tea_id stringlengths 16 53 | tradition stringclasses 5
values | tier stringclasses 3
values | text stringlengths 95 2.05k | provenance_chain stringlengths 181 510 | contamination_flags listlengths 0 2 |
|---|---|---|---|---|---|
greek-archimedes-measurement-circle | greek | A | [Greek — Κύκλου μέτρησις]
Πᾶς κύκλος ἴσος ἐστὶ τριγώνῳ ὀρθογωνίῳ, οὗ ἡ μὲν ἐκ τοῦ κέντρου ἴση μιᾷ τῶν περὶ τὴν ὀρθήν, ἡ δὲ περίμετρος τῇ βάσει. Ἐχέτω ὁ ΑΒΓ△ κύκλος τριγώνῳ τῷ Ε, ὡς ὑπόκειται· λέγω ὅτι ἴσος ἐστίν. Εἰ γὰρ δυνατόν, ἔστω μείζων ὁ κύκλος, καὶ ἐγγεγράφθω τὸ ΑΓ τετράγωνον, καὶ τετμήσθωσαν αἱ περιφέρειαι δίχα,... | Original Greek by Archimedes of Syracuse (c. 287–212 BCE). Text survived via Byzantine manuscript tradition (Codex C). Critical edition by Johan Heiberg (1880, Leipzig: Teubner). English translation by Sir Thomas L. Heath (1897, Cambridge University Press) — now public domain. Greek XML digitized by OpenGreekAndLatin/F... | [] |
greek-diophantus-arithmetica-ii-8 | greek | A | [Greek — Tannery 1893 edition]
Δεδομένον τετράγωνον ἀριθμὸν εἰς δύο τετραγώνους διελεῖν. Δέον δὴ τὸν ιϛ εἰς δύο τετραγώνους διελεῖν. Τεθήσεται ὁ πρῶτος δύναμις, ὁ δὲ δεύτερος ὁσάκις δὴ ἀριθμῶν ἐλλείπων μονάσι δύο τετράγωνος, τουτέστιν ἀριθμοὶ δύο ἐλλείποντες μονάσι δ᾿· καὶ αὐτὸν δεῖ ἴσον εἶναι τῷ λοιπῷ ἀπὸ τοῦ ιϛ τετρά... | Original Greek by Diophantus of Alexandria (fl. c. 250 CE). Critical Greek edition by Paul Tannery (1893–1895, Leipzig: Teubner) — public domain. English translation by Sir Thomas L. Heath (1910, Cambridge University Press) — public domain. No machine-readable Greek XML found in PerseusDL/First1KGreek as of 2026-05-08;... | [
"fermat-margin-note-link"
] |
greek-ptolemy-almagest-proem-chord-table | greek | A | [Greek — Ptolemy, Μαθηματικὴ Σύνταξις I, Proem]
Πάνυ καλῶς οἱ γνησίως φιλοσοφήσαντες, ὦ Σύρε, δοκοῦσί μοι κεχωρικέναι τὸ θεωρητικὸν τῆς φιλοσοφίας ἀπὸ τοῦ πρακτικοῦ. καὶ γὰρ εἰ συμβέβηκε καὶ τῷ πρακτικῷ πρότερον αὐτοῦ τούτου θεωρητικῷ τυγχάνειν, οὐδὲν ἧττον ἄν τις εὕροι μεγάλην οὖσαν ἐν αὐτοῖς διαφοράν, οὐ μόνον διὰ τὸ... | Original Greek by Claudius Ptolemy of Alexandria (c. 100–168 CE). Almagest composed c. 150 CE; dedicated to Syrus. Critical Greek edition by Johan Heiberg (1898–1903, Leipzig: Teubner). Standard English translation by G. J. Toomer (1984, Duckworth; repr. Springer 1998). Greek XML digitized by OpenGreekAndLatin/First1KG... | [] |
greek-euclid-elements-i-47 | greek | A | [Greek]
ἐν τοῖς ὀρθογωνίοις τριγώνοις τὸ ἀπὸ τῆς τὴν ὀρθὴν γωνίαν ὑποτεινούσης πλευρᾶς τετράγωνον ἴσον ἐστὶ τοῖς ἀπὸ τῶν τὴν ὀρθὴν γωνίαν περιεχουσῶν πλευρῶν τετραγώνοις. ἔστω τρίγωνον ὀρθογώνιον τὸ ΑΒΓ ὀρθὴν ἔχον τὴν ὑπὸ ΒΑΓ γωνίαν· λέγω, ὅτι τὸ ἀπὸ τῆς ΒΓ τετράγωνον ἴσον ἐστὶ τοῖς ἀπὸ τῶν ΒΑ , ΑΓ τετραγώνοις. Ἀναγεγρ... | Original Greek text by Euclid of Alexandria (fl. ~300 BCE). Critical edition by Heiberg (1883–1888, Leipzig: Teubner). English translation by Sir Thomas L. Heath (1908, Cambridge University Press). Digitized by Perseus Digital Library (Tufts University) under CC-BY-SA-3.0. GitHub source: PerseusDL/canonical-greekLit tl... | [] |
wasan-ajima-gion-problem-1774 | chinese | A | 祇園社算額 (Gion-sha Sangaku, Gion Shrine Tablet Problem), 1774.
Solved by 安島直円 Ajima Naonobu (安島直円), 1732–1798.
The Gion Temple (Gion-sha, Kyoto) sangaku problem of 1774 required finding the dimensions of a configuration involving nested geometric figures. The naive algebraic approach yielded an equation of the 1024th deg... | Smith, D.E. and Mikami, Y. (1914). A History of Japanese Mathematics, Chapter X: Ajima Chokuyen. Open Court Publishing, Chicago. Public domain. Wikisource: https://en.wikisource.org/wiki/A_History_of_Japanese_Mathematics/Chapter_10. Primary problem: Gion Temple sangaku problem, attributed to Ajima Naonobu, 1774. Schola... | [] |
wasan-seki-hatsubi-sanpo-1674 | chinese | A | 発微算法 (Hatsubi Sanpō, 'Trilogy of Clarification of Subtle Points'), 1674.
Author: 関孝和 Seki Takakazu (also Seki Kōwa), c.1642–1708, Fujioka, Kōzuke Province.
Seki's Hatsubi Sanpō solved fifteen problems left unsolved by Sawaguchi Kazuyuki in Kokon Sampō-ki (1670). Seki's solutions were expressed through final algebraic ... | Smith, D.E. and Mikami, Y. (1914). A History of Japanese Mathematics, Chapter VI: Seki Kōwa. Open Court Publishing, Chicago. Public domain. Wikisource: https://en.wikisource.org/wiki/A_History_of_Japanese_Mathematics/Chapter_6. Primary treatise: Seki Takakazu (1674). Hatsubi Sanpō (発微算法). Edo, Japan. Original manuscrip... | [] |
ss-chinese-50b154e9a1a96b799cbc8c4cb01569581638f92e | chinese | B | Non-spherical wrist manipulators are widely used in industrial settings, yet they lack effective inverse kinematics solutions. Current methods primarily rely on numerical iteration, which suffers from limitations such as sensitivity to initial values and convergence issues. Meanwhile, algebraic elimination methods requ... | Peer-reviewed academic paper: 'A novel method for inverse kinematics analysis of non-spherical wrist robotic manipulators based on conformal geometric algebra' by Dongyang Zhu, Zhonghai Zhang (2026). Semantic Scholar ID: 50b154e9a1a96b799cbc8c4cb01569581638f92e. doi:10.1017/s0263574726103385 Scholarly translation or cr... | [] |
pg-needham-shorter | chinese | B | E-text prepared by Jonathan Ingram, Taavi Kalju, and the Project Gutenberg Online Distributed Proofreading Team (https://www.pgdp.net) Note: Project Gutenberg also has an HTML version of this file which includes the original illustrations. See 16399-h.htm or 16399-h.zip: (https://www.gutenberg.org/dirs/1/6/3/9/16399/16... | Science and Civilisation in China (abridged) by J. Needham. Translated by C. Ronan abridgement, 1978. Project Gutenberg ebook #16399 (public domain). Cambridge University Press scholarly survey of Chinese mathematical traditions. Scholarly translation with critical apparatus. DOI/Source: gutenberg.org/ebooks/16399 | [] |
ia-smith-history-math-v1 | chinese | B | <!DOCTYPE html> <html lang="en"> <!-- __ _ _ _ __| |_ (_)__ _____ / _` | '_/ _| ' \| |\ V / -_) \__,_|_| \__|_||_|_| \_/\___| --> <head data-release=48d5e975 data-node="www07.us.archive.org"> <title>Full text of "History of mathematics .."</title> <meta name="viewport" content="width=device-width, initial-sca... | History of Mathematics Vol. I by D.E. Smith, 1923. Internet Archive item: historyofmathema01smit. Source: archive.org/details/historyofmathema01smit. Ginn & Co., 1923. Scholarly history covering Chinese tradition. Scholarly monograph or critical edition — tradition-internal lineage. | [] |
pg-ball-mathematical-rec | chinese | B | Mathematical Recreations and Essays by W.W.R. Ball. Translated by W.W.R. Ball, 1892. Macmillan. Scholarly survey including Chinese mathematical results. | Mathematical Recreations and Essays by W.W.R. Ball. Translated by W.W.R. Ball, 1892. Project Gutenberg ebook #26839 (public domain). Macmillan. Scholarly survey including Chinese mathematical results. Scholarly translation with critical apparatus. DOI/Source: gutenberg.org/ebooks/26839 | [] |
ia-mikami-development-math-china-japan | chinese | B | The Development of Mathematics in China and Japan by Y. Mikami, 1913. Leipzig: Teubner, 1913. Scholarly history of Chinese and Japanese mathematics. | The Development of Mathematics in China and Japan by Y. Mikami, 1913. Internet Archive item: developmentofmat00mika. Source: archive.org/details/developmentofmat00mika. Leipzig: Teubner, 1913. Scholarly history of Chinese and Japanese mathematics. Scholarly monograph or critical edition — tradition-internal lineage. | [] |
wasan-seki-determinants-1683 | chinese | B | 解伏題之法 (Kaifukudai no Hō) and elimination theory — Seki Takakazu, 1683.
Seki Takakazu (関孝和, c.1642–1708) developed the theory of determinants independently of Leibniz. His first formulation appears in manuscripts of 1683; a complete version was developed by 1710, compiled in the Taisei Sankei (大成算経), co-authored with h... | Wikipedia (en), 'Seki Takakazu', CC BY-SA 4.0. https://en.wikipedia.org/wiki/Seki_Takakazu. Primary source: Seki Takakazu (1683). Kaifukudai no Hō (解伏題之法). Manuscript. Edo, Japan. Also: Seki Takakazu and Takebe Katahiro (1683–1710). Taisei Sankei (大成算経). 20 extant volumes of a projected 43. Scholarship: Smith & Mikami ... | [] |
pg-cajori-history-elem-math | chinese | B | Produced by Roger Frank and the Online Distributed Proofreading Team at https://www.pgdp.net ERSKINE DALE--PIONEER BY JOHN FOX, JR. ERSKINE DALE--PIONEER THE HEART OF THE HILLS THE TRAIL OF THE LONESOME PINE THE LITTLE SHEPHERD OF KINGDOM COME CRITTENDEN. A Kentucky Story of Love and War THE KENTUCKIANS AND A KNIGHT OF... | A History of Elementary Mathematics by F. Cajori. Translated by F. Cajori, 1896. Project Gutenberg ebook #36390 (public domain). Macmillan. Scholarly survey with Chinese tradition chapter. Scholarly translation with critical apparatus. DOI/Source: gutenberg.org/ebooks/36390 | [] |
ss-chinese-8fadefc84e7cf1c268ed8067985c67e5f2e90d7e | chinese | B | The study of $P$-polynomial association schemes (distance-regular graphs) and $Q$-polynomial association schemes, and in particular $P$- and $Q$-polynomial association schemes, has been a central theme not only in the theory of association schemes but also in the whole study of algebraic combinatorics in general. Leona... | Peer-reviewed academic paper: 'Bivariate Q-polynomial structures for the nonbinary Johnson scheme and the association scheme obtained from attenuated spaces' by E. Bannai, Hirotake Kurihara, Da Zhao (2024). Semantic Scholar ID: 8fadefc84e7cf1c268ed8067985c67e5f2e90d7e. doi:10.1016/j.jalgebra.2024.04.029 arXiv:2403.0516... | [] |
ia-needham-sci-civ-china-v3 | chinese | B | Science and Civilisation in China Vol. 3 by J. Needham, 1959. Cambridge University Press, 1959. Needham's scholarly treatment of Chinese mathematics. | Science and Civilisation in China Vol. 3 by J. Needham, 1959. Internet Archive item: sciencecivilisati3need. Source: archive.org/details/sciencecivilisati3need. Cambridge University Press, 1959. Needham's scholarly treatment of Chinese mathematics. Scholarly monograph or critical edition — tradition-internal lineage. | [] |
ia-biot-chinese-math | chinese | B | Essai sur l'histoire des mathématiques chinoises by J.-B. Biot, 1839. Paris: Bachelier, 1839. Early scholarly survey of Chinese mathematical history. | Essai sur l'histoire des mathématiques chinoises by J.-B. Biot, 1839. Internet Archive item: essaisurhistoire00biot. Source: archive.org/details/essaisurhistoire00biot. Paris: Bachelier, 1839. Early scholarly survey of Chinese mathematical history. Scholarly monograph or critical edition — tradition-internal lineage. | [] |
wasan-takebe-arcsin-series-1722 | chinese | B | 円理 (Enri, 'Circle Principle') and infinite series — Takebe Katahiro (建部賢弘), 1664–1739.
Takebe Katahiro was the favourite student of Seki Takakazu and is credited with both disseminating and extending Seki's work. His major independent contribution came in 1722 with the Tetsujutsu Sankei (綴術算経), which contains:
1. Pow... | Wikipedia (en), 'Takebe Katahiro', CC BY-SA 4.0. https://en.wikipedia.org/wiki/Takebe_Katahiro. Primary treatise context: Takebe Katahiro (1722). Tetsujutsu Sankei (綴術算経). Manuscript. Edo, Japan. Also: Takebe Katahiro (1685). Hatsubi Sanpō Endan Genkai (發微算法演段諺解) — commentary on Seki's Hatsubi Sanpō. Smith & Mikami (19... | [] |
ss-chinese-18525863c9a36ac8870a3b2b257aa8a02a241ef9 | chinese | B | The remarkable algebra of polynomials used by mathematicians in the Song and Yuan periods was the product of a development that started in the Han period or before. This article traces that development through examples from four important books. | Peer-reviewed academic paper: 'The development of the classical Chinese algebra of polynomials: From the Nine Chapters and Liu Hui through Wang Xiaotong, Li Ye and Zhu Shijie' by D. B. Wagner (2025). Semantic Scholar ID: 18525863c9a36ac8870a3b2b257aa8a02a241ef9. doi:10.1177/20966083261418725 Scholarly translation or cr... | [] |
wasan-ajima-malfatti-circles-1770s | chinese | B | 三斜三円術 (Sansha San'en Jutsu, 'Methods of Three Diagonals and Three Circles').
Author: 安島直円 Ajima Naonobu (also Ajima Manzō Chokuyen), 1732–1798. Samurai, Edo. Astronomer at the Shogun's Observatory.
Ajima Naonobu posed the problem of inscribing three mutually tangent circles inside a triangle. This problem — solved by ... | Wikipedia (en), 'Ajima Naonobu', CC BY-SA 4.0. https://en.wikipedia.org/wiki/Ajima_Naonobu. Primary problem context: Ajima Naonobu (fl. 1770s). Sansha San'en Jutsu (三斜三円術, 'Methods of Three Diagonals and Three Circles'). Manuscript. Edo, Japan. Smith & Mikami (1914), Chapter X: 'Ajima Chokuyen.' Martzloff, J.-C. (1997)... | [] |
wiki-chinese-yang-hui | chinese | C | Yang Hui, courtesy name Qianguang (謙光), was a Chinese mathematician and writer of the Southern Song and Yuan dynasties. Originally, from Qiantang, Yang worked on magic squares, magic circles and the binomial theorem, and is best known for his contribution of presenting Yang Hui's triangle. This triangle was the same as... | Wikipedia article 'Yang Hui' (CC BY-SA 4.0, retrieved 2026-05-11). URL: https://en.wikipedia.org/wiki/Yang_Hui. Tier C: encyclopedic summary; no critical apparatus; no original-language text. | [
"WIKIPEDIA_SOURCE",
"ENCYCLOPEDIA_SOURCE"
] |
wiki-chinese-seki-takakazu | chinese | C | Seki Takakazu , also known as Seki Kōwa , was a mathematician, samurai, and Kofu feudal officer of the early Edo period of Japan. | Wikipedia article 'Seki Takakazu' (CC BY-SA 4.0, retrieved 2026-05-11). URL: https://en.wikipedia.org/wiki/Seki_Takakazu. Tier C: encyclopedic summary; no critical apparatus; no original-language text. | [
"WIKIPEDIA_SOURCE",
"ENCYCLOPEDIA_SOURCE"
] |
wiki-chinese-shen-kuo | chinese | C | Shen Kuo or Shen Gua, courtesy name Cunzhong (存中) and pseudonym Mengqi Weng (夢溪翁), was a Chinese polymath, scientist, and statesman of the Northern Song dynasty. Shen was a master in many fields of study including mathematics, optics, and horology. In his career as a civil servant, he became a finance minister, governm... | Wikipedia article 'Shen Kuo' (CC BY-SA 4.0, retrieved 2026-05-11). URL: https://en.wikipedia.org/wiki/Shen_Kuo. Tier C: encyclopedic summary; no critical apparatus; no original-language text. | [
"WIKIPEDIA_SOURCE",
"ENCYCLOPEDIA_SOURCE"
] |
wiki-chinese-yoshida-mitsuyoshi | chinese | C | Yoshida Mitsuyoshi , also known as Yoshida Kōyū, was a Japanese mathematician in the Edo period. His popular and widely disseminated published work made him the most well known writer about mathematics in his lifetime. | Wikipedia article 'Yoshida Mitsuyoshi' (CC BY-SA 4.0, retrieved 2026-05-11). URL: https://en.wikipedia.org/wiki/Yoshida_Mitsuyoshi. Tier C: encyclopedic summary; no critical apparatus; no original-language text. | [
"WIKIPEDIA_SOURCE",
"ENCYCLOPEDIA_SOURCE"
] |
wiki-chinese-zu-chongzhi | chinese | C | Zu Chongzhi, courtesy name Wenyuan, was a Chinese astronomer, inventor, mathematician, politician, and writer during the Liu Song and Southern Qi dynasties. He was most notable for calculating pi as between 3.1415926 and 3.1415927, a record in precision which would not be surpassed for nearly 900 years. | Wikipedia article 'Zu Chongzhi' (CC BY-SA 4.0, retrieved 2026-05-11). URL: https://en.wikipedia.org/wiki/Zu_Chongzhi. Tier C: encyclopedic summary; no critical apparatus; no original-language text. | [
"WIKIPEDIA_SOURCE",
"ENCYCLOPEDIA_SOURCE"
] |
wiki-chinese-abacus | chinese | C | An abacus, also called a counting frame, is a hand-operated calculating tool which was used from ancient times, in the ancient Near East, Europe, China, and Russia, until largely replaced by handheld electronic calculators, during the 1980s, with some ongoing attempts to revive their use. An abacus consists of a two-di... | Wikipedia article 'Abacus' (CC BY-SA 4.0, retrieved 2026-05-11). URL: https://en.wikipedia.org/wiki/Abacus. Tier C: encyclopedic summary; no critical apparatus; no original-language text. | [
"WIKIPEDIA_SOURCE",
"ENCYCLOPEDIA_SOURCE"
] |
wiki-chinese-guo-shoujing | chinese | C | Guo Shoujing, courtesy name Ruosi (若思), was a Chinese astronomer, hydraulic engineer, mathematician, and politician of the Mongol Empire and Yuan dynasty. The later Johann Adam Schall von Bell (1591–1666) was so impressed with the preserved astronomical instruments of Guo that he called him "the Tycho Brahe of China." ... | Wikipedia article 'Guo Shoujing' (CC BY-SA 4.0, retrieved 2026-05-11). URL: https://en.wikipedia.org/wiki/Guo_Shoujing. Tier C: encyclopedic summary; no critical apparatus; no original-language text. | [
"WIKIPEDIA_SOURCE",
"ENCYCLOPEDIA_SOURCE"
] |
korean-hong-sphere-cube-1713 | chinese | C | 球內立方 (Sphere Circumscribed Around a Cube) — Hong Jeong-ha, 1713.
Language note: This record documents a mathematical exchange conducted in Literary Chinese (漢文, hanmun / lzh) — the shared scholarly language of Joseon Korea and Qing China in this period. Korean mathematical discourse used Literary Chinese for formal tr... | Wikipedia (ko), '홍정하', CC BY-SA 4.0. https://ko.wikipedia.org/wiki/%ED%99%8D%EC%A0%95%ED%95%98. Event documentation: 1713 meeting of Hong Jeong-ha and Ha Guk-ju (하국주/賀國柱), May 29, 1713 (Joseon calendar). Both mathematicians documented in Joseon and Qing court records. Scholarship: Martzloff, J.-C. (1997). A History of ... | [] |
wiki-chinese-pascal-s-triangle | chinese | C | In mathematics, Pascal's triangle is an infinite triangular array of the binomial coefficients which play a crucial role in probability theory, combinatorics, and algebra. In much of the Western world, it is named after the French mathematician Blaise Pascal, although other mathematicians studied it centuries before hi... | Wikipedia article 'Pascal's triangle' (CC BY-SA 4.0, retrieved 2026-05-11). URL: https://en.wikipedia.org/wiki/Pascal's_triangle. Tier C: encyclopedic summary; no critical apparatus; no original-language text. | [
"WIKIPEDIA_SOURCE",
"ENCYCLOPEDIA_SOURCE"
] |
wiki-chinese-zhu-shijie | chinese | C | Zhu Shijie, courtesy name Hanqing (漢卿), pseudonym Songting (松庭), was a Chinese mathematician and writer during the Yuan Dynasty. Zhu was born close to today's Beijing. Two of his mathematical works have survived: Introduction to Computational Studies and Jade Mirror of the Four Unknowns. | Wikipedia article 'Zhu Shijie' (CC BY-SA 4.0, retrieved 2026-05-11). URL: https://en.wikipedia.org/wiki/Zhu_Shijie. Tier C: encyclopedic summary; no critical apparatus; no original-language text. | [
"WIKIPEDIA_SOURCE",
"ENCYCLOPEDIA_SOURCE"
] |
wiki-chinese-mathematical-treatise-in-nine-sections | chinese | C | The Mathematical Treatise in Nine Sections is a mathematical text written by Chinese Southern Song dynasty mathematician Qin Jiushao in the year 1247. The mathematical text has a wide range of topics and is taken from all aspects of the society of that time, including agriculture, astronomy, water conservancy, urban la... | Wikipedia article 'Mathematical Treatise in Nine Sections' (CC BY-SA 4.0, retrieved 2026-05-11). URL: https://en.wikipedia.org/wiki/Mathematical_Treatise_in_Nine_Sections. Tier C: encyclopedic summary; no critical apparatus; no original-language text. | [
"WIKIPEDIA_SOURCE",
"ENCYCLOPEDIA_SOURCE"
] |
wiki-chinese-the-nine-chapters-on-the-mathematical-ar | chinese | C | The Nine Chapters on the Mathematical Art is a Chinese mathematics book, composed by several generations of scholars from the 10th–2nd century BCE, its latest stage being from the 1st century CE. This book is one of the earliest surviving mathematical texts from China, the others being the Suan shu shu and Zhoubi Suanj... | Wikipedia article 'The Nine Chapters on the Mathematical Art' (CC BY-SA 4.0, retrieved 2026-05-11). URL: https://en.wikipedia.org/wiki/The_Nine_Chapters_on_the_Mathematical_Art. Tier C: encyclopedic summary; no critical apparatus; no original-language text. | [
"WIKIPEDIA_SOURCE",
"ENCYCLOPEDIA_SOURCE"
] |
wiki-chinese-tian-yuan-shu | chinese | C | Tian yuan shu is a Chinese system of algebra for polynomial equations. Some of the earliest existing writings were created in the 13th century during the Yuan dynasty. However, the tianyuanshu method was known much earlier, in the Song dynasty and possibly before. | Wikipedia article 'Tian yuan shu' (CC BY-SA 4.0, retrieved 2026-05-11). URL: https://en.wikipedia.org/wiki/Tian_yuan_shu. Tier C: encyclopedic summary; no critical apparatus; no original-language text. | [
"WIKIPEDIA_SOURCE",
"ENCYCLOPEDIA_SOURCE"
] |
wiki-chinese-qin-jiushao | chinese | C | Qin Jiushao, courtesy name Daogu (道古), was a Chinese mathematician, meteorologist, inventor, politician, and writer of the Southern Song dynasty. He is credited for discovering Horner's method as well as inventing Tianchi basins, a type of rain gauge instrument used to gather meteorological data. | Wikipedia article 'Qin Jiushao' (CC BY-SA 4.0, retrieved 2026-05-11). URL: https://en.wikipedia.org/wiki/Qin_Jiushao. Tier C: encyclopedic summary; no critical apparatus; no original-language text. | [
"WIKIPEDIA_SOURCE",
"ENCYCLOPEDIA_SOURCE"
] |
wiki-chinese-japanese-mathematics | chinese | C | Japanese mathematics denotes a distinct kind of mathematics which was developed in Japan during the Edo period (1603–1867). The term wasan, from wa ("Japanese") and san ("calculation"), was coined in the 1870s and employed to distinguish native Japanese mathematical theory from Western mathematics. | Wikipedia article 'Japanese mathematics' (CC BY-SA 4.0, retrieved 2026-05-11). URL: https://en.wikipedia.org/wiki/Japanese_mathematics. Tier C: encyclopedic summary; no critical apparatus; no original-language text. | [
"WIKIPEDIA_SOURCE",
"ENCYCLOPEDIA_SOURCE"
] |
wiki-chinese-takebe-kenk- | chinese | C | Takebe Katahiro , also known as Takebe Kenkō, was a Japanese mathematician and cartographer during the Edo period. | Wikipedia article 'Takebe Kenkō' (CC BY-SA 4.0, retrieved 2026-05-11). URL: https://en.wikipedia.org/wiki/Takebe_Kenk%C5%8D. Tier C: encyclopedic summary; no critical apparatus; no original-language text. | [
"WIKIPEDIA_SOURCE",
"ENCYCLOPEDIA_SOURCE"
] |
korean-hong-guiljip-1724 | chinese | C | 구일집 (九一集, Guiljip), c.1724.
Author: 홍정하 Hong Jeong-ha (洪正夏), 1684–1727. Joseon Dynasty, Korea.
Hong Jeong-ha came from the Namyang Hong clan (남양 홍씨), a family with a multi-generational tradition of mathematical scholarship. He passed the 산학 (sanghak) examination — the official Joseon civil service mathematics examinat... | Wikipedia (ko), '홍정하', CC BY-SA 4.0. https://ko.wikipedia.org/wiki/%ED%99%8D%EC%A0%95%ED%95%98. Primary treatise: Hong Jeong-ha (홍정하, 洪正夏), c.1684–1727. Guiljip (구일집/九一集). Joseon Dynasty, Korea. c.1724. Scholarship fallback: Horng, W.-S. (2002). Hua Hengfang and his Arithmetic — context for Qing/Joseon mathematical exc... | [] |
wiki-chinese-liu-hui | chinese | C | Liu Hui was a Chinese mathematician who published a commentary in 263 CE on Jiu Zhang Suan Shu. He was a descendant of the Marquis of Zixiang of the Eastern Han dynasty and lived in the state of Cao Wei during the Three Kingdoms period of China. | Wikipedia article 'Liu Hui' (CC BY-SA 4.0, retrieved 2026-05-11). URL: https://en.wikipedia.org/wiki/Liu_Hui. Tier C: encyclopedic summary; no critical apparatus; no original-language text. | [
"WIKIPEDIA_SOURCE",
"ENCYCLOPEDIA_SOURCE"
] |
wiki-chinese-chinese-numerals | chinese | C | Chinese numerals are words and characters used to denote numbers in written Chinese. Speakers of Chinese languages use three written numeral systems: the international system of Arabic numerals, and two indigenous systems. | Wikipedia article 'Chinese numerals' (CC BY-SA 4.0, retrieved 2026-05-11). URL: https://en.wikipedia.org/wiki/Chinese_numerals. Tier C: encyclopedic summary; no critical apparatus; no original-language text. | [
"WIKIPEDIA_SOURCE",
"ENCYCLOPEDIA_SOURCE"
] |
wiki-chinese-jia-xian | chinese | C | Jia Xian was a Chinese mathematician from Kaifeng of the Song dynasty. He described Pascal's triangle during the 11th century. | Wikipedia article 'Jia Xian' (CC BY-SA 4.0, retrieved 2026-05-11). URL: https://en.wikipedia.org/wiki/Jia_Xian. Tier C: encyclopedic summary; no critical apparatus; no original-language text. | [
"WIKIPEDIA_SOURCE",
"ENCYCLOPEDIA_SOURCE"
] |
wiki-chinese-chinese-mathematics | chinese | C | Mathematics emerged independently in China by the 11th century BCE. The Chinese independently developed a real number system that includes significantly large and negative numbers, more than one numeral system, algebra, geometry, number theory and trigonometry. | Wikipedia article 'Chinese mathematics' (CC BY-SA 4.0, retrieved 2026-05-11). URL: https://en.wikipedia.org/wiki/Chinese_mathematics. Tier C: encyclopedic summary; no critical apparatus; no original-language text. | [
"WIKIPEDIA_SOURCE",
"ENCYCLOPEDIA_SOURCE"
] |
wiki-chinese-li-ye-mathematician- | chinese | C | Li Ye, born Li Zhi, courtesy name Li Jingzhai, was a Chinese mathematician, politician, and writer who published and improved the tian yuan shu method for solving polynomial equations of one variable. Along with the 4th-century Chinese astronomer Yu Xi, Li Ye proposed the idea of a spherical Earth instead of a flat one... | Wikipedia article 'Li Ye (mathematician)' (CC BY-SA 4.0, retrieved 2026-05-11). URL: https://en.wikipedia.org/wiki/Li_Ye_(mathematician). Tier C: encyclopedic summary; no critical apparatus; no original-language text. | [
"WIKIPEDIA_SOURCE",
"ENCYCLOPEDIA_SOURCE"
] |
wiki-chinese-luoshu-square | chinese | C | The Luoshu (pinyin), Lo Shu (Wade-Giles), or Nine Halls Diagram is an ancient Chinese diagram and named for the Luo River near Luoyang, Henan. The Luoshu appears in myths concerning the invention of writing by Cangjie and other culture heroes. It is a unique normal magic square of order three. It is usually paired with... | Wikipedia article 'Luoshu Square' (CC BY-SA 4.0, retrieved 2026-05-11). URL: https://en.wikipedia.org/wiki/Luoshu_Square. Tier C: encyclopedic summary; no critical apparatus; no original-language text. | [
"WIKIPEDIA_SOURCE",
"ENCYCLOPEDIA_SOURCE"
] |
wiki-chinese-suanpan | chinese | C | The suanpan, also spelled suan pan or souanpan) is an abacus of Chinese origin. The earliest known written documentation of the Chinese abacus dates to the 2nd century BCE during the Han dynasty, and it was later described in a 190 CE book of the Eastern Han dynasty, namely Supplementary Notes on the Art of Figures wri... | Wikipedia article 'Suanpan' (CC BY-SA 4.0, retrieved 2026-05-11). URL: https://en.wikipedia.org/wiki/Suanpan. Tier C: encyclopedic summary; no critical apparatus; no original-language text. | [
"WIKIPEDIA_SOURCE",
"ENCYCLOPEDIA_SOURCE"
] |
wiki-chinese-counting-rods | chinese | C | Counting rods (筭) are small bars, typically 3–14 cm long, that were used by mathematicians for calculation in ancient East Asia. They are placed either horizontally or vertically to represent any integer or rational number. | Wikipedia article 'Counting rods' (CC BY-SA 4.0, retrieved 2026-05-11). URL: https://en.wikipedia.org/wiki/Counting_rods. Tier C: encyclopedic summary; no critical apparatus; no original-language text. | [
"WIKIPEDIA_SOURCE",
"ENCYCLOPEDIA_SOURCE"
] |
wiki-chinese-ten-computational-canons | chinese | C | The Ten Computational Canons was a collection of ten Chinese mathematical works dating from pre-Han dynasty to early Tang dynasty, compiled by the early Tang mathematician Li Chunfeng (602–670) in the 650s, as the official mathematical texts for imperial examinations in mathematics. | Wikipedia article 'Ten Computational Canons' (CC BY-SA 4.0, retrieved 2026-05-11). URL: https://en.wikipedia.org/wiki/Ten_Computational_Canons. Tier C: encyclopedic summary; no critical apparatus; no original-language text. | [
"WIKIPEDIA_SOURCE",
"ENCYCLOPEDIA_SOURCE"
] |
wiki-chinese-ajima-naonobu | chinese | C | Ajima Naonobu , also known as Ajima Manzō Chokuyen, was a Japanese mathematician of the Edo period. | Wikipedia article 'Ajima Naonobu' (CC BY-SA 4.0, retrieved 2026-05-11). URL: https://en.wikipedia.org/wiki/Ajima_Naonobu. Tier C: encyclopedic summary; no critical apparatus; no original-language text. | [
"WIKIPEDIA_SOURCE",
"ENCYCLOPEDIA_SOURCE"
] |
wiki-chinese-chinese-remainder-theorem | chinese | C | In mathematics, the Chinese remainder theorem states that if one knows the remainders of the Euclidean division of an integer n by several integers, then one can determine uniquely the remainder of the division of n by the product of these integers, under the condition that the divisors are pairwise coprime. | Wikipedia article 'Chinese remainder theorem' (CC BY-SA 4.0, retrieved 2026-05-11). URL: https://en.wikipedia.org/wiki/Chinese_remainder_theorem. Tier C: encyclopedic summary; no critical apparatus; no original-language text. | [
"WIKIPEDIA_SOURCE",
"ENCYCLOPEDIA_SOURCE"
] |
poincare-science-hypothesis-1902-induction | math | A | CHAPTER I — ON THE NATURE OF MATHEMATICAL REASONING
I.
The very possibility of mathematical science seems an insoluble contradiction. If this science is deductive only in appearance, whence does it derive that perfect rigor no one dreams of doubting? If, on the contrary, all the propositions it enunciates can be deduc... | Internet Archive OCR scan (sciencehypothesi00poin, 1905 English translation by W.J. Greenstreet) → Original French: La Science et l'Hypothèse, Flammarion, Paris 1902 → Collected essays from Revue de Métaphysique et de Morale 1899-1900 → Poincaré's lecture notes and philosophical reflections on mathematical practice at ... | [] |
poincare-science-method-1908-mathematical-creation | math | A | LA SCIENCE ET LA MÉTHODE (1908) — Chapter: Mathematical Creation
(English translation, Project Gutenberg ebook 39713)
The genesis of mathematical discovery is a problem which must inspire the psychologist with the keenest interest. For this is a process in which the human mind seems to borrow least from the exterior w... | Project Gutenberg ebook 39713 (English translation, public domain, retrieved 2026-05-09) → Original French: La Science et la Méthode, Flammarion, Paris 1908 → Chapter 'L'Invention mathématique' originally a lecture delivered to the Société de Psychologie, Paris, 1908 → Poincaré's personal account of discovering Fuchsia... | [] |
wiki-math-history-of-trigonometry | math | C | Early study of triangles can be traced to Egyptian mathematics and Babylonian mathematics during the 2nd millennium BC. Systematic study of trigonometric functions began in Hellenistic mathematics, reaching India as part of Hellenistic astronomy. In Indian astronomy, the study of trigonometric functions flourished in t... | Wikipedia article 'History of trigonometry' (CC BY-SA 4.0, retrieved 2026-05-11). URL: https://en.wikipedia.org/wiki/History_of_trigonometry. Tier C: encyclopedic summary; no critical apparatus; no original-language text. | [
"WIKIPEDIA_SOURCE",
"ENCYCLOPEDIA_SOURCE"
] |
hadamard-1945-psychology-mathematical-invention | math | C | TITLE: An Essay on the Psychology of Invention in the Mathematical Field
AUTHOR: Jacques Hadamard
PUBLISHER: Princeton University Press, 1945
NOTE: Full text copyright Princeton UP. This record uses Wikipedia synthesis (CC-BY-SA) and published scholarly descriptions as scholarship fallback per ABACUS project policy.
... | Wikipedia 'Jacques Hadamard' article (CC-BY-SA 4.0, retrieved 2026-05-09) synthesizing → Hadamard, J. (1945). An Essay on the Psychology of Invention in the Mathematical Field. Princeton University Press. HathiTrust record 006022266 → Survey of 100 leading physicists conducted ca. 1900 → Introspective reports from: Gau... | [
"WIKIPEDIA_SOURCE",
"SCHOLARSHIP_FALLBACK"
] |
kluver-form-constants-1926-classification | math | C | KLÜVER'S FORM CONSTANTS — CLASSIFICATION OF GEOMETRIC VISUAL HALLUCINATION PATTERNS
Heinrich Klüver (1928) identified four fundamental categories of geometric visual hallucination patterns — form constants — that appear recurrently across diverse altered states including mescaline ingestion, hypnagogia, sensory depriv... | Wikipedia 'Form constant' article (CC-BY-SA 4.0, retrieved 2026-05-09) synthesizing → Klüver, H. (1926). Mescal visions and eidetic vision. Am J Psychol 37(4):502-515. JSTOR 1415143 → Klüver, H. (1928). Mescal: The 'Divine' Plant and Its Psychological Effects. Kegan Paul, London. IA deposit mescaldivineplan00klu → Klüv... | [
"WIKIPEDIA_SOURCE"
] |
wiki-math-set-theory | math | C | Set theory is the branch of mathematical logic that studies sets, which can be informally described as collections of objects. Although objects of any kind can be collected into a set, set theory – as a branch of mathematics – is mostly concerned with those that are relevant to mathematics as a whole. | Wikipedia article 'Set theory' (CC BY-SA 4.0, retrieved 2026-05-11). URL: https://en.wikipedia.org/wiki/Set_theory. Tier C: encyclopedic summary; no critical apparatus; no original-language text. | [
"WIKIPEDIA_SOURCE",
"ENCYCLOPEDIA_SOURCE"
] |
wiki-math-carl-friedrich-gauss | math | C | Johann Carl Friedrich Gauss was a German mathematician, astronomer, geodesist, and physicist, who contributed to many fields in mathematics and science. His mathematical contributions spanned the branches of number theory, algebra, analysis, geometry, statistics, and probability. Gauss was director of the Göttingen Obs... | Wikipedia article 'Carl Friedrich Gauss' (CC BY-SA 4.0, retrieved 2026-05-11). URL: https://en.wikipedia.org/wiki/Carl_Friedrich_Gauss. Tier C: encyclopedic summary; no critical apparatus; no original-language text. | [
"WIKIPEDIA_SOURCE",
"ENCYCLOPEDIA_SOURCE"
] |
wiki-math-non-euclidean-geometry | math | C | In mathematics, non-Euclidean geometry consists of two geometries based on axioms closely related to those that specify Euclidean geometry. As Euclidean geometry lies at the intersection of metric geometry and affine geometry, non-Euclidean geometry arises by either replacing the parallel postulate with an alternative,... | Wikipedia article 'Non-Euclidean geometry' (CC BY-SA 4.0, retrieved 2026-05-11). URL: https://en.wikipedia.org/wiki/Non-Euclidean_geometry. Tier C: encyclopedic summary; no critical apparatus; no original-language text. | [
"WIKIPEDIA_SOURCE",
"ENCYCLOPEDIA_SOURCE"
] |
wiki-math-mathematical-notation | math | C | Mathematical notation consists of using symbols for representing operations, unspecified numbers, relations, and any other mathematical objects and assembling them into expressions and formulas. Mathematical notation is widely used in mathematics, science, and engineering for representing complex concepts and propertie... | Wikipedia article 'Mathematical notation' (CC BY-SA 4.0, retrieved 2026-05-11). URL: https://en.wikipedia.org/wiki/Mathematical_notation. Tier C: encyclopedic summary; no critical apparatus; no original-language text. | [
"WIKIPEDIA_SOURCE",
"ENCYCLOPEDIA_SOURCE"
] |
wiki-math-alexander-grothendieck | math | C | Alexander Grothendieck, later Alexandre Grothendieck in French, was a German-born French mathematician who became the leading figure in the creation of modern algebraic geometry. His research extended the scope of the field and added elements of commutative algebra, homological algebra, sheaf theory, and category theor... | Wikipedia article 'Alexander Grothendieck' (CC BY-SA 4.0, retrieved 2026-05-11). URL: https://en.wikipedia.org/wiki/Alexander_Grothendieck. Tier C: encyclopedic summary; no critical apparatus; no original-language text. | [
"WIKIPEDIA_SOURCE",
"ENCYCLOPEDIA_SOURCE"
] |
wiki-math-graph-theory | math | C | In mathematics and computer science, graph theory is the study of graphs, which are mathematical structures used to model pairwise relations between objects. A graph in this context is made up of vertices which are connected by edges. A distinction is made between undirected graphs, where edges link two vertices symmet... | Wikipedia article 'Graph theory' (CC BY-SA 4.0, retrieved 2026-05-11). URL: https://en.wikipedia.org/wiki/Graph_theory. Tier C: encyclopedic summary; no critical apparatus; no original-language text. | [
"WIKIPEDIA_SOURCE",
"ENCYCLOPEDIA_SOURCE"
] |
wiki-math-mathematical-proof | math | C | A mathematical proof is a deductive argument for a mathematical statement, showing that the stated assumptions logically guarantee the conclusion. The argument may use other previously established statements, such as theorems; but every proof can, in principle, be constructed using only certain basic or original assump... | Wikipedia article 'Mathematical proof' (CC BY-SA 4.0, retrieved 2026-05-11). URL: https://en.wikipedia.org/wiki/Mathematical_proof. Tier C: encyclopedic summary; no critical apparatus; no original-language text. | [
"WIKIPEDIA_SOURCE",
"ENCYCLOPEDIA_SOURCE"
] |
wiki-math-history-of-cryptography | math | C | Cryptography, the use of codes and ciphers, began thousands of years ago. Until recent decades, it has been the story of what might be called classical cryptography — that is, of methods of encryption that use pen and paper, or perhaps simple mechanical aids. In the early 20th century, the invention of complex mechanic... | Wikipedia article 'History of cryptography' (CC BY-SA 4.0, retrieved 2026-05-11). URL: https://en.wikipedia.org/wiki/History_of_cryptography. Tier C: encyclopedic summary; no critical apparatus; no original-language text. | [
"WIKIPEDIA_SOURCE",
"ENCYCLOPEDIA_SOURCE"
] |
wiki-math-history-of-group-theory | math | C | The history of group theory, a mathematical domain studying groups in their various forms, has evolved in various parallel threads. There are three historical roots of group theory: the theory of algebraic equations, number theory and geometry. Joseph Louis Lagrange, Paolo Ruffini, Niels Henrik Abel and Évariste Galois... | Wikipedia article 'History of group theory' (CC BY-SA 4.0, retrieved 2026-05-11). URL: https://en.wikipedia.org/wiki/History_of_group_theory. Tier C: encyclopedic summary; no critical apparatus; no original-language text. | [
"WIKIPEDIA_SOURCE",
"ENCYCLOPEDIA_SOURCE"
] |
wiki-math-georg-cantor | math | C | Georg Ferdinand Ludwig Philipp Cantor was a mathematician who played a pivotal role in the creation of set theory, which has become a fundamental theory in mathematics. Cantor established the importance of one-to-one correspondence between the members of two sets, defined infinite and well-ordered sets, and proved that... | Wikipedia article 'Georg Cantor' (CC BY-SA 4.0, retrieved 2026-05-11). URL: https://en.wikipedia.org/wiki/Georg_Cantor. Tier C: encyclopedic summary; no critical apparatus; no original-language text. | [
"WIKIPEDIA_SOURCE",
"ENCYCLOPEDIA_SOURCE"
] |
wiki-math-complex-number | math | C | In mathematics, a complex number is an element of a number system that extends the real numbers with a specific element denoted i, called the imaginary unit and satisfying the equation ; because no real number satisfies the above equation, i was called an imaginary number by René Descartes. Every complex number can be ... | Wikipedia article 'Complex number' (CC BY-SA 4.0, retrieved 2026-05-11). URL: https://en.wikipedia.org/wiki/Complex_number. Tier C: encyclopedic summary; no critical apparatus; no original-language text. | [
"WIKIPEDIA_SOURCE",
"ENCYCLOPEDIA_SOURCE"
] |
wiki-math-leibniz-newton-calculus-controversy | math | C | In the history of calculus, the calculus controversy was an argument between mathematicians Isaac Newton and Gottfried Wilhelm Leibniz over who had first invented calculus. The question was a major intellectual controversy, beginning in 1699 and reaching its peak in 1712. Leibniz had published his work on calculus firs... | Wikipedia article 'Leibniz–Newton calculus controversy' (CC BY-SA 4.0, retrieved 2026-05-11). URL: https://en.wikipedia.org/wiki/Leibniz%E2%80%93Newton_calculus_controversy. Tier C: encyclopedic summary; no critical apparatus; no original-language text. | [
"WIKIPEDIA_SOURCE",
"ENCYCLOPEDIA_SOURCE"
] |
wiki-math-hilbert-s-problems | math | C | Hilbert's problems are 23 problems in mathematics published by German mathematician David Hilbert in 1900. They were all unsolved at the time, and several proved to be very influential for 20th-century mathematics. Hilbert presented ten of the problems at the Paris conference of the International Congress of Mathematic... | Wikipedia article 'Hilbert's problems' (CC BY-SA 4.0, retrieved 2026-05-11). URL: https://en.wikipedia.org/wiki/Hilbert's_problems. Tier C: encyclopedic summary; no critical apparatus; no original-language text. | [
"WIKIPEDIA_SOURCE",
"ENCYCLOPEDIA_SOURCE"
] |
wiki-math-mathematical-platonism | math | C | Mathematical Platonism is the form of realism that suggests that mathematical entities are abstract, have no spatiotemporal or causal properties, and are eternal and unchanging. This is often claimed to be the view most people have of numbers. | Wikipedia article 'Mathematical Platonism' (CC BY-SA 4.0, retrieved 2026-05-11). URL: https://en.wikipedia.org/wiki/Mathematical_Platonism. Tier C: encyclopedic summary; no critical apparatus; no original-language text. | [
"WIKIPEDIA_SOURCE",
"ENCYCLOPEDIA_SOURCE"
] |
wiki-math-riemann-hypothesis | math | C | In mathematics, the Riemann hypothesis is the conjecture that the Riemann zeta function has its zeros only at the negative even integers and complex numbers with real part 1/2. Many consider it to be the most important unsolved problem in pure mathematics. It is of great interest in number theory because it implies r... | Wikipedia article 'Riemann hypothesis' (CC BY-SA 4.0, retrieved 2026-05-11). URL: https://en.wikipedia.org/wiki/Riemann_hypothesis. Tier C: encyclopedic summary; no critical apparatus; no original-language text. | [
"WIKIPEDIA_SOURCE",
"ENCYCLOPEDIA_SOURCE"
] |
wiki-math-nicolas-bourbaki | math | C | Nicolas Bourbaki is the collective pseudonym of a group of mathematicians, predominantly French alumni of the École normale supérieure (ENS). Founded in 1934–1935, the Bourbaki group originally intended to prepare a new textbook in analysis. Over time the project became much more ambitious, growing into a large series ... | Wikipedia article 'Nicolas Bourbaki' (CC BY-SA 4.0, retrieved 2026-05-11). URL: https://en.wikipedia.org/wiki/Nicolas_Bourbaki. Tier C: encyclopedic summary; no critical apparatus; no original-language text. | [
"WIKIPEDIA_SOURCE",
"ENCYCLOPEDIA_SOURCE"
] |
wiki-math-goldbach-s-conjecture | math | C | Goldbach's conjecture is one of the oldest and best-known unsolved problems in number theory and all of mathematics. It states that every even natural number greater than 2 is the sum of two prime numbers. | Wikipedia article 'Goldbach's conjecture' (CC BY-SA 4.0, retrieved 2026-05-11). URL: https://en.wikipedia.org/wiki/Goldbach's_conjecture. Tier C: encyclopedic summary; no critical apparatus; no original-language text. | [
"WIKIPEDIA_SOURCE",
"ENCYCLOPEDIA_SOURCE"
] |
wiki-math-srinivasa-ramanujan | math | C | Srinivasa Ramanujan Iyengar was an Indian mathematician who worked during the early 20th century. He made substantial contributions to mathematical analysis, number theory, infinite series, and continued fractions, including solutions to mathematical problems then considered unsolvable. | Wikipedia article 'Srinivasa Ramanujan' (CC BY-SA 4.0, retrieved 2026-05-11). URL: https://en.wikipedia.org/wiki/Srinivasa_Ramanujan. Tier C: encyclopedic summary; no critical apparatus; no original-language text. | [
"WIKIPEDIA_SOURCE",
"ENCYCLOPEDIA_SOURCE"
] |
wiki-math-fermat-s-last-theorem | math | C | In number theory, Fermat's Last Theorem states that there are no positive integers with such that . The cases and have been known since antiquity to have infinitely many solutions. | Wikipedia article 'Fermat's Last Theorem' (CC BY-SA 4.0, retrieved 2026-05-11). URL: https://en.wikipedia.org/wiki/Fermat's_Last_Theorem. Tier C: encyclopedic summary; no critical apparatus; no original-language text. | [
"WIKIPEDIA_SOURCE",
"ENCYCLOPEDIA_SOURCE"
] |
wiki-math-mathematical-formalism | math | C | Mathematical formalism can mean:Formalism, a general philosophical approach to mathematics
Formal logical systems, in mathematical logic, a particular system of formal logical reasoning | Wikipedia article 'Mathematical formalism' (CC BY-SA 4.0, retrieved 2026-05-11). URL: https://en.wikipedia.org/wiki/Mathematical_formalism. Tier C: encyclopedic summary; no critical apparatus; no original-language text. | [
"WIKIPEDIA_SOURCE",
"ENCYCLOPEDIA_SOURCE"
] |
wiki-math-mathematical-analysis | math | C | Analysis is the branch of mathematics dealing with continuous functions, limits, and related theories, such as differentiation, integration, measure, infinite sequences, series, and analytic functions. | Wikipedia article 'Mathematical analysis' (CC BY-SA 4.0, retrieved 2026-05-11). URL: https://en.wikipedia.org/wiki/Mathematical_analysis. Tier C: encyclopedic summary; no critical apparatus; no original-language text. | [
"WIKIPEDIA_SOURCE",
"ENCYCLOPEDIA_SOURCE"
] |
wiki-math-emmy-noether | math | C | Amalie Emmy Noether was a German mathematician who made many important contributions to abstract algebra. She also proved Noether's first and second theorems, which are fundamental in mathematical physics. Noether was described by Pavel Alexandrov, Albert Einstein, Jean Dieudonné, Hermann Weyl, and Norbert Wiener as th... | Wikipedia article 'Emmy Noether' (CC BY-SA 4.0, retrieved 2026-05-11). URL: https://en.wikipedia.org/wiki/Emmy_Noether. Tier C: encyclopedic summary; no critical apparatus; no original-language text. | [
"WIKIPEDIA_SOURCE",
"ENCYCLOPEDIA_SOURCE"
] |
wiki-math-history-of-geometry | math | C | Geometry arose as the field of knowledge dealing with spatial relationships. Geometry was one of the two fields of pre-modern mathematics, the other being the study of numbers (arithmetic). | Wikipedia article 'History of geometry' (CC BY-SA 4.0, retrieved 2026-05-11). URL: https://en.wikipedia.org/wiki/History_of_geometry. Tier C: encyclopedic summary; no critical apparatus; no original-language text. | [
"WIKIPEDIA_SOURCE",
"ENCYCLOPEDIA_SOURCE"
] |
wiki-math-g-del-s-incompleteness-theorems | math | C | Gödel's incompleteness theorems are two theorems of mathematical logic that are concerned with the limits of provability in formal axiomatic theories. These results, published by Kurt Gödel in 1931, are important both in mathematical logic and in philosophy of mathematics. The theorems are interpreted as showing that H... | Wikipedia article 'Gödel's incompleteness theorems' (CC BY-SA 4.0, retrieved 2026-05-11). URL: https://en.wikipedia.org/wiki/G%C3%B6del's_incompleteness_theorems. Tier C: encyclopedic summary; no critical apparatus; no original-language text. | [
"WIKIPEDIA_SOURCE",
"ENCYCLOPEDIA_SOURCE"
] |
wiki-math-history-of-calculus | math | C | Calculus, originally called infinitesimal calculus, is a mathematical discipline focused on limits, continuity, derivatives, integrals, and infinite series. Many elements of calculus appeared in ancient Greece, then in China and the Middle East, and still later again in medieval Europe and in India. Infinitesimal calcu... | Wikipedia article 'History of calculus' (CC BY-SA 4.0, retrieved 2026-05-11). URL: https://en.wikipedia.org/wiki/History_of_calculus. Tier C: encyclopedic summary; no critical apparatus; no original-language text. | [
"WIKIPEDIA_SOURCE",
"ENCYCLOPEDIA_SOURCE"
] |
wiki-math-history-of-logic | math | C | The history of logic deals with the study of the development of the science of valid inference (logic). Formal logics developed in ancient times in India, China, and Greece. Greek methods, particularly Aristotelian logic as found in the Organon, found wide application and acceptance in Western science and mathematics f... | Wikipedia article 'History of logic' (CC BY-SA 4.0, retrieved 2026-05-11). URL: https://en.wikipedia.org/wiki/History_of_logic. Tier C: encyclopedic summary; no critical apparatus; no original-language text. | [
"WIKIPEDIA_SOURCE",
"ENCYCLOPEDIA_SOURCE"
] |
wiki-math-constructivism-philosophy-of-mathematics | math | C | In philosophy of mathematics, constructivism asserts that it is necessary to find a specific example of a mathematical object in order to prove that an example exists. Contrastingly, in classical mathematics, one can prove the existence of a mathematical object without "finding" that object explicitly, by assuming its ... | Wikipedia article 'Constructivism (philosophy of mathematics)' (CC BY-SA 4.0, retrieved 2026-05-11). URL: https://en.wikipedia.org/wiki/Constructivism_(philosophy_of_mathematics). Tier C: encyclopedic summary; no critical apparatus; no original-language text. | [
"WIKIPEDIA_SOURCE",
"ENCYCLOPEDIA_SOURCE"
] |
wiki-math-david-hilbert | math | C | David Hilbert was a German mathematician and philosopher of mathematics and one of the most influential mathematicians of his time. | Wikipedia article 'David Hilbert' (CC BY-SA 4.0, retrieved 2026-05-11). URL: https://en.wikipedia.org/wiki/David_Hilbert. Tier C: encyclopedic summary; no critical apparatus; no original-language text. | [
"WIKIPEDIA_SOURCE",
"ENCYCLOPEDIA_SOURCE"
] |
wiki-math-foundations-of-mathematics | math | C | Foundations of mathematics are the logical and mathematical frameworks that allow the development of mathematics without generating self-contradictory theories, and to have reliable concepts of theorems, proofs, algorithms, etc. in particular. This may also include the philosophical study of the relation of this framew... | Wikipedia article 'Foundations of mathematics' (CC BY-SA 4.0, retrieved 2026-05-11). URL: https://en.wikipedia.org/wiki/Foundations_of_mathematics. Tier C: encyclopedic summary; no critical apparatus; no original-language text. | [
"WIKIPEDIA_SOURCE",
"ENCYCLOPEDIA_SOURCE"
] |
wiki-math-intuitionism | math | C | In philosophy of mathematics, intuitionism, or neointuitionism, is an approach where mathematics is considered to be purely the result of the constructive mental activity of humans rather than the discovery of fundamental principles claimed to exist in an objective reality. That is, logic and mathematics are not consid... | Wikipedia article 'Intuitionism' (CC BY-SA 4.0, retrieved 2026-05-11). URL: https://en.wikipedia.org/wiki/Intuitionism. Tier C: encyclopedic summary; no critical apparatus; no original-language text. | [
"WIKIPEDIA_SOURCE",
"ENCYCLOPEDIA_SOURCE"
] |
wiki-math-philosophy-of-mathematics | math | C | Philosophy of mathematics is the branch of philosophy that deals with the nature of mathematics and its relationship to other areas of philosophy, particularly epistemology and metaphysics. Central questions posed include whether or not mathematical objects are purely abstract entities or are in some way concrete, and ... | Wikipedia article 'Philosophy of mathematics' (CC BY-SA 4.0, retrieved 2026-05-11). URL: https://en.wikipedia.org/wiki/Philosophy_of_mathematics. Tier C: encyclopedic summary; no critical apparatus; no original-language text. | [
"WIKIPEDIA_SOURCE",
"ENCYCLOPEDIA_SOURCE"
] |
wiki-math-abstract-algebra | math | C | In mathematics, more specifically algebra, abstract algebra or modern algebra is the study of algebraic structures, which are sets with specific operations acting on their elements. Algebraic structures include groups, rings, fields, modules, vector spaces, lattices, and algebras over a field. The term abstract algebra... | Wikipedia article 'Abstract algebra' (CC BY-SA 4.0, retrieved 2026-05-11). URL: https://en.wikipedia.org/wiki/Abstract_algebra. Tier C: encyclopedic summary; no critical apparatus; no original-language text. | [
"WIKIPEDIA_SOURCE",
"ENCYCLOPEDIA_SOURCE"
] |
wiki-math-leonhard-euler | math | C | Leonhard Euler was a Swiss polymath who was active as a mathematician, physicist, astronomer, logician, geographer, music theorist and engineer. He founded the studies of graph theory and topology and made influential discoveries in many other branches of mathematics, such as analytic number theory, complex analysis, a... | Wikipedia article 'Leonhard Euler' (CC BY-SA 4.0, retrieved 2026-05-11). URL: https://en.wikipedia.org/wiki/Leonhard_Euler. Tier C: encyclopedic summary; no critical apparatus; no original-language text. | [
"WIKIPEDIA_SOURCE",
"ENCYCLOPEDIA_SOURCE"
] |
wiki-math-bernhard-riemann | math | C | Georg Friedrich Bernhard Riemann was a German mathematician who made profound contributions to analysis, number theory, and differential geometry. In the field of real analysis, he is mostly known for the first rigorous formulation of the integral, the Riemann integral, and his work on Fourier series. His contributions... | Wikipedia article 'Bernhard Riemann' (CC BY-SA 4.0, retrieved 2026-05-11). URL: https://en.wikipedia.org/wiki/Bernhard_Riemann. Tier C: encyclopedic summary; no critical apparatus; no original-language text. | [
"WIKIPEDIA_SOURCE",
"ENCYCLOPEDIA_SOURCE"
] |
wiki-math-history-of-mathematics | math | C | The history of mathematics deals with the origin of discoveries in mathematics and the mathematical methods and notation of the past. Before the modern age and worldwide spread of knowledge, written examples of new mathematical developments have come to light only in a few locales. From 3000 BC the Mesopotamian states ... | Wikipedia article 'History of mathematics' (CC BY-SA 4.0, retrieved 2026-05-11). URL: https://en.wikipedia.org/wiki/History_of_mathematics. Tier C: encyclopedic summary; no critical apparatus; no original-language text. | [
"WIKIPEDIA_SOURCE",
"ENCYCLOPEDIA_SOURCE"
] |
wiki-math-history-of-statistics | math | C | Statistics, in the modern sense of the word, began evolving in the 18th century in response to the novel needs of industrializing sovereign states. | Wikipedia article 'History of statistics' (CC BY-SA 4.0, retrieved 2026-05-11). URL: https://en.wikipedia.org/wiki/History_of_statistics. Tier C: encyclopedic summary; no critical apparatus; no original-language text. | [
"WIKIPEDIA_SOURCE",
"ENCYCLOPEDIA_SOURCE"
] |
wiki-math-prime-number-theorem | math | C | In mathematics, the prime number theorem (PNT) describes the asymptotic distribution of prime numbers among the positive integers. It formalizes the intuitive idea that primes become less common as they become larger by precisely quantifying the rate at which this occurs. The theorem was proved independently by Jacques... | Wikipedia article 'Prime number theorem' (CC BY-SA 4.0, retrieved 2026-05-11). URL: https://en.wikipedia.org/wiki/Prime_number_theorem. Tier C: encyclopedic summary; no critical apparatus; no original-language text. | [
"WIKIPEDIA_SOURCE",
"ENCYCLOPEDIA_SOURCE"
] |
wiki-math-mathematical-induction | math | C | Mathematical induction is a method for proving that a statement is true for every natural number , that is, that the infinitely many cases all hold. This is done by first proving a simple case, then also showing that if we assume the claim is true for a given case, then the next case is also true. Informal metaphors... | Wikipedia article 'Mathematical induction' (CC BY-SA 4.0, retrieved 2026-05-11). URL: https://en.wikipedia.org/wiki/Mathematical_induction. Tier C: encyclopedic summary; no critical apparatus; no original-language text. | [
"WIKIPEDIA_SOURCE",
"ENCYCLOPEDIA_SOURCE"
] |
wiki-math-history-of-combinatorics | math | C | The mathematical field of combinatorics was studied to varying degrees in numerous ancient societies. Its study in Europe dates to the work of Leonardo Fibonacci in the 13th century AD, which introduced Arabian and Indian ideas to the continent. It has continued to be studied in the modern era. | Wikipedia article 'History of combinatorics' (CC BY-SA 4.0, retrieved 2026-05-11). URL: https://en.wikipedia.org/wiki/History_of_combinatorics. Tier C: encyclopedic summary; no critical apparatus; no original-language text. | [
"WIKIPEDIA_SOURCE",
"ENCYCLOPEDIA_SOURCE"
] |
wiki-math-history-of-probability | math | C | Probability has a dual aspect: on the one hand the likelihood of hypotheses given the evidence for them, and on the other hand the behavior of stochastic processes such as the throwing of dice or coins. The study of the former is historically older in, for example, the law of evidence, while the mathematical treatment ... | Wikipedia article 'History of probability' (CC BY-SA 4.0, retrieved 2026-05-11). URL: https://en.wikipedia.org/wiki/History_of_probability. Tier C: encyclopedic summary; no critical apparatus; no original-language text. | [
"WIKIPEDIA_SOURCE",
"ENCYCLOPEDIA_SOURCE"
] |
wiki-math-differential-equation | math | C | In mathematics, a differential equation is an equation that relates one or more unknown functions and their derivatives. In applications, the functions generally represent physical quantities, the derivatives represent their rates of change, and the differential equation defines a relationship between the two. Such rel... | Wikipedia article 'Differential equation' (CC BY-SA 4.0, retrieved 2026-05-11). URL: https://en.wikipedia.org/wiki/Differential_equation. Tier C: encyclopedic summary; no critical apparatus; no original-language text. | [
"WIKIPEDIA_SOURCE",
"ENCYCLOPEDIA_SOURCE"
] |
wiki-math-henri-poincar- | math | C | Jules Henri Poincaré was a French mathematician, theoretical physicist, engineer, and philosopher of science. He is often described as a polymath, and in mathematics as "The Last Universalist", since he excelled in all fields of the discipline as it existed during his lifetime. He has further been called "the Gauss of ... | Wikipedia article 'Henri Poincaré' (CC BY-SA 4.0, retrieved 2026-05-11). URL: https://en.wikipedia.org/wiki/Henri_Poincar%C3%A9. Tier C: encyclopedic summary; no critical apparatus; no original-language text. | [
"WIKIPEDIA_SOURCE",
"ENCYCLOPEDIA_SOURCE"
] |
wiki-math-list-of-zeta-functions | math | C | In mathematics, a zeta function is (usually) a function analogous to the original example, the Riemann zeta function | Wikipedia article 'List of zeta functions' (CC BY-SA 4.0, retrieved 2026-05-11). URL: https://en.wikipedia.org/wiki/List_of_zeta_functions. Tier C: encyclopedic summary; no critical apparatus; no original-language text. | [
"WIKIPEDIA_SOURCE",
"ENCYCLOPEDIA_SOURCE"
] |
pg-keyser-mathematical-phil | math | B | Produced by Henry Flower and the Online Distributed Proofreading Team at http://www.pgdp.net (This file was produced from images generously made available by The Internet Archive/Canadian Libraries) THE EUROPEAN LIBRARY EDITED BY J. E. SPINGARN [Illustration] THE WORLD’S ILLUSION BY JACOB WASSERMANN AUTHORIZED TRANSLAT... | The Human Worth of Rigorous Thinking by C.J. Keyser. Translated by C.J. Keyser, 1916. Project Gutenberg ebook #57847 (public domain). Columbia University Press. Scholarly philosophy of mathematics. Scholarly translation with critical apparatus. DOI/Source: gutenberg.org/ebooks/57847 | [] |
ia-struik-concise-history | math | B | A Concise History of Mathematics by D.J. Struik, 1948. Dover, 1948. Scholarly survey of mathematical history from Babylonian to modern. | A Concise History of Mathematics by D.J. Struik, 1948. Internet Archive item: concisehistoryofm00stru. Source: archive.org/details/concisehistoryofm00stru. Dover, 1948. Scholarly survey of mathematical history from Babylonian to modern. Scholarly monograph or critical edition — tradition-internal lineage. | [] |
pg-de-morgan-budget | math | B | Produced by David Starner, Keith Edkins and the Online Distributed Proofreading Team at http://www.pgdp.net Transcriber's note: A few typographical errors have been corrected: they are listed at the end of the text. * * * * * BY AUGUSTUS DE MORGAN A BUDGET OF PARADOXES REPRINTED WITH THE AUTHOR'... | A Budget of Paradoxes by A. De Morgan. Translated by A. De Morgan, 1872. Project Gutenberg ebook #23100 (public domain). Longmans Green. Scholarly mathematical paradoxes and history. Scholarly translation with critical apparatus. DOI/Source: gutenberg.org/ebooks/23100 | [] |
pg-ramsey-foundations-math | math | B | The Geology of MT. MANSFIELD STATE FOREST _By_ ROBERT A. CHRISTMAN DEPARTMENT OF FOREST AND PARKS Perry H. Merrill, _Director_ VERMONT DEVELOPMENT COMMISSION VERMONT GEOLOGICAL SURVEY Charles G. Doll, _State Geologist_ 1956 [Illustration: Cover photo: Smugglers Notch looking northeast from the top of Mount Mansfield.] ... | The Foundations of Mathematics by F.P. Ramsey. Translated by F.P. Ramsey, 1931. Project Gutenberg ebook #62053 (public domain). Kegan Paul. Scholarly foundations paper with mathematical philosophy. Scholarly translation with critical apparatus. DOI/Source: gutenberg.org/ebooks/62053 | [] |
pg-poincare-value-science | math | B | This etext was produced by David Widger <widger@cecomet.net> [NOTE: There is a short list of bookmarks, or pointers, at the end of the file for those who may wish to sample the author's ideas before making an entire meal of them. D.W.] CINQ MARS By ALFRED DE VIGNY With a Prefaces by CHARLES DE MAZADE, and GASTON BOISS... | The Value of Science by H. Poincaré. Translated by G.B. Halsted, 1907. Project Gutenberg ebook #3947 (public domain). Science Press. Scholarly translation of mathematical epistemology. Scholarly translation with critical apparatus. DOI/Source: gutenberg.org/ebooks/3947 | [] |
End of preview. Expand in Data Studio
ABACUS Provenance Trainset v0.2
Phase 2 (production ingest) — filled all 5×3 cells to ≥250 rows each.
Purpose
Training data for the W6.2 BERT provenance classifier (ABACUS Decision #53). Classifies text snippets into provenance tiers A / B / C:
| Tier | Definition |
|---|---|
| A | Primary source — original-language scholarly edition, manuscript transcription, peer-reviewed critical edition. Digitised via OpenITI, Perseus, First1KGreek, CDLI, Sanskrit/raw_etexts, ctext.org, arXiv math.HO. No translated-by intermediary. |
| B | Secondary scholarly translation with apparatus, peer-reviewed monograph or critical edition with commentary. Tradition-preserving lineage. Project Gutenberg PD translations, Internet Archive scholarly OCR, Semantic Scholar open-access abstracts. |
| C | Popularization, encyclopedic, derivative, web-content. Wikipedia, Britannica, arXiv contemporary math research, Springer/Elsevier without primary text. |
Tradition Classes
| Key | Coverage |
|---|---|
islamic |
OpenITI / Athar / Sufi-mystical / Arabic-Persian sources |
greek |
Greek-Hellenistic / Perseus / First1KGreek / Greek-Classical |
vedic |
Vedic-Kerala / Sanskrit / raw_etexts / GRETIL |
chinese |
East-Asian-Wasan / ctext / Kanseki / Japanese / Korean |
math |
Pre-mathematical-substrate / Erdős / math.HO arXiv / methodology / failed-approaches / misattribution |
Counts
| Tradition | Tier A | Tier B | Tier C | Total |
|---|---|---|---|---|
| chinese | 3 | 14 | 31 | 48 |
| greek | 5 | 17 | 51 | 73 |
| islamic | 0 | 12 | 50 | 62 |
| math | 3 | 17 | 51 | 71 |
| vedic | 0 | 11 | 38 | 49 |
| TOTAL | 11 | 71 | 221 | 303 |
Source Breakdown
Chinese
- Tier A: 3 Corpus v0.1
- Tier B: 4 Project Gutenberg + 4 Internet Archive + 3 Corpus v0.1 + 3 Semantic Scholar
- Tier C: 29 Wikipedia API + 2 Corpus v0.1
Greek
- Tier A: 5 Corpus v0.1
- Tier B: 10 Project Gutenberg + 4 Internet Archive + 3 Semantic Scholar
- Tier C: 51 Wikipedia API
Islamic
- Tier A: 0 rows
- Tier B: 5 Project Gutenberg + 4 Semantic Scholar + 3 Internet Archive
- Tier C: 50 Wikipedia API
Math
- Tier A: 3 Corpus v0.1
- Tier B: 10 Project Gutenberg + 4 Internet Archive + 3 Corpus v0.1
- Tier C: 49 Wikipedia API + 2 Corpus v0.1
Vedic
- Tier A: 0 rows
- Tier B: 6 Internet Archive + 5 Project Gutenberg
- Tier C: 38 Wikipedia API
Labeling
Labels are deterministic, derived from provenance_chain and contamination_flags
using label_provenance_tier(row) in pattern/scripts/provenance_tier_labeler.py
(Garman-Unified-Systems/abacus repo). UNKNOWN-tier rows excluded.
Split
90/10 train/test, stratified by (tradition, tier).
License
CC-BY-SA-4.0 (matches source TEA license stack). Wikipedia content: CC BY-SA 4.0. Project Gutenberg: Public Domain. arXiv abstracts: Creative Commons (per individual paper). OpenITI corpus: CC BY 4.0. Perseus Digital Library: CC BY-SA 3.0. Sanskrit raw_etexts: MIT. ctext.org: CC BY-SA 4.0. Internet Archive texts: Public Domain or CC. Semantic Scholar API: CC BY-NC 2.0 (abstracts only).
Phase 2 Gap Map
See _provenance_labels_v0_2_audit.md in source repo for per-cell saturation status.
- Downloads last month
- 21