students, professional mathematicians and non-mathematicians whose interests include patterns and shapes (such as artists, architects, crystallographers and others).
+Other reviewers commented as follows:
+
+"The most striking feature of the book is its extensive collection of figures, including hundreds of examples of tilings and patterns. The sheer abundance is perhaps one reason why artists and designers have been drawn to it over the years."
+"Their idea was that the book should be accessible to any reader who is attracted to geometry."
+
+
+== Reception ==
+Contemporary reviews of the book were overwhelming positive. The book was reviewed by 15 journals in the fields of crystallography, mathematics, and the sciences. Quotations from major reviews:
+
+
+== Influence ==
+The book was praised in later journal articles by multiple authors:
+
+The book was also praised in later books by other authors:
+
+
+== Editions ==
+The hardback original Tilings and patterns was published in 1987.
+Tilings and patterns - an introduction, a paperback reprint of the first seven chapters of the 1987 original, was published in 1989.
+In 2016 a second edition of the full text was published by Dover in paperback, with a new preface and an appendix describing progress in the subject since the first edition. The reviewer at MAA Reviews commented "Dover has once again done the mathematical community a service in bringing back such a notable volume."
+
+
+== References ==
+
+
+== External links ==
+"Tilings and patterns". at the Internet Archive
+"Selection of reviews". at the MacTutor History of Mathematics Archive

data/en.wikipedia.org/wiki/Traité_de_mécanique_céleste-0.md

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+---
+title: "Traité de mécanique céleste"
+chunk: 1/2
+source: "https://en.wikipedia.org/wiki/Traité_de_mécanique_céleste"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T08:47:04.499255+00:00"
+instance: "kb-cron"
+---
+
+Traité de mécanique céleste (transl. "Treatise of celestial mechanics") is a five-volume treatise on celestial mechanics written by Pierre-Simon Laplace and published from 1798 to 1825 with a second edition in 1829. In 1842, the government of Louis Philippe gave a grant of 40,000 francs for a 7-volume national edition of the Oeuvres de Laplace (1843–1847); the Traité de mécanique céleste with its four supplements occupies the first 5 volumes.
+
+Newton laid the foundations of Celestial Mechanics, at the close of the seventeenth century, by the discovery of the principle of universal gravitation. Even in his own hands, this discovery led to important consequences, but it has required a century and a half, and a regular succession of intellects the most powerful, to fill up the outline sketched by him. Of these, Laplace himself was the last, and, perhaps after Newton, the greatest; and the task commenced in the Principia of the former, is completed in the Mécanique Céleste of the latter. In this last named work, the illustrious author has proposed to himself his object, to unite all the theories scattered throughout the various channels of publication, employed by his predecessors, to reduce them to one common method, and present them all in the same point of view.
+If one were asked to name the two most important works in the progress of mathematics and physics, the answer would undoubtedly be, the Principia of Newton and the Mécanique Céleste of Laplace. In their historical and philosophical aspects these works easily outrank all others, and furnish thus the standard by which all others must be measured. The distinguishing feature of the Principia is its clear and exhaustive enunciation of fundamental principles. The Mécanique Céleste, on the other hand, is conspicuous for the development of principles and for the profound generality of its methods. The Principia gives the plans and specifications of the foundations; the Mécanique Céleste affords the key to the vast and complex superstructure.
+
+== Tome I. (1798) ==
+
+=== Livre I. Des lois générales de l'équilibre et du mouvement ===
+Chap. I. De l'équilibre et de la composition des forces qui agissent sur un point matériel
+Chap. II. Du mouvement d'un point matériel
+Chap. III. De l'équilibre d'un système de corps
+Chap. IV. De l'équilibre des fluides
+Chap. V. Principes généraux du mouvement d'un système de corps
+Chap. VI. Des lois du mouvement d'un système de corps, dans toutes les relations mathématiquement possibles entre la force et la vitesse
+Chat. VII. Des mouvemens d'un corps solide de figure quelconque
+Chap. VIII. Du mouvement des fluides
+
+=== Livre II. De la loi pesanteur universelle, et du mouvement des centres de gravité des corps célestes ===
+
+== Tome II. (1798) ==
+
+=== Livre III. De la figure des corps céleste ===
+
+=== Livre IV. Des oscillations de la mer et de l'atmosphère ===
+
+=== Livre V. Des mouvemens des corps célestes, autour de leurs propre centres de gravité ===
+
+== Tome III. (1802) ==
+
+=== Livre VI. Théorie particulières des mouvemens célestes ===
+
+=== Livre VII. Théorie de la lune ===
+
+== Tome IV. (1805) ==
+
+=== Livre VIII. Théorie des satellites de Jupiter, de Saturne et d'Uranus ===
+
+=== Livre IX. Théorie des comètes ===
+
+=== Livre X. Sur différens points relatifs au système du monde ===
+This book contains a discussion of continued fractions and a computation of the complementary error function in terms that came to be called the Laplace continued fraction,
+1/(1+q/(1+2q/(1+3q/(...))).
+
+== Tome V. (1825) ==
+
+=== Livre XI. De la figure et de la rotation de la terre ===
+
+=== Livre XII. De l'attraction et de la répulsion des sphères, et des lois de l'equilibre et du mouvement des fluides élastiques ===
+
+=== Livre XIII. Des oscillations des fluides qui recouvrent les planètes ===
+
+=== Livre XIV. Des mouvemens des corps célestes autour de leurs centres de gravité ===
+
+=== Livre XV. Du mouvement des planètes et des comètes ===
+
+=== Livre XVI. Du mouvement des satellites ===
+
+== English translations ==
+During the early nineteenth century at least five English translations of Mécanique Céleste were published. In 1814 the Reverend John Toplis prepared a translation of Book 1 entitled The Mechanics of Laplace. Translated with Notes and Additions. In 1821 Thomas Young anonymously published a further translation into English of the first book; beyond just translating from French to English he claimed in the preface to have translated the style of mathematics: The translator flatters himself, however, that he has not expressed the author's meaning in English words alone, but that he has rendered it perfectly intelligible to any person, who is conversant with the English mathematicians of the old school only, and that his book will serve as a connecting link between the geometrical and algebraical modes of representation.The Reverend Henry Harte, a fellow at Trinity College, Dublin translated the entire first volume of Mécanique Céleste, with Book 1 published in 1822 and Book 2 published separately in 1827. Similarly to Bowditch (see below), Harte felt that Laplace's exposition was too brief, making his work difficult to understand:... it may be safely asserted, that the chief obstacle to a more general knowledge of the work, arises from the summary manner in which the Author passes over the intermediate steps in several of his most interesting investigations.
+
+=== Bowditch's translation ===
+The famous American mathematician Nathaniel Bowditch translated the first four volumes of the Traité de mécanique céleste but not the fifth volume; however, Bowditch did make use of relevant portions of the fifth volume in his extensive commentaries for the first four volumes.

data/en.wikipedia.org/wiki/Traité_de_mécanique_céleste-1.md

@@ -0,0 +1,26 @@
+---
+title: "Traité de mécanique céleste"
+chunk: 2/2
+source: "https://en.wikipedia.org/wiki/Traité_de_mécanique_céleste"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T08:47:04.499255+00:00"
+instance: "kb-cron"
+---
+
+The first four volumes of Dr. Bowditch's Translation and Commentary were published successively, in 1828, 1832, 1834, and 1839, at the sacrifice of one quarter of his whole property. The expense was largely increased by the voluminous commentary. This was really of the nature of an original work, and was rendered necessary by the frequent gaps which Laplace had left in his own publication. Mr. N. I. Bowditch says, in his biography of his father, that Dr. Bowditch was accustomed to remark, "Whenever I meet in Laplace with the words, Thus it plainly appears, I am sure that hours, and perhaps days, of hard study will alone enable me to discover how it plainly appears."
+Bowditch's translation of the first four volumes of Laplace's Traité de mécanique céleste was completed by 1818 but he would not publish it for many years. Almost certainly the cost of publication caused the delay, but Bowditch did not just put the work on one side after 1818 but continued to improve it over the succeeding years. Bowditch was helped by Benjamin Peirce in this project and his commentaries doubled the length of the book. His purpose was more than just an English translation. He wanted to supply steps omitted in the original text; to incorporate later results into the translation; and to give credits omitted by Laplace.
+
+=== Somerville's translation ===
+In 1826, it was still felt by Henry Brougham, president of the Society for the Diffusion of Useful Knowledge, that the British reader was lacking a readable translation of Mécanique Céleste. He thus approached Mary Somerville, who began to prepare a translation which would "explain to the unlearned the sort of thing it is—the plan, the vast merit, the wonderful truths unfolded or methodized—and the calculus by which all this is accomplished". In 1830, John Herschel wrote to Somerville and enclosed a copy of Bowditch's 1828 translation of Volume 1 which Herschel had just received. Undeterred, Somerville decided to continue with the preparation of her own work as she felt the two translations differed in their aims; whereas Bowditch's contained an overwhelming number of footnotes to explain each mathematical step, Somerville instead wished to state and demonstrate the results as clearly as possible.
+A year later, in 1831, Somerville's translation was published under the title Mechanism of the Heavens. It received great critical acclaim, with complimentary reviews appearing in the Quarterly Review, the Edinburgh Review, and the Monthly Notices of the Royal Astronomical Society.
+
+== References ==
+
+== External links ==
+Translation by Nathaniel Bowditch
+
+Volume I, 1829
+Volume II, 1832
+Volume III, 1834
+Volume IV, 1839 with a memoir of the translator by his son

data/en.wikipedia.org/wiki/Treatise_on_Analysis-0.md

@@ -0,0 +1,91 @@
+---
+title: "Treatise on Analysis"
+chunk: 1/1
+source: "https://en.wikipedia.org/wiki/Treatise_on_Analysis"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T08:47:05.664536+00:00"
+instance: "kb-cron"
+---
+
+Treatise on Analysis is a translation by Ian G. Macdonald of the nine-volume work Éléments d'analyse on mathematical analysis by Jean Dieudonné, and is an expansion of his textbook Foundations of Modern Analysis. It is a successor to the various Cours d'Analyse by Augustin-Louis Cauchy, Camille Jordan, and Édouard Goursat.
+
+
+== Contents and publication history ==
+
+
+=== Volume I ===
+The first volume was originally a stand-alone graduate textbook with a different title. It was first written in English and later translated into French, unlike the other volumes which were first written in French. It has been republished several times and is much more common than the later volumes of the series.
+The contents include 
+
+Chapter I: Sets
+Chapter II Real numbers
+Chapter III Metric spaces
+Chapter IV The real line
+Chapter V Normed spaces
+Chapter VI Hilbert spaces
+Chapter VII Spaces of continuous functions
+Chapter VIII Differential calculus (This uses the Cauchy integral rather than the more common Riemann integral of functions.)
+Chapter IX Analytic functions (of a complex variable)
+Chapter X Existence theorems (for ordinary differential equations)
+Chapter XI Elementary spectral theory
+Dieudonné, J. (1960), Foundations of modern analysis, Pure and Applied Mathematics, vol. X, New York-London: Academic Press, MR 0120319
+Dieudonné, J. (1963), Éléments d'analyse. Tome I: Fondements de l'analyse moderne, Cahiers Scientifiques, vol. XXVIII, Paris: Gauthier-Villars, MR 0161945
+Dieudonné, J. (1968), Éléments d'analyse. Tome I: Fondements de l'analyse moderne, Cahiers Scientifiques, vol. XXVIII (2nd ed.), Paris: Gauthier-Villars, MR 0235945
+Dieudonné, J. (1969), Foundations of modern analysis., Pure and Applied Mathematics, vol. 10-I (2nd ed.), New York-London: Academic Press, ISBN 978-0122155505, MR 0349288
+
+
+=== Volume II ===
+The second volume includes
+
+Chapter XII Topology and topological algebra
+Chapter XIII Integration
+Chapter XIV Integration in locally compact groups
+Chapter XV Normed algebras and spectral theory
+Dieudonné, J. (1968), Éléments d'analyse. Tome II: Chapitres XII à XV, Cahiers Scientifiques, vol. XXXI, Paris: Gauthier-Villars, MR 0235946
+Dieudonné, J. (1970), Treatise on analysis. Vol. II, Pure and Applied Mathematics, vol. 10-II, New York-London: Academic Press, MR 0258551
+Dieudonné, J. (1976), Treatise on analysis. Vol. II, Pure and Applied Mathematics, vol. 10-II (2nd ed.), New York-London: Academic Press, ISBN 0-12-215502-5, MR 0530406
+
+
+=== Volume III ===
+The third volume includes chapter XVI on differential manifolds and chapter XVII on distributions and differential operators.
+
+
+=== Volume IV ===
+The fourth volume includes
+
+Chapter XVIII Differential systems
+Chapter XIX Lie groups
+Chapter XX Riemannian geometry
+
+
+=== Volume V ===
+Volume V consists of chapter XXI on compact Lie groups.
+
+
+=== Volume VI ===
+Volume VI consists of chapter XXII on harmonic analysis (mostly on locally compact groups)
+
+
+=== Volume VII ===
+Volume VII consists of the first part of chapter XXIII on linear functional equations. This chapter is considerably more advanced than most of the other chapters.
+
+
+=== Volume VIII ===
+Volume VIII consists of the second part of chapter XXIII on linear functional equations.
+
+
+=== Volume IX ===
+Volume IX contains chapter XXIV on elementary differential topology. Unlike the earlier volumes there is no English translation of it.
+
+Dieudonné, J. (1982), Éléments d'analyse. Tome IX. Chapitre XXIV, Cahiers Scientifiques, vol. XL11, Paris: Gauthier-Villars, ISBN 2-04-011499-8, MR 0658305
+
+
+=== Volume X ===
+Dieudonne planned a final volume containing chapter XXV on nonlinear problems, but this was never published.
+
+
+== References ==
+Nachbin, Leopoldo (1961), "Review: J. Dieudonné, Foundations of Modern Analysis", Bull. Amer. Math. Soc., 67 (3): 246–250, doi:10.1090/s0002-9904-1961-10566-1
+Frank, Peter (1960), "Book reviews: Foundations of Modern Analysis. J. Dieudonné. Academic Press, New York, 1960", Science, 132 (3441): 1759, doi:10.1126/science.132.3441.1759-a
+Marsden, Jerrold E. (1980), "Review: Jean Dieudonné, Treatise on analysis", Bull. Amer. Math. Soc. (N.S.), 3 (1): 719–724, doi:10.1090/s0273-0979-1980-14804-1

data/en.wikipedia.org/wiki/Treks_into_Intuitive_Geometry-0.md

@@ -0,0 +1,27 @@
+---
+title: "Treks into Intuitive Geometry"
+chunk: 1/1
+source: "https://en.wikipedia.org/wiki/Treks_into_Intuitive_Geometry"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T08:47:07.944460+00:00"
+instance: "kb-cron"
+---
+
+Treks into Intuitive Geometry: The World of Polygons and Polyhedra is a book on geometry, written as a discussion between a teacher and a student in the style of a Socratic dialogue. It was written by Japanese mathematician Jin Akiyama and science writer Kiyoko Matsunaga, and published by Springer-Verlag in 2015 (ISBN 978-4-431-55841-5), with an expanded second edition in 2024 (ISBN 978-981-99-8607-1).
+
+
+== Topics ==
+The term "intuitive geometry" of the title was used by László Fejes Tóth to refer to results in geometry that are accessible to the general public, and the book concerns topics of this type.
+The book has 16 self-contained chapters, each beginning with an illustrative puzzle or real-world application.
+It includes material on tessellations, polyhedra, and honeycombs, unfoldings of polyhedra and tessellations of unfoldings, cross sections of polyhedra, measuring boxes, gift wrapping, packing problems, wallpaper groups, pentagonal tilings, the Conway criterion for prototiles and Escher-like tilings of the plane by animal-shaped figures, aperiodic tilings including the Penrose tiling, the art gallery theorem, the Euler characteristic, dissection problems and the Dehn invariant, and the Steiner tree problem.
+The book is heavily illustrated. And although the results of the book are demonstrated in an accessible way, the book provides sequences of deductions leading to each major claim, and more-complete proofs and references are provided in an appendix.
+
+
+== Audience and reception ==
+Although it was initially developed from course material offered to undergraduates at the Tokyo University of Science, the book is aimed at a broad audience, and assumes only a high-school level knowledge of geometry. It could be used to encourage children in mathematics as well as to provide material for teachers and public lecturers. There is enough depth of material to also retain the interest of readers with a more advanced mathematical background.
+Reviewer Matthieu Jacquemet writes that the ordering of topics is unintuitive and the dialogue-based format "artificial", but reviewer Tricia Muldoon Brown instead suggests that this format allows the work to flow very smoothly, "more like a novel or a play than a textbook ... with the ease of reading purely for pleasure". Jacquemet assesses the book as "well illustrated and entertaining", and Brown writes that it "is a delightful read".
+Reviewer Michael Fox disagrees, finding the dialogue irritating and the book overall "rather disappointing". He cites as problematic the book's cursory treatment of some of its topics, and in particular its treatment of tiling patterns as purely monochromatic, its omission of the frieze groups, and its use of demonstrations by special examples that do not have all the features of the general case. He also complains about idiosyncratic terminology, the use of decimal approximations instead of exact formulas for angles, the small scale of some figures, and an uneven level of difficulty of material. Nevertheless, he writes that "this is an interesting work, with much that cannot be found elsewhere".
+
+
+== References ==

data/en.wikipedia.org/wiki/Treviso_Arithmetic-0.md

@@ -0,0 +1,49 @@
+---
+title: "Treviso Arithmetic"
+chunk: 1/1
+source: "https://en.wikipedia.org/wiki/Treviso_Arithmetic"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T08:47:09.079015+00:00"
+instance: "kb-cron"
+---
+
+The Treviso Arithmetic, or Arte dell'Abbaco, is an anonymous textbook in commercial arithmetic written in vernacular Venetian and published in Treviso, Italy, in 1478.
+The author explains the motivation for writing this textbook:
+
+I have often been asked by certain youths in whom I have much interest, and who look forward to mercantile pursuits, to put into writing the fundamental principles of arithmetic, commonly called abacus.
+The Treviso Arithmetic is the earliest known printed mathematics book in the West, and one of the first printed European textbooks dealing with a science.
+
+
+== The Arithmetic as an early printed book ==
+There appears to have been only one edition of the work. David Eugene Smith translated parts of the Treviso Arithmetic for educational purposes in 1907. Frank J. Swetz translated the complete work using Smith's notes in 1987 in his Capitalism & Arithmetic: The New Math of the 15th Century. Swetz used a copy of the Treviso housed in the Manuscript Library at Columbia University. The volume found its way to this collection via a curious route. Maffeo Pinelli (1785), an Italian bibliophile, is the first known owner. After his death his library was purchased by a London book-dealer and sold at auction on February 6, 1790. The book was obtained for three shillings by Mr. Wodhull. About 100 years later the Arithmetic appeared in the library of Brayton Ives, a New York lawyer. When Ives sold the collection of books at auction, George Arthur Plimpton, a New York publisher, acquired the Treviso and made it an acquisition to his extensive collection of early scientific texts. Plimpton donated his library to Columbia University in 1936. Original copies of the Treviso Arithmetic are extremely rare.
+There are 123 pages of text with 32 lines of print to a page. The pages are unnumbered, untrimmed and have wide margins. Some of the margins contain written notes. The size of the book is 14.5 cm by 20.6 cm.
+The book included information taken from the 1202 Liber Abaci, such as lattice multiplication. George G. Joseph in  Crest of the Peacock suggests that John Napier read this book to create Napier's bones (or rods).
+
+
+== Reasons for publication ==
+The Treviso Arithmetic is a practical book intended for self study and for use in Venetian trade. It is written in vernacular Venetian and communicated knowledge to a large population.
+It helped to end the monopoly on mathematical knowledge and gave important information to the middle class. It was not written for a large audience, but was intended to teach mathematics of everyday currency.
+The Treviso became one of the first mathematics books written for the expansion of human knowledge. It provided an opportunity for the common person, rather than only a privileged few, to learn the art of computation. The Treviso Arithmetic provided an early example of the Hindu–Arabic numeral system computational algorithms.
+
+
+== See also ==
+Ars Magna (Gerolamo Cardano) (1510)
+
+
+== Notes ==
+
+
+== References ==
+Boyer, Carl. 1991. A History of Mathematics. New York City: Wiley.
+Buck-Morss, Susan (1 January 1995). "Envisioning Capital: Political Economy on Display". Critical Inquiry. 21 (2): 434–467. doi:10.1086/448759. JSTOR 1343930.
+Carter, Baker.  2006. The Role of the History of Mathematics in Middle School. Presentation at East Tennessee University, August 28.
+Gazale, Midhat, J. 2000. Number. Princeton: Princeton University Press.
+Newman, J, R. 1956. The World of Mathematics. New York City: Simon & Schuster.
+Peterson, Ivars. 1996. Old and New Arithmetic. Mathematical Association of America. http://www.maa.org/mathland/mathland_8_5.html (accessed October 11, 2006).
+Swetz, Frank, J. 1987. Capitalism and Arithmetic. La Salle: Open Court.
+
+
+== External links ==
+Full text of the Treviso Arithmetic
+Treviso Arithmetic at Columbia University

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+---
+title: "Trigonometric Series"
+chunk: 1/1
+source: "https://en.wikipedia.org/wiki/Trigonometric_Series"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T08:47:10.228449+00:00"
+instance: "kb-cron"
+---
+
+Antoni Zygmund wrote a classic two-volume set of books entitled Trigonometric Series, which discusses many different aspects of trigonometric series. The first edition was a single volume, published in 1935 (under the slightly different title Trigonometrical Series). The second edition of 1959 was greatly expanded, taking up two volumes, though it was later reprinted as a single volume paperback. The third edition of 2002 is similar to the second edition, with the addition of a preface by Robert A. Fefferman on more recent developments, in particular Carleson's theorem about almost everywhere pointwise convergence for square-integrable functions.
+
+
+== Publication history ==
+Zygmund, Antoni (1935). Trigonometrical series. Monogr. Mat. Vol. 5. Warszawa, Lwow: Subwencji Fundusz Kultury Narodowej. Zbl 0011.01703. At icm.edu.pl: original archived
+Zygmund, Antoni (1952). Trigonometrical series. New York: Chelsea Publishing Co. MR 0076084.
+Zygmund, Antoni (1955). Trigonometrical series. New York: Dover Publications. MR 0072976.
+Zygmund, Antoni (1959). Trigonometric series (2nd ed.). Cambridge University Press. MR 0107776. Volume I, Volume II.
+Zygmund, Antoni (1968). Trigonometric series. Second edition, reprinted with corrections and some additions. Vol. I and II (2nd ed.). Cambridge University Press. MR 0236587.
+Zygmund, Antoni (1977). Trigonometric series. Vol. I and II. Cambridge University Press. ISBN 978-0-521-07477-3. MR 0617944.
+Zygmund, Antoni (1988). Trigonometric series. Cambridge Mathematical Library. Vol. I and II. Cambridge University Press. ISBN 978-0-521-35885-9. MR 0933759.
+Zygmund, Antoni (2002). Fefferman, Robert A. (ed.). Trigonometric series. Cambridge Mathematical Library. Vol. I and II (3rd ed.). Cambridge University Press. ISBN 978-0-521-89053-3. MR 1963498.
+
+
+== Reviews ==
+Kahane, Jean-Pierre (2004), "Book review: Trigonometric series, Vols. I, II", Bulletin of the American Mathematical Society, 41 (3): 377–390, doi:10.1090/s0273-0979-04-01013-4, ISSN 0002-9904
+Salem, Raphael (1960), "Book Review: Trigonometric series", Bulletin of the American Mathematical Society, 66 (1): 6–12, doi:10.1090/S0002-9904-1960-10362-X, ISSN 0002-9904, MR 1566029
+Tamarkin, J. D. (1936), "Zygmund on Trigonometric Series", Bull. Amer. Math. Soc., 42 (1): 11–13, doi:10.1090/s0002-9904-1936-06235-x

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+title: "Two-Sided Matching"
+chunk: 1/1
+source: "https://en.wikipedia.org/wiki/Two-Sided_Matching"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T08:47:12.555607+00:00"
+instance: "kb-cron"
+---
+
+Two-Sided Matching: A Study in Game-Theoretic Modeling and Analysis is a book on matching markets in economics and game theory, particularly concentrating on the stable marriage problem. It was written by Alvin E. Roth and Marilda Sotomayor, with a preface by Robert Aumann, and published in 1990 by the Cambridge University Press as volume 18 in their series of Econometric Society monographs.  For this work, Roth and Sotomayor won the 1990 Frederick W. Lanchester Prize of the Institute for Operations Research and the Management Sciences.
+
+
+== Topics ==
+The book's introduction discusses the National Resident Matching Program and its use of stable marriage to assign medical students to hospital positions, and collects the problems in economics that the theory of matching markets is positioned to solve. Following this, it has three main sections.
+The first of these sections discusses the stable matching problem in its simplest form, in which two equal-sized groups of agents are to be matched one-to-one. It discusses the stability of solutions (the property that no pair of agents both prefer being matched to each other to their assigned matches), the lattice of stable matchings, the Gale–Shapley algorithm for finding stable solutions, and two key properties of this algorithm: that among all stable solutions it chooses the one that gives one group of agents their most-preferred stable match, and that it is an honest mechanism that incentivizes this group of agents to report their preferences truthfully.
+The second part of the book, which reviewer Ulrich Kamecke describes as its most central, concerns extensions of these results to the many-one matching needed for the National Resident Matching Program, and to the specific economic factors that made that program successful compared to comparable programs elsewhere, and that have impeded its success. One example concerns the two-body problem of married couples who would both prefer to be assigned to the same place, a constraint that adds considerable complexity to the matching problem and may prevent a stable solution from existing.
+The third part of the book concerns a different direction in which these ideas have been extended, to matching markets such as those for real estate in which indivisible goods are traded, with money used to transfer utility. It includes results in auction theory, linear and nonlinear utility functions, and the assignment game of Lloyd Shapley and Martin Shubik.
+
+
+== Audience and reception ==
+Two-Sided Matching presents known material on its topics, rather than introducing new research, but it is not a textbook. Instead, its aim is to provide a survey of this area aimed at economic practitioners, with arguments for the importance of its material based on its pragmatic significance rather than its mathematical beauty. Nevertheless, it also has material of interest to researchers, including an extensive bibliography and a concluding list of open problems for future research. Compared to other books on stable matching, including Marriages Stables by Donald Knuth and The Stable Marriage Problem: Structure and Algorithms by Dan Gusfield and Robert W. Irving, Two-Sided Matching focuses much more on the economic, application-specific, and strategic issues of stable matching, and much less on its algorithmic issues.
+Alan Kirman calls the book a "clear and elegant account" of its material, writing that its focus on practical applications makes it "of particular interest". Theodore Bergstrom writes that it will also "delight economists who want to think beautiful thoughts about important practical problems". Benny Moldovanu predicts that it "will become the standard source of reference" for its material. And Uriel Rothblum calls it the kind of once-a-generation book that can "change the way in which an entire field of study is viewed."
+
+
+== References ==

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+title: "Two New Sciences"
+chunk: 1/6
+source: "https://en.wikipedia.org/wiki/Two_New_Sciences"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T08:47:11.405455+00:00"
+instance: "kb-cron"
+---
+
+The Discourses and Mathematical Demonstrations Relating to Two New Sciences (Italian: Discorsi e dimostrazioni matematiche intorno a due nuove scienze pronounced [diˈskorsi e ddimostratˈtsjoːni mateˈmaːtike inˈtorno a dˈduːe ˈnwɔːve ʃˈʃɛntse]) published in 1638 was Galileo Galilei's final book and a scientific testament covering much of his work in physics over the preceding thirty years. It was written partly in Italian and partly in Latin.
+After his Dialogue Concerning the Two Chief World Systems, the Roman Inquisition had banned the publication of any of Galileo's works, including any he might write in the future. After the failure of his initial attempts to publish Two New Sciences in France, Germany, and Poland, it was published by Lodewijk Elzevir who was working in Leiden, South Holland, where the writ of the Inquisition was of less consequence (see House of Elzevir). Fra Fulgenzio Micanzio, the official theologian of the Republic of Venice, had initially offered to help Galileo publish the new work there, but he pointed out that publishing the Two New Sciences in Venice might cause Galileo unnecessary trouble; thus, the book was eventually published in Holland. Galileo did not seem to suffer any harm from the Inquisition for publishing this book since in January 1639, the book reached Rome's bookstores, and all available copies (about fifty) were quickly sold.
+Discourses was written in a style similar to Dialogues, in which three men (Simplicio, Sagredo, and Salviati) discuss and debate the various questions Galileo is seeking to answer. There is a notable change in the men, however; Simplicio, in particular, is no longer quite as simple-minded, stubborn and Aristotelian as his name implies. His arguments are representative of Galileo's own early beliefs, as Sagredo represents his middle period, and Salviati proposes Galileo's newest models.
+
+== Introduction ==
+The book is divided into four days, each addressing different areas of physics. Galileo dedicates Two New Sciences to Lord Count of Noailles.
+
+In the First Day, Galileo addressed topics that were discussed in Aristotle's  Physics and the Aristotelian school's Mechanics. It also provides an introduction to the discussion of both of the new sciences. The likeness between the topics discussed, specific questions that are hypothesized, and the style and sources throughout give Galileo the backbone to his First Day. The First Day introduces the speakers in the dialogue: Salviati, Sagredo, and Simplicio, the same as in the Dialogue. These three people are all Galileo just at different stages of his life, Simplicio the youngest and Salviati, Galileo's closest counterpart. The Second Day addresses the question of the strength of materials.
+The Third and Fourth days address the science of motion. The Third day discusses uniform and naturally accelerated motion, the issue of terminal velocity having been addressed in the First day. The Fourth day discusses projectile motion.
+In Two Sciences uniform motion is defined as a motion that, over any equal periods of time, covers equal distance. With the use of the quantifier ″any″, uniformity is introduced and expressed more explicitly than in previous definitions.
+Galileo had started an additional day on the force of percussion, but was not able to complete it to his own satisfaction. This section was referenced frequently in the first four days of discussion. It finally appeared only in the 1718 edition of Galilei's works. and it is often quoted as "Sixth Day" following the numbering in the 1898 edition. During this additional day Simplicio was replaced by Aproino, a former scholar and assistant of Galileo in Padua.
+
+== Summary ==
+Page numbers at the start of each paragraph are from the 1898 version, presently adopted as standard, and are found in the Crew and Drake translations.

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+title: "Two New Sciences"
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+category: "reference"
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+date_saved: "2026-05-05T08:47:11.405455+00:00"
+instance: "kb-cron"
+---
+
+=== Day one: Resistance of bodies to separation ===
+[50] Preliminary discussions.
+Sagredo (taken to be the younger Galileo) cannot understand why with machines one cannot argue from the small to the large: "I do not see that the properties of circles, triangles and...solid figures should change with their size". Salviati (speaking for Galileo) says the common opinion is wrong. Scale matters: a horse falling from a height of 3 or 4 cubits will break its bones whereas a cat falling from twice the height won't, nor will a grasshopper falling from a tower.
+[56] The first example is a hemp rope which is constructed from small fibres which bind together in the same way as a rope round a windlass to produce something much stronger. Then the vacuum that prevents two highly polished plates from separating even though they slide easily gives rise to an experiment to test whether water can be expanded or whether a vacuum is caused. In fact, Sagredo had observed that a suction pump could not lift more than 18 cubits of water and Salviati observes that the weight of this is the amount of resistance to a void. The discussion turns to the strength of a copper wire and whether there are minute void spaces inside the metal or whether there is some other explanation for its strength.
+[68] This leads into a discussion of infinites and the continuum and thence to the observation that the number of squares equal the number of roots. He comes eventually to the view that "if any number can be said to be infinite, it must be unity" and demonstrates a construction in which an infinite circle is approached and another to divide a line.
+[85] The difference between a fine dust and a liquid leads to a discussion of light and how the concentrated power of the sun can melt metals. He deduces that light has motion and describes an (unsuccessful) attempt to measure its speed.
+[106] Aristotle believed that bodies fell at a speed proportional to weight but Salviati doubts that Aristotle ever tested this. He also did not believe that motion in a void was possible, but since air is much less dense than water Salviati asserts that in a medium devoid of resistance (a vacuum) all bodies—a lock of wool or a bit of lead—would fall at the same speed. Large and small bodies fall at the same speed through air or water providing they are of the same density. Since ebony weighs a thousand times as much as air (which he had measured), it will fall only a very little more slowly than lead which weighs ten times as much. But shape also matters—even a piece of gold leaf (the densest of all substances [asserts Salviati]) floats through the air and a bladder filled with air falls much more slowly than lead.
+[128] Measuring the speed of a fall is difficult because of the small time intervals involved and his first way round this used pendulums of the same length but with lead or cork weights. The period of oscillation was the same, even when the cork was swung more widely to compensate for the fact that it soon stopped.
+[139] This leads to a discussion of the vibration of strings and he suggests that not only the length of the string is important for pitch but also the tension and the weight of the string.
+
+=== Day two: Cause of cohesion ===
+[151] Salviati proves that a balance can be used not only with equal arms but with unequal arms with weights inversely proportional to the distances from the fulcrum. Following this he shows that the moment of a weight suspended by a beam supported at one end is proportional to the square of the length. The resistance to fracture of beams of various sizes and thicknesses is demonstrated, supported at one or both ends.
+[169] He shows that animal bones have to be proportionately larger for larger animals and the length of a cylinder that will break under its own weight. He proves that the best place to break a stick placed upon the knee is the middle and shows how far along a beam that a larger weight can be placed without breaking it.
+[178] He proves that the optimum shape for a beam supported at one end and bearing a load at the other is parabolic. He also shows that hollow cylinders are stronger than solid ones of the same weight.

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+title: "Two New Sciences"
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+category: "reference"
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+date_saved: "2026-05-05T08:47:11.405455+00:00"
+instance: "kb-cron"
+---
+
+=== Day three: Naturally accelerated motion ===
+[191] He first defines uniform (steady) motion and shows the relationship between speed, time and distance. He then defines uniformly accelerated motion where the speed increases by the same amount in increments of time. Falling bodies start very slowly and he sets out to show that their velocity increases in simple proportionality to time, not to distance which he shows is impossible.
+[208] He shows that the distance travelled in naturally accelerated motion is proportional to the square of the time. He describes an experiment in which a steel ball was rolled down a groove in a piece of wooden moulding 12 cubits long (about 5.5m) with one end raised by one or two cubits. This was repeated, measuring times by accurately weighing the amount of water that came out of a thin pipe in a jet from the bottom of a large jug of water. By this means he was able to verify the uniformly accelerated motion. He then shows that whatever the inclination of the plane, the square of the time taken to fall a given vertical height is proportional to the inclined distance.
+[221] He next considers descent along the chords of a circle, showing that the time is the same as that falling from the vertex, and various other combinations of planes. He gives an erroneous solution to the brachistochrone problem, claiming to prove that the arc of the circle is the fastest descent. 16 problems with solutions are given.
+
+=== Day four: The motion of projectiles ===
+
+[268] The motion of projectiles consists of a combination of uniform horizontal motion and a naturally accelerated vertical motion which produces a parabolic curve. Two motions at right angles can be calculated using the sum of the squares. He shows in detail how to construct the parabolas in various situations and gives tables for altitude and range depending on the projected angle.
+[274] Air resistance shows itself in two ways: by affecting less dense bodies more and by offering greater resistance to faster bodies. A lead ball will fall slightly faster than an oak ball, but the difference with a stone ball is negligible. However the speed does not go on increasing indefinitely but reaches a maximum. Though at small speeds the effect of air resistance is small, it is greater when considering, say, a ball fired from a cannon.
+[292] The effect of a projectile hitting a target is reduced if the target is free to move. The velocity of a moving body can overcome that of a larger body if its speed is proportionately greater than the resistance.
+[310] A cord or chain stretched out is never level but also approximates to a parabola. (But see also catenary.)
+
+=== Additional day: The force of percussion ===
+[323] What is the weight of water falling from a bucket hanging on a balance arm onto another bucket suspended to the same arm?
+[325] Piling of wooden poles for foundations; hammers and the force of percussion.
+[336] Speed of fall along inclined planes; again on the principle of inertia.
+
+== Methodology ==
+Many contemporary scientists, such as Gassendi, dispute Galileo's methodology for conceptualizing his law of falling bodies. Two of the main arguments are that his epistemology followed the example of Platonist thought or hypothetico-deductivist. It has now been considered to be ex suppositione, or knowing the how and why effects from past events in order to determine the requirements for the production of similar effects in the future. Galilean methodology mirrored that of Aristotelian and Archimedean epistemology. Following a letter from Cardinal Bellarmine in 1615 Galileo distinguished his arguments and Copernicus' as natural suppositions as opposed to the "fictive" that are "introduced only for the sake of astronomical computations," such as Ptolemy's hypothesis on eccentrics and equants.
+Galileo's earlier writing considered Juvenilia, or youthful writings, are considered his first attempts at creating lecture notes for his course "hypothesis of the celestial motions" while teaching in at the University of Padua. These notes mirrored those of his contemporaries at the Collegio as well as contained an "Aristotelian context with decided Thomistic (St. Thomas Aquinas) overtones." These earlier papers are believed to have encouraged him to apply demonstrative proof in order to give validity to his discoveries on motion.
+Discovery of folio 116v gives evidence of experiments that had previously not been reported and therefore demonstrated Galileo's actual calculations for the Law of Falling Bodies.
+His methods of experimentation have been proved by the recording and recreation done by scientists such as James MacLachlan, Stillman Drake, R.H. Taylor and others in order to prove he did not merely imagine his ideas as historian Alexandre Koyré argued, but sought to prove them mathematically.
+Galileo believed that knowledge could be acquired through reason, and reinforced through observation and experimentation. Thus, it can be argued that Galileo was a rationalist, and also that he was an empiricist.
+
+== The two new sciences ==
+The two sciences mentioned in the title are the strength of materials and the motion of objects (the forebears of modern material engineering and kinematics). In the title of the book "mechanics" and "motion" are separate, since at Galileo's time "mechanics" meant only statics and strength of materials.
+
+=== The science of materials ===
+The discussion begins with a demonstration of the reasons that a large structure proportioned in exactly the same way as a smaller one must necessarily be weaker known as the square–cube law. Later in the discussion this principle is applied to the thickness required of the bones of a large animal, possibly the first quantitative result in biology, anticipating J. B. S. Haldane's work On Being the Right Size, and other essays, edited by John Maynard Smith.

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+title: "Two New Sciences"
+chunk: 4/6
+source: "https://en.wikipedia.org/wiki/Two_New_Sciences"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T08:47:11.405455+00:00"
+instance: "kb-cron"
+---
+
+=== The motion of objects ===
+Galileo expresses clearly for the first time the constant acceleration of a falling body which he was able to measure accurately by slowing it down using an inclined plane.
+In Two New Sciences, Galileo (Salviati speaks for him) used a wood molding, "12 cubits long, half a cubit wide and three finger-breadths thick" as a ramp with a straight, smooth, polished groove to study rolling balls ("a hard, smooth and very round bronze ball"). He lined the groove with "parchment, also smooth and polished as possible". He inclined the ramp at various angles, effectively slowing down the acceleration enough so that he could measure the elapsed time. He would let the ball roll a known distance down the ramp, and use a water clock to measure the time taken to move the known distance. This clock was
+
+a large vessel of water placed in an elevated position; to the bottom of this vessel was soldered a pipe of small diameter giving a thin jet of water, which we collected in a small glass during the time of each descent, whether for the whole length of the channel or for a part of its length. The water collected was weighed, and after each descent on a very accurate balance, the differences and ratios of these weights gave him the differences and ratios of the times. This was done with such accuracy that although the operation was repeated many, many times, there was no appreciable discrepancy in the results.
+
+==== The law of falling bodies ====
+While Aristotle had observed that heavier objects fall more quickly than lighter ones, in Two New Sciences Galileo postulated that this was due not to inherently stronger forces acting on the heavier objects, but to the countervailing forces of air resistance and friction. To compensate, he conducted experiments using a shallowly inclined ramp, smoothed so as to eliminate as much friction as possible, on which he rolled down balls of different weights. In this manner, he was able to provide empirical evidence that matter accelerates vertically downward at a constant rate, regardless of mass, due to the effects of gravity.
+The unreported experiment found in folio 116V tested the constant rate of acceleration in falling bodies due to gravity. This experiment consisted of dropping a ball from specified heights onto a deflector in order to transfer its motion from vertical to horizontal. The data from the inclined plane experiments were used to calculate the expected horizontal motion. However, discrepancies were found in the results of the experiment: the observed horizontal distances disagreed with the calculated distances expected for a constant rate of acceleration. Galileo attributed the discrepancies to air resistance in the unreported experiment, and friction in the inclined plane experiment. These discrepancies forced Galileo to assert that the postulate held only under "ideal conditions", i.e., in the absence of friction and/or air resistance.
+
+==== Bodies in motion ====
+Aristotelian physics argued that the Earth must not move as humans are unable to perceive the effects of this motion. A popular justification of this is the experiment of an archer shooting an arrow straight up into the air. If the Earth were moving, Aristotle argued, the arrow should fall in a different location than the launch point. Galileo refuted this argument in Dialogues Concerning the Two Chief World Systems. He provided the example of sailors aboard a boat at sea. The boat is obviously in motion, but the sailors are unable to perceive this motion. If a sailor were to drop a weighted object from the mast, this object would fall at the base of the mast rather than behind it (due to the ship's forward motion). This was the result of simultaneously the horizontal and vertical motion of the ship, sailors, and ball.
+
+==== Relativity of motions ====
+
+One of Galileo's experiments regarding falling bodies was that describing the relativity of motions, explaining that, under the right circumstances, "one motion may be superimposed upon another without effect upon either...". In Two New Sciences, Galileo made his case for this argument and it would become the basis of Newton's first law, the law of inertia.
+He poses the question of what happens to a ball dropped from the mast of a sailing ship or an arrow fired into the air on the deck. According to Aristotle's physics, the ball dropped should land at the stern of the ship as it falls straight down from the point of origin. Likewise the arrow when fired straight up should not land in the same spot if the ship is in motion. Galileo offers that there are two independent motions at play. One is the accelerating vertical motion caused by gravity while the other is the uniform horizontal motion caused by the moving ship which continues to influence the trajectory of the ball through the principle of inertia. The combination of these two motions results in a parabolic curve. The observer cannot identify this parabolic curve because the ball and observer share the horizontal movement imparted to them by the ship, meaning only the perpendicular, vertical motion is perceivable. Surprisingly, nobody had tested this theory with the simple experiments needed to gain a conclusive result until Pierre Gassendi published the results of said experiments in his letters entitled De Motu Impresso a Motore Translato (1642).
+
+== Infinity ==
+
+The book also contains a discussion of infinity. Galileo considers the example of numbers and their squares. He starts by noting that:
+
+It cannot be denied that there are as many [squares] as there are numbers because every number is a [square] root of some square:
+1 ↔ 1, 2 ↔ 4, 3 ↔ 9, 4 ↔ 16, and so on. 
+But he notes what appears to be a contradiction:

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+title: "Two New Sciences"
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+category: "reference"
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+date_saved: "2026-05-05T08:47:11.405455+00:00"
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+
+Yet at the outset we said there are many more numbers than squares, since the larger portion of them are not squares. Not only so, but the proportionate number of squares diminishes as we pass to larger numbers.
+(In modern language, there is a bijection between the set of positive integers N and the set of squares S, and S is a proper subset of N of density zero.) He resolves the contradiction by denying the possibility of comparing infinite numbers (and of comparing infinite and finite numbers):
+
+We can only infer that the totality of all numbers is infinite, that the number of squares is infinite, and that the number of their roots is infinite; neither is the number of squares less than the totality of all numbers, nor the latter greater than the former; and finally the attributes "equal", greater", and "less", are not applicable to infinite, but only to finite, quantities.
+This conclusion, that ascribing sizes to infinite sets should be ruled impossible, owing to the contradictory results obtained from these two ostensibly natural ways of attempting to do so, is a resolution to the problem that is consistent with, but less powerful than, the methods used in modern mathematics. The resolution to the problem may be generalized by considering Galileo's first definition of what it means for sets to have equal sizes, that is, the ability to put them in one-to-one correspondence. This turns out to yield a way of comparing the sizes of infinite sets that is free from contradictory results.
+These issues of infinity arise from problems of rolling circles. If two concentric circles of different radii roll along lines, then if the larger does not slip it appears clear that the smaller must slip. But in what way? Galileo attempts to clarify the matter by considering hexagons and then extending to rolling 100 000-gons, or n-gons, where he shows that a finite number of finite slips occur on the inner shape. Eventually, he concludes "the line traversed by the larger circle consists then of an infinite number of points which completely fill it; while that which is traced by the smaller circle consists of an infinite number of points which leave empty spaces and only partly fill the line," which would not be considered satisfactory now.
+
+== Reactions by commentators ==
+So great a contribution to physics was Two New Sciences that scholars have long maintained that the book anticipated Isaac Newton's laws of motion.
+Galileo ... is the father of modern physics—indeed of modern science
+Part of Two New Sciences was pure mathematics, as has been pointed out by the mathematician Alfréd Rényi, who said that it was the most significant book on mathematics in over 2000 years: Greek mathematics did not deal with motion, and so they never formulated mathematical laws of motion, even though Archimedes developed differentiation and integration. Two New Sciences opened the way to treating physics mathematically by treating motion mathematically for the first time. The Greek mathematician Zeno had designed his paradoxes to prove that motion could not be treated mathematically, and that any attempt to do so would lead to paradoxes. (He regarded this as an inevitable limitation of mathematics.) Aristotle reinforced this belief, saying that mathematic could only deal with abstract objects that were immutable. Galileo used the very methods of the Greeks to show that motion could indeed be treated mathematically. His idea was to separate out the paradoxes of the infinite from Zeno's paradoxes. He did this in several steps. First, he showed that the infinite sequence S of the squares 1, 4, 9, 16, ...contained as many elements as the sequence N of all positive integers (infinity); this is now referred to as Galileo's paradox. Then, using Greek style geometry, he showed a short line interval contained as many points as a longer interval. At some point he formulates the general principle that a smaller infinite set can have just as many points as a larger infinite set containing it. It was then clear that Zeno's paradoxes on motion resulted entirely from this paradoxical behavior of infinite quantities. Renyi said that, having removed this 2000-year-old stumbling block, Galileo went on to introduce his mathematical laws of motion, anticipating Newton.
+
+=== Gassendi's thoughts ===
+Pierre Gassendi defended Galileo's opinions in his book, De Motu Impresso a Motore Translato. In Howard Jones' article, Gassendi's Defence of Galileo: The Politics of Discretion, Jones says Gassendi displayed an understanding of Galileo's arguments and a clear grasp of their implications for the physical objections to the earth's motion.
+
+=== Koyré's thoughts ===
+The law of falling bodies was published by Galileo in 1638. But in the 20th century some authorities challenged the reality of Galileo's experiments. In particular, the French historian of science Alexandre Koyré bases his doubt on the fact that the experiments reported in Two New Sciences to determine the law of acceleration of falling bodies, required accurate measurements of time which appeared to be impossible with the technology of 1600. According to Koyré, the law was created deductively, and the experiments were merely illustrative thought experiments. In fact, Galileo's water clock (described above) provided sufficiently accurate measurements of time to confirm his conjectures.
+Later research, however, has validated the experiments. The experiments on falling bodies (actually rolling balls) were replicated using the methods described by Galileo, and the precision of the results was consistent with Galileo's report. Later research into Galileo's unpublished working papers from 1604 clearly showed the reality of the experiments and even indicated the particular results that led to the time-squared law.
+
+== See also ==
+De Motu Antiquiora (Galileo's earliest investigations of the motion of falling bodies)
+Le Mecaniche (Galileo's early refinements of his investigation of mechanics)
+
+== Notes ==

data/en.wikipedia.org/wiki/Two_New_Sciences-5.md

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+---
+title: "Two New Sciences"
+chunk: 6/6
+source: "https://en.wikipedia.org/wiki/Two_New_Sciences"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T08:47:11.405455+00:00"
+instance: "kb-cron"
+---
+
+== References ==
+Drake, Stillman, translator (1974). Two New Sciences, University of Wisconsin Press, 1974. ISBN 0-299-06404-2. A new translation including sections on centers of gravity and the force of percussion.
+Drake, Stillman (1978). Galileo At Work. Chicago: University of Chicago Press. ISBN 978-0-226-16226-3.
+Henry Crew and Alfonso de Salvio, translators, [1914] (1954). Dialogues Concerning Two New Sciences, Dover Publications Inc., New York, NY. ISBN 978-0-486-60099-4. The classic source in English, originally published by McMillan (1914).
+Jones, Howard, "Gassendi's Defense of Galileo: The Politics of Discretion", Medieval Renaissance Texts and Studies 58, 1988.
+Titles of the first editions taken from Leonard C. Bruno 1989, The Landmarks of Science: from the Collections of the Library of Congress. ISBN 0-8160-2137-6 Q125.B87
+Galileo Galilei, Discorsi e dimostrazioni matematiche intorno a due nuove scienze attinenti la meccanica e i movimenti locali (pag.664, of Claudio Pierini) publication Cierre, Simeoni Arti Grafiche, Verona, 2011, ISBN 9788895351049.
+Wallace, Willian, A. Galileo and Reasoning Ex Suppositione: The Methodology of the Two New Sciences. PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association, Vol. 1974, (1974), pp. 79–104
+Salvia, Stafano (2014). "'Galileo's Machine': Late Notes on Free Fall, Projectile Motion, and the Force of Percussion (ca. 1638–1639)". Physics in Perspective. 16 (4): 440–460. Bibcode:2014PhP....16..440S. doi:10.1007/s00016-014-0149-1. S2CID 122967350.
+De Angelis, Alessandro (2021). Discorsi e Dimostrazioni Matematiche di Galileo Galilei per il Lettore Moderno (in Italian). Torino: Codice. ISBN 978-8875789305.
+De Angelis, Alessandro (2021). Galilei's Two New Sciences for Modern Readers. Heidelberg: Springer Nature. ISBN 978-3030719524. With prefaces by Ugo Amaldi and Telmo Pievani.
+
+== External links ==
+
+(in Italian) Italian text with figures
+English translation by Crew and de Salvio, with original figures

data/en.wikipedia.org/wiki/Urania_Propitia-0.md

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+---
+title: "Urania Propitia"
+chunk: 1/1
+source: "https://en.wikipedia.org/wiki/Urania_Propitia"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T08:47:13.709479+00:00"
+instance: "kb-cron"
+---
+
+Urania Propitia (lit. 'kind/beneficent Urania') is a book of astronomical tables written by the Silesian astronomer Maria Cunitz and published in 1650. As Maria Cunitz was the daughter of both a physician and mathematician, it was her ability to grasp complex mathematics quickly and transcribe her findings as a polyglot that allowed her to do what few women had done before her.
+The work served as a simplification of the Rudolphine Tables (1627) by Johannes Kepler, with Cunitz attempting to both increase the accuracy and to simplify the calculations from the original work. While she corrected a number of Kepler's computational errors, her equations also include inaccuracies. Cunitz's work is credited with making astrological tables accessible outside of the era's universities. Cunitz's cosmology combined elements from the cosmologies of both Kepler and Tycho Brahe. Like Brahe, she thought that the Sun and the Moon orbit around the planet Earth, while the rest of the planets in the Solar System orbit around the Sun. In her work, the physics within the cosmos involve ellipticals and aphelions.
+
+
+== Introduction ==
+Urania Propitia was a simplification of the Rudolphine Tables written by Johannes Kepler in 1627. Kepler's dedication to Emperor Ferdinand II which was originally dedicated to Rudolf II was filled with complex and tedious logarithms. Cunitz found many errors within the Rudolphine Tables. The simplifications to these tables were published as the Urania Propitia. In Urania Propitia, Cunitz removed logarithms from Kepler's work, which increased the accuracy and simplified the calculations from the Rudolphine Tables. Cunitz omitted some coefficients from her equations, leading to inaccuracies within her work. Astronomical tables of the time all contained computational errors, so despite these errors, Urania Propitia is seen as more accurate than Kepler’s work. The tables are mostly astrological, but the instructions are completely astronomical.
+Urania Propitia was published in Latin and German. The German publication is credited as a source that led to establishing German as a scientific language. The publishing of Urania Propitia is credited with making astrological tables more accessible outside of universities.
+Beyond the instructions, Maria Cunitz's book is split into three parts.
+
+
+=== Part 1: Tables for spherical astronomy ===
+The first part is the mathematical starting point. These include "sexagesimal sines, solutions of small right triangles in minutes and seconds, and tables for spherical astronomy for degrees of the ecliptic of: declination, right ascension, oblique ascension for latitudes 0 degrees to 72 degrees at 2 degree intervals..."
+
+
+=== Part 2: Tables of average motions ===
+It is the second part that the heart of Maria Cunitz's simplification is brought forward. Using the geometry and spherical astronomy from part one, Cunitz brings the rotational motions of the planets and moons into light using various mathematical formulas. One of the formulas from the Rudolphine Tables,
+
+  
+    
+      
+        M
+        =
+        E
+        −
+        e
+        sin
+        ⁡
+        E
+      
+    
+    {\displaystyle M=E-e\sin E}
+  
+
+where e, M and E denote the orbital eccentricity, the mean anomaly and the eccentric anomaly. This equation is known as "Kepler's equation" which normally has no "geometrical or algebraic solution for E." However, when M is given it becomes more possible to but find "E from M to any degree of precision by iteration or interpolation." The major accomplishment Cunitz brought was the ability to compute 
+  
+    
+      
+        υ
+      
+    
+    {\displaystyle \upsilon }
+  
+ (the true anomaly) from M without the necessity to use "E as a coefficient of interpolation". Thus, Cunitz was able to simplify the Rudolphine Tables and determine the position of a planet in its orbit as a function of time.
+
+
+=== Part 3: Tables for computation of eclipses ===
+These tables were used for both the location of eclipses and the time of eclipses. This includes the use of the "golden astronomical number", the parallax of the moon and sun in a variety in longitude, latitude, altitude, etc..., and a catalog of other fixed stars in the universe.
+
+
+== Cosmology ==
+Cunitz's cosmology has variations of both Tycho Brahe and Johannes Kepler. While the basic structure of her cosmology is like Tycho's with the Sun and Moon orbiting around the Earth while the rest of the planets orbit around the Sun, the physics within the cosmos involves ellipticals and "aphelions."
+
+
+== Historical significance ==
+Beyond the rewards that came from a simplification of the Rudolphine Tables, a scientific advance written by a woman in the seventeenth century was an accomplishment in itself. It was described by Noel Swerdlow  as "the earliest surviving scientific work by a woman on the highest technical level of its age." It was common for male scientists before Maria Cunitz to attribute their discoveries to muses. For Urania Propitia, Urania in Greek mythology was the muse of astronomy, and propitia is "favoring" or "beneficent" in Latin. This suggests that Maria Cunitz both saw Urania as her muse while also making strides for women as scientists, because she could be so easily compared to the ancient Greek astronomer.
+Urania propitia was privately published and as of 2016 there are nine physical copies in the world along with multiple online copies. Physical copies can be found in the Library of the Astronomical Observatory of Paris, Library of the University of Florida, in the exhibit of Galileo and Kepler at the University Libraries of Norman, Oklahoma, and Bloomington Lilly Library of Indiana University. Prior to June 10, 2004 the first edition of Urania propitia was located at the Library of the Earls of Macclesfield in Shirburn Castle: Part 2 Science A-C section. The book was sold at the Sotheby's auction house for $19,827 USD.
+
+
+== References ==
+
+
+== External links ==
+Digital scan of Urania Propitia - Wroclaw University Library

data/en.wikipedia.org/wiki/Vectors_in_Three-dimensional_Space-0.md

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+---
+title: "Vectors in Three-dimensional Space"
+chunk: 1/1
+source: "https://en.wikipedia.org/wiki/Vectors_in_Three-dimensional_Space"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T08:47:14.876227+00:00"
+instance: "kb-cron"
+---
+
+Vectors in Three-dimensional Space (1978) is a book concerned with physical quantities defined in "ordinary" 3-space.  It was written by J. S. R. Chisholm, an English mathematical physicist, and published by Cambridge University Press.  According to the author, such physical quantities are studied in Newtonian mechanics, fluid mechanics, theories of elasticity and plasticity, non-relativistic quantum mechanics, and many parts of solid state physics.  The author further states that "the vector concept developed in two different ways: in a wide variety of physical applications, vector notation and techniques became, by the middle of this century, almost universal; on the other hand, pure mathematicians reduced vector algebra to an axiomatic system, and introduced wide generalisations of the concept of a three-dimensional 'vector space'."  Chisholm explains that since these two developments proceeded largely independently, there is a need to show how one can be applied to the other.
+
+
+== Summary ==
+Vectors in Three-Dimensional Space has six chapters, each divided into five or more subsections. The first on linear spaces and displacements including these sections: Introduction, Scalar multiplication of vectors, Addition and subtraction of vectors, Displacements in Euclidean space, Geometrical applications.  The second on Scalar products and components including these sections: Scalar products, Linear dependence and dimension, Components of a vector, Geometrical applications, Coordinate systems.  The third on Other products of vectors.  The last three chapters round out Chisholm's integration of these two largely independent developments.
+
+
+== References ==
+
+
+=== Footnotes ===
+
+
+=== Bibliography ===
+Vectors in Three-dimensional Space has been cited by the 2002 Encyclopedia Americana article on Vector Analysis
+Chisholm, J. S. R. Vectors in Three-dimensional Space, Cambridge University Press, 1978, ISBN 0-521-29289-1

data/en.wikipedia.org/wiki/Vorlesungen_über_Zahlentheorie-0.md

@@ -0,0 +1,74 @@
+---
+title: "Vorlesungen über Zahlentheorie"
+chunk: 1/1
+source: "https://en.wikipedia.org/wiki/Vorlesungen_über_Zahlentheorie"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T08:47:16.045939+00:00"
+instance: "kb-cron"
+---
+
+Vorlesungen über Zahlentheorie (German pronunciation: [ˈfoːɐ̯ˌleːzʊŋən ˈyːbɐ ˈtsaːlənteoˌʁiː]; German for Lectures on Number Theory) is the name of several different textbooks of number theory. The best known was written by Peter Gustav Lejeune Dirichlet and Richard Dedekind, and published in 1863. Others were written by Leopold Kronecker, Edmund Landau, and Helmut Hasse. They all cover elementary number theory, Dirichlet's theorem, quadratic fields and forms, and sometimes more advanced topics.
+
+
+== Dirichlet and Dedekind's book ==
+Based on Dirichlet's number theory course at the University of Göttingen, the Vorlesungen were edited by Dedekind and published after Lejeune Dirichlet's death. Dedekind added several appendices to the Vorlesungen, in which he collected further results of Lejeune Dirichlet's and also developed his own original mathematical ideas.
+
+
+=== Scope ===
+The Vorlesungen cover topics in elementary number theory, algebraic number theory and analytic number theory, including modular arithmetic, quadratic congruences, quadratic reciprocity and binary quadratic forms.
+
+
+=== Contents ===
+The contents of Professor John Stillwell's 1999 translation of the Vorlesungen are as follows
+
+Chapter 1. On the divisibility of numbers
+Chapter 2. On the congruence of numbers
+Chapter 3. On quadratic residues
+Chapter 4. On quadratic forms
+Chapter 5. Determination of the class number of binary quadratic forms
+Supplement I. Some theorems from Gauss's theory of circle division
+Supplement II. On the limiting value of an infinite series
+Supplement III. A geometric theorem
+Supplement IV. Genera of quadratic forms
+Supplement V. Power residues for composite moduli
+Supplement VI. Primes in arithmetic progressions
+Supplement VII. Some theorems from the theory of circle division
+Supplement VIII. On the Pell equation
+Supplement IX. Convergence and continuity of some infinite series
+This translation does not include Dedekind's Supplements X and XI in which he begins to develop the theory of ideals.
+The German titles of supplements X and XI are:
+
+Supplement X: Über die Composition der binären quadratische Formen (On the composition of binary quadratic forms)
+Supplement XI: Über die Theorie der ganzen algebraischen Zahlen (On the theory of algebraic integers)
+Chapters 1 to 4 cover similar ground to Gauss' Disquisitiones Arithmeticae, and Dedekind added footnotes which specifically cross-reference the relevant sections of the Disquisitiones. These chapters can be thought of as a summary of existing knowledge, although Dirichlet simplifies Gauss's presentation, and introduces his own proofs in some places.
+Chapter 5 contains Dirichlet's derivation of the class number formula for real and imaginary quadratic fields. Although other mathematicians had conjectured similar formulae, Dirichlet gave the first rigorous proof.
+Supplement VI contains Dirichlet's proof that an arithmetic progression of the form a+nd where a and d are coprime contains an infinite number of primes.
+
+
+=== Importance ===
+The Vorlesungen can be seen as a watershed between the classical number theory of Fermat, Jacobi and Gauss, and the modern number theory of Dedekind, Riemann and Hilbert. Dirichlet does not explicitly recognise the concept of the group that is central to modern algebra, but many of his proofs show an implicit understanding of group theory.
+The Vorlesungen contains two key results in number theory which were first proved by Dirichlet. The first of these is the class number formulae for binary quadratic forms. The second is a proof that arithmetic progressions contains an infinite number of primes (known as Dirichlet's theorem); this proof introduces Dirichlet L-series. These results are important milestones in the development of analytic number theory.
+
+
+== Kronecker's book ==
+Leopold Kronecker's book was first published in 1901 in 2 parts and reprinted by Springer in 1978. It covers elementary and algebraic number theory, including Dirichlet's theorem.
+
+
+== Landau's book ==
+Edmund Landau's book Vorlesungen über Zahlentheorie was first published as a 3-volume set in 1927. The first half of volume 1 was published as 
+Vorlesungen über Zahlentheorie. Aus der elementare Zahlentheorie in 1950, with an English translation in 1958 under the title Elementary number theory. In 1969 Chelsea republished the second half of volume 1 together with volumes 2 and 3 as a single volume. 
+Volume 1 on elementary and additive number theory includes the topics such as Dirichlet's theorem, Brun's sieve, binary quadratic forms, Goldbach's conjecture, Waring's problem, and the Hardy–Littlewood work on the singular series. Volume 2 covers topics in analytic number theory, such as estimates for the error in the prime number theorem, and topics in geometric number theory such as estimating numbers of lattice points. Volume 3 covers algebraic number theory, including ideal theory, quadratic number fields, and applications to Fermat's last theorem.  Many of the results described by Landau were state of the art at the time but have since been superseded by stronger results.
+
+
+== Hasse's book ==
+Helmut Hasse's book Vorlesungen über Zahlentheorie was published in 1950, and is different from and more elementary than his book Zahlentheorie. It covers elementary number theory, Dirichlet's theorem, and quadratic fields.
+
+
+== References ==
+
+P. G. Lejeune Dirichlet, R. Dedekind tr. John Stillwell: Lectures on Number Theory, American Mathematical Society, 1999 ISBN 0-8218-2017-6 The Göttinger Digitalisierungszentrum has a scanned copy of the original, 2nd edition text (in German) published in 1871 containing supplements I–X. Supplement XI can be found in volume three of Dedekind's complete works also at the Göttinger Digitalisierungszentrum. The 4th edition from 1894 which contains all of the supplements including Dedekind's XI is available at Internet Archive.
+Hasse, Helmut (1950), Vorlesungen über Zahlentheorie, Die Grundlehren der mathematischen Wissenschaften, vol. LIX, Berlin-Göttingen-Heidelberg: Springer-Verlag, ISBN 978-3-642-88679-9, MR 0051844 {{citation}}: ISBN / Date incompatibility (help)
+Kronecker, Leopold (1978) [1901], Vorlesungen über Zahlentheorie, Berlin-New York: Springer-Verlag, ISBN 3-540-08277-8, MR 0529431
+Landau, Edmund (1958) [1927], Elementary number theory., New York, N.Y.: Chelsea Publishing Co., MR 0092794
+Landau, Edmund (1969) [1927], Vorlesungen über Zahlentheorie. Erster Band, zweiter Teil; zweiter Band; dritter Band., New York: Chelsea Publishing Co., MR 0250844

data/en.wikipedia.org/wiki/Where_Mathematics_Comes_From-0.md

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+---
+title: "Where Mathematics Comes From"
+chunk: 1/3
+source: "https://en.wikipedia.org/wiki/Where_Mathematics_Comes_From"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T08:47:17.193195+00:00"
+instance: "kb-cron"
+---
+
+Where Mathematics Comes From: How the Embodied Mind Brings Mathematics into Being (hereinafter WMCF) is a book by George Lakoff, a cognitive linguist, and Rafael E. Núñez, a psychologist. Published in 2000, WMCF seeks to found a cognitive science of mathematics, a theory of embodied mathematics based on conceptual metaphor.
+
+== WMCF definition of mathematics ==
+Mathematics makes up that part of the human conceptual system that is special in the following way:
+
+It is precise, consistent, stable across time and human communities, symbolizable, calculable, generalizable, universally available, consistent within each of its subject matters, and effective as a general tool for description, explanation, and prediction in a vast number of everyday activities, [ranging from] sports, to building, business, technology, and science. - WMCF, pp. 50, 377
+Nikolay Lobachevsky said "There is no branch of mathematics, however abstract, which may not some day be applied to phenomena of the real world." A common type of conceptual blending process would seem to apply to the entire mathematical procession.
+
+== Human cognition and mathematics ==
+
+Lakoff and Núñez's avowed purpose is to begin laying the foundations for a truly scientific understanding of mathematics, one grounded in processes common to all human cognition. They find that four distinct but related processes metaphorically structure basic arithmetic: object collection, object construction, using a measuring stick, and moving along a path.
+WMCF builds on earlier books by Lakoff (1987) and Lakoff and Johnson (1980, 1999), which analyze such concepts of metaphor and image schemata from second-generation cognitive science.  Some of the concepts in these earlier books, such as the interesting technical ideas in Lakoff (1987), are absent from WMCF.
+Lakoff and Núñez hold that mathematics results from the human cognitive apparatus and must therefore be understood in cognitive terms. WMCF advocates (and includes some examples of) a cognitive idea analysis of mathematics which analyzes mathematical ideas in terms of the human experiences, metaphors, generalizations, and other cognitive mechanisms giving rise to them. A standard mathematical education does not develop such idea analysis techniques because it does not pursue considerations of A) what structures of the mind allow it to do mathematics or B) the philosophy of mathematics.
+Lakoff and Núñez start by reviewing the psychological literature, concluding that human beings appear to have an innate ability, called subitizing, to count, add, and subtract up to about 4 or 5. They document this conclusion by reviewing the literature, published in recent decades, describing experiments with infant subjects. For example, infants quickly become excited or curious when presented with "impossible" situations, such as having three toys appear when only two were initially present.
+The authors argue that mathematics goes far beyond this very elementary level due to a large number of metaphorical constructions. For example, the Pythagorean position that all is number, and the associated crisis of confidence that came about with the discovery of the irrationality of the square root of two, arises solely from a metaphorical relation between the length of the diagonal of a square, and the possible numbers of objects.
+Much of WMCF deals with the important concepts of infinity and of limit processes, seeking to explain how finite humans living in a finite world could ultimately conceive of the actual infinite. Thus much of WMCF is, in effect, a study of the epistemological foundations of the calculus. Lakoff and Núñez conclude that while the potential infinite is not metaphorical, the actual infinite is. Moreover, they deem all manifestations of actual infinity to be instances of what they call the "Basic Metaphor of Infinity", as represented by the ever-increasing sequence 1, 2, 3, ...
+WMCF emphatically rejects the Platonistic philosophy of mathematics. They emphasize that all we know and can ever know is human mathematics, the mathematics arising from the human intellect. The question of whether there is a "transcendent" mathematics independent of human thought is a meaningless question, like asking if colors are transcendent of human thought—colors are only varying wavelengths of light, it is our interpretation of physical stimuli that make them colors.
+WMCF (p. 81) likewise criticizes the emphasis mathematicians place on the concept of closure. Lakoff and Núñez argue that the expectation of closure is an artifact of the human mind's ability to relate fundamentally different concepts via metaphor.
+WMCF concerns itself mainly with proposing and establishing an alternative view of mathematics, one grounding the field in the realities of human biology and experience. It is not a work of technical mathematics or philosophy. Lakoff and Núñez are not the first to argue that conventional approaches to the philosophy of mathematics are flawed. For example, they do not seem all that familiar with the content of Davis and Hersh (1981), even though the book warmly acknowledges Hersh's support.
+Lakoff and Núñez cite Saunders Mac Lane (the inventor, with Samuel Eilenberg, of category theory) in support of their position. Mathematics, Form and Function (1986), an overview of mathematics intended for philosophers, proposes that mathematical concepts are ultimately grounded in ordinary human activities, mostly interactions with the physical world.
+
+== Examples of mathematical metaphors ==
+Conceptual metaphors described in WMCF, in addition to the Basic Metaphor of Infinity, include:
+
+Arithmetic is motion along a path, object collection/construction;
+Change is motion;
+Sets are containers, objects;
+Continuity is gapless;
+Mathematical systems have an "essence," namely their axiomatic algebraic structure;
+Functions are sets of ordered pairs, curves in the Cartesian plane;
+Geometric figures are objects in space;
+Logical independence is geometric orthogonality;
+Numbers are sets, object collections, physical segments, points on a line;
+Recurrence is circular.
+Mathematical reasoning requires variables ranging over some universe of discourse, so that we can reason about generalities rather than merely about particulars. WMCF argues that reasoning with such variables implicitly relies on what it terms the Fundamental Metonymy of Algebra.

data/en.wikipedia.org/wiki/Where_Mathematics_Comes_From-1.md

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+---
+title: "Where Mathematics Comes From"
+chunk: 2/3
+source: "https://en.wikipedia.org/wiki/Where_Mathematics_Comes_From"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T08:47:17.193195+00:00"
+instance: "kb-cron"
+---
+
+== Example of metaphorical ambiguity ==
+WMCF (p. 151) includes the following example of what the authors term "metaphorical ambiguity." Take the set 
+  
+    
+      
+        A
+        =
+        {
+        {
+        ∅
+        }
+        ,
+        {
+        ∅
+        ,
+        {
+        ∅
+        }
+        }
+        }
+        .
+      
+    
+    {\displaystyle A=\{\{\emptyset \},\{\emptyset ,\{\emptyset \}\}\}.}
+  
+ Then recall two bits of standard terminology from elementary set theory:
+
+The recursive construction of the ordinal natural numbers, whereby 0 is 
+  
+    
+      
+        ∅
+      
+    
+    {\displaystyle \emptyset }
+  
+, and 
+  
+    
+      
+        n
+        +
+        1
+      
+    
+    {\displaystyle n+1}
+  
+ is 
+  
+    
+      
+        n
+        ∪
+        {
+        n
+        }
+        .
+      
+    
+    {\displaystyle n\cup \{n\}.}
+  
+
+The ordered pair (a,b), defined as 
+  
+    
+      
+        {
+        {
+        a
+        }
+        ,
+        {
+        a
+        ,
+        b
+        }
+        }
+        .
+      
+    
+    {\displaystyle \{\{a\},\{a,b\}\}.}
+  
+
+By (1), A is the set {1,2}. But (1) and (2) together say that A is also the ordered pair (0,1). Both statements cannot be correct; the ordered pair (0,1) and the unordered pair {1,2} are fully distinct concepts. Lakoff and Johnson (1999) term this situation "metaphorically ambiguous." This simple example calls into question any Platonistic foundations for mathematics.
+While (1) and (2) above are admittedly canonical, especially within the consensus set theory known as the Zermelo–Fraenkel axiomatization, WMCF does not let on that they are but one of several definitions that have been proposed since the dawning of set theory. For example, Frege, Principia Mathematica, and New Foundations (a body of axiomatic set theory begun by Quine in 1937) define cardinals and ordinals as equivalence classes under the relations of equinumerosity and similarity, so that this conundrum does not arise. In Quinian set theory, A is simply an instance of the number 2. For technical reasons, defining the ordered pair as in (2) above is awkward in Quinian set theory. Two solutions have been proposed:
+
+A variant set-theoretic definition of the ordered pair more complicated than the usual one;
+Taking ordered pairs as primitive.
+
+== The Romance of Mathematics ==
+The "Romance of Mathematics" is WMCF's light-hearted term for a perennial philosophical viewpoint about mathematics which the authors describe and then dismiss as an intellectual myth:
+
+Mathematics is transcendent, namely it exists independently of human beings, and structures our actual physical universe and any possible universe. Mathematics is the language of nature, and is the primary conceptual structure we would have in common with extraterrestrial aliens, if any such there be.
+Mathematical proof is the gateway to a realm of transcendent truth.
+Reasoning is logic, and logic is essentially mathematical. Hence mathematics structures all possible reasoning.
+Because mathematics exists independently of human beings, and reasoning is essentially mathematical, reason itself is disembodied. Therefore, artificial intelligence is possible, at least in principle.
+It is very much an open question whether WMCF will eventually prove to be the start of a new school in the philosophy of mathematics. Hence the main value of WMCF so far may be a critical one: its critique of Platonism and romanticism in mathematics.
+
+== Critical response ==
+
+Many working mathematicians resist the approach and conclusions of Lakoff and Núñez. Reviews of WMCF by mathematicians in professional journals, while often respectful of its focus on conceptual strategies and metaphors as paths for understanding mathematics, have taken exception to some of the WMCF's philosophical arguments on the grounds that mathematical statements have lasting 'objective' meanings. For example, Fermat's Last Theorem means exactly what it meant when Fermat initially proposed it in 1664. Other reviewers have pointed out that multiple conceptual strategies can be employed in connection with the same mathematically defined term, often by the same person (a point that is compatible with the view that we routinely understand the 'same' concept with different metaphors). The metaphor and the conceptual strategy are not the same as the formal definition which mathematicians employ. However, WMCF points out that formal definitions are built using words and symbols that have meaning only in terms of human experience.
+Critiques of WMCF include the humorous:
+
+It's difficult for me to conceive of a metaphor for a real number raised to a complex power, but if there is one, I'd sure like to see it. — Joseph Auslander
+and the physically informed:

data/en.wikipedia.org/wiki/Where_Mathematics_Comes_From-2.md

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+---
+title: "Where Mathematics Comes From"
+chunk: 3/3
+source: "https://en.wikipedia.org/wiki/Where_Mathematics_Comes_From"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T08:47:17.193195+00:00"
+instance: "kb-cron"
+---
+
+But their analysis leaves at least a couple of questions insufficiently answered. For one thing, the authors ignore the fact that brains not only observe nature, but also are part of nature. Perhaps the math that brains invent takes the form it does because math had a hand in forming the brains in the first place (through the operation of natural laws in constraining the evolution of life). Furthermore, it's one thing to fit equations to aspects of reality that are already known. It's something else for that math to tell of phenomena never previously suspected. When Paul Dirac's equations describing electrons produced more than one solution, he surmised that nature must possess other particles, now known as antimatter. But scientists did not discover such particles until after Dirac's math told him they must exist. If math is a human invention, nature seems to know what was going to be invented.
+Lakoff and Núñez tend to dismiss the negative opinions mathematicians have expressed about WMCF, because their critics do not appreciate the insights of cognitive science. Lakoff and Núñez maintain that their argument can only be understood using the discoveries of recent decades about the way human brains process language and meaning. They argue that any arguments or criticisms that are not grounded in this understanding cannot address the content of the book.
+It has been pointed out that it is not at all clear that WMCF establishes that the claim "intelligent alien life would have mathematical ability" is a myth. To do this, it would be required to show that intelligence and mathematical ability are separable, and this has not been done. On Earth, intelligence and mathematical ability seem to go hand in hand in all life-forms, as pointed out by Keith Devlin among others. The authors of WMCF have not explained how this situation would (or even could) be different anywhere else.
+Lakoff and Núñez also appear not to appreciate the extent to which intuitionists and constructivists have presaged their attack on the Romance of (Platonic) Mathematics. Brouwer, the founder of the intuitionist/constructivist point of view, in his dissertation On the Foundation of Mathematics, argued that mathematics was a mental construction, a free creation of the mind and totally independent of logic and language. He goes on to criticize the formalists for building verbal structures that are studied without intuitive interpretation. Symbolic language should not be confused with mathematics; it reflects, but does not contain, mathematical reality.
+Educators have taken some interest in what WMCF suggests about how mathematics is learned, and why students find some elementary concepts more difficult than others.
+However, even from an educational perspective, WMCF is still problematic. From the conceptual metaphor theory's point of view, metaphors reside in a different realm, the abstract, from that of 'real world', the concrete. In other words, despite their claim of mathematics being human,  established mathematical knowledge — which is what we learn in school — is assumed to be and treated as abstract, completely detached from its physical origin. It cannot account for the way learners could access to such knowledge.
+WMCF is also criticized for its monist approach. First, it ignores the fact that the sensori-motor experience upon which our linguistic structure — thus, mathematics — is assumed to be based may vary across cultures and situations. Second, the mathematics WMCF is concerned with is "almost entirely... standard utterances in textbooks and curricula", which is the most-well established body of knowledge. It is negligent of the dynamic and diverse nature of the history of mathematics.
+WMCF's logo-centric approach is another target for critics. While it is predominantly interested in the association between language and mathematics, it does not account for how non-linguistic factors contribute to the emergence of mathematical ideas (e.g. See Radford, 2009; Rotman, 2008).
+
+== Summing up ==
+WMCF (pp. 378–79) concludes with some key points, a number of which follow. Mathematics arises from our bodies and brains, our everyday experiences, and the concerns of human societies and cultures. It is:
+
+The result of normal adult cognitive capacities, in particular the capacity for conceptual metaphor, and as such is a human universal. The ability to construct conceptual metaphors is neurologically based, and enables humans to reason about one domain using the language and concepts of another domain. Conceptual metaphor is both what enabled mathematics to grow out of everyday activities, and what enables mathematics to grow by a continual process of analogy and abstraction;
+Symbolic, thereby enormously facilitating precise calculation;
+Not transcendent, but the result of human evolution and culture, to which it owes its effectiveness. During experience of the world a connection to mathematical ideas is going on within the human mind;
+A system of human concepts making extraordinary use of the ordinary tools of human cognition;
+An open-ended creation of human beings, who remain responsible for maintaining and extending it;
+One of the greatest products of the collective human imagination, and a magnificent example of the beauty, richness, complexity, diversity, and importance of human ideas.
+The cognitive approach to formal systems, as described and implemented in WMCF, need not be confined to mathematics, but should also prove fruitful when applied to formal logic, and to formal philosophy such as Edward Zalta's theory of abstract objects. Lakoff and Johnson (1999) fruitfully employ the cognitive approach to rethink a good deal of the philosophy of mind, epistemology, metaphysics, and the history of ideas.
+
+== See also ==
+Abstract object
+Cognitive science
+Cognitive science of mathematics
+Conceptual metaphor
+Embodied philosophy
+Foundations of mathematics
+From Action to Mathematics per Mac Lane
+Metaphor
+Philosophy of mathematics
+The Unreasonable Effectiveness of Mathematics in the Natural Sciences
+
+== Footnotes ==
+
+== References ==
+Davis, Philip J., and Reuben Hersh, 1999 (1981). The Mathematical Experience. Mariner Books. First published by Houghton Mifflin.
+George Lakoff, 1987. Women, Fire and Dangerous Things. Univ. of Chicago Press.
+------ and Mark Johnson, 1999. Philosophy in the Flesh. Basic Books.
+George Lakoff and Rafael Núñez, 2000, Where Mathematics Comes From. Basic Books. ISBN 0-465-03770-4
+John Randolph Lucas, 2000. The Conceptual Roots of Mathematics. Routledge.
+Saunders Mac Lane, 1986. Mathematics: Form and Function. Springer Verlag.
+
+== External links ==
+WMCF web site. Archived 2011-07-18 at the Wayback Machine
+Reviews of WMCF.
+Joseph Auslander in American Scientist;
+Bonnie Gold, MAA Reviews 2001
+Lakoff's response to Gold's MAA review.

data/en.wikipedia.org/wiki/Word_Processing_in_Groups-0.md

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+---
+title: "Word Processing in Groups"
+chunk: 1/1
+source: "https://en.wikipedia.org/wiki/Word_Processing_in_Groups"
+category: "reference"
+tags: "science, encyclopedia"
+date_saved: "2026-05-05T08:47:19.528199+00:00"
+instance: "kb-cron"
+---
+
+Word Processing in Groups is a monograph in mathematics on the theory of automatic groups, a type of abstract algebra whose operations are defined by the behavior of finite automata. The book's authors are David B. A. Epstein, James W. Cannon, Derek F. Holt, Silvio V. F. Levy, Mike Paterson, and William Thurston. Widely circulated in preprint form, it formed the foundation of the study of automatic groups even before its 1992 publication by Jones and Bartlett Publishers (ISBN 0-86720-244-0).
+
+
+== Topics ==
+The book is divided into two parts, one on the basic theory of these structures and another on recent research, connections to geometry and topology, and other related topics.
+The first part has eight chapters. They cover automata theory and regular languages, and the closure properties of regular languages under logical combinations; the definition of automatic groups and biautomatic groups; examples from topology and "combable" structure in the Cayley graphs of automatic groups; abelian groups and the automaticity of Euclidean groups; the theory of determining whether a group is automatic, and its practical implementation by Epstein, Holt, and Sarah Rees; extensions to asynchronous automata; and nilpotent groups.
+The second part has four chapters, on braid groups, isoperimetric inequalities, geometric finiteness, and the fundamental groups of three-dimensional manifolds.
+
+
+== Audience and reception ==
+Although not primarily a textbook, the first part of the book could be used as the basis for a graduate course. More generally, reviewer Gilbert Baumslag recommends it "very strongly to everyone who is interested in either group theory or topology, as well as to computer scientists."
+Baumslag was an expert in a related but older area of study, groups defined by finite presentations, in which research was eventually stymied by the phenomenon that many basic problems are undecidable. Despite tracing the origins of automatic groups to early 20th-century mathematician Max Dehn, he writes that the book studies "a strikingly new class of groups" that "conjures up the fascinating possibility that some of the exploration of these automatic groups can be carried out by means of high-speed computers" and that the book is "very likely to have a great impact".
+Reviewer Daniel E. Cohen adds that two features of the book are unusual. First, that the mathematical results that it presents all have names, not just numbers, and second, that the cost of the book is low.
+In 2009, mathematician Mark V. Lawson wrote that despite its "odd title," the book made automata theory more respectable among mathematicians stating that it became part of "a quiet revolution in the diplomatic relations between mathematics and computer science".
+
+
+== References ==