250 CE
Diophantus Writes Arithmetica
Diophantus of Alexandria writes Arithmetica, a foundational text in number theory and algebraic geometry, introducing symbolic notation and solving polynomial equations. #algebra #history
Chronological Storyline (45 Milestones)
263 CE
Liu Hui's Geometric Algebra
Chinese mathematician Liu Hui provides commentary on The Nine Chapters on the Mathematical Art, introducing algebraic methods for solving geometric problems, including area and volume calculations. #algebra #china
By Unknown - "Liu Hui (220 - 280) - Biography - MacTutor History of Mathematics" https://mathshistory.st-andrews.ac.uk/Biographies/Liu_Hui/, CC BY-SA 4.0, https://commons.wikimedia.org/w/index.php?curid=130481910
628 CE
Brahmagupta's Work on Quadratic Equations
Indian mathematician Brahmagupta presents solutions to quadratic equations and introduces rules for zero in his text Brahmasphutasiddhanta, influencing later algebraic geometry. #algebra #india
820 CE
Al-Khwarizmi's Algebra
Persian mathematician Al-Khwarizmi writes 'The Compendious Book on Calculation by Completion and Balancing', introducing systematic solving of linear and quadratic equations. #algebra #islamic
By Zarateman - Own work, CC0, https://commons.wikimedia.org/w/index.php?curid=162213187
1070 CE
Omar Khayyam's Geometric Solutions to Cubic Equations
Persian mathematician Omar Khayyam classifies cubic equations and solves them geometrically using intersecting conics, advancing algebraic geometry. #algebra #islamic
By Alireza Javaheri - https://web.archive.org/web/20161024154356/http://www.panoramio.com/photo/85093358, CC BY 3.0, https://commons.wikimedia.org/w/index.php?curid=55909539
1150 CE
Bhaskara II's Algebraic Treatises
Indian mathematician Bhaskara II writes Bijaganita (Algebra) and Siddhanta Siromani, solving quadratic and cubic equations and introducing concepts of zero and infinity. #algebra #india
By Unknown author - Own work, Public domain, https://commons.wikimedia.org/w/index.php?curid=150275955
1247 CE
Qin Jiushao's Numerical Solutions of Polynomials
Chinese mathematician Qin Jiushao develops methods for solving high-degree polynomial equations using a form of Horner's method, contributing to algebraic geometry. #algebra #china
By Qin Jiushao 秦九韶 - 1842 printing Shu Shu Jiu Zhang, Public domain, https://commons.wikimedia.org/w/index.php?curid=3414657
1270 CE
Al-Tusi's Treatise on Cubics
Nasir al-Din al-Tusi classifies cubic equations and provides geometric solutions, advancing algebraic geometry in the Islamic world. #algebra #islamic
By Unknown author - scan of stamp 30 May 2006, Public domain, https://commons.wikimedia.org/w/index.php?curid=829461
1591 CE
Vieta's Symbolic Algebra
François Viète introduces symbolic algebra, using letters for unknowns and constants, paving the way for algebraic geometry. #algebra #history
By Unknown author, Public domain, https://commons.wikimedia.org/w/index.php?curid=81021
1637 CE
Descartes' Analytic Geometry
René Descartes publishes La Géométrie, linking algebra and geometry by representing curves with equations, laying the foundation for algebraic geometry. #geometry #algebra
By Original uploader was User:Caton at [1] - Originally from fr.wikipedia; description page is/was here., Public domain, https://commons.wikimedia.org/w/index.php?curid=1379032
1658 CE
Pascal's Hexagrammum Mysticum
Blaise Pascal discovers the mystic hexagram theorem for conics, an early result in projective algebraic geometry. #geometry #algebra
By Wcherowi - Own work, CC BY-SA 3.0, https://commons.wikimedia.org/w/index.php?curid=22820278
1665 CE
Newton's Work on Curves
Isaac Newton develops the binomial theorem and applies algebraic methods to study curves, contributing to the theory of plane algebraic curves. #algebra #curves
By Godfrey Kneller - File:Portrait of Sir Isaac Newton, 1689.jpg from https://exhibitions.lib.cam.ac.uk/linesofthought/artifacts, Public domain, https://commons.wikimedia.org/w/index.php?curid=132521185
1729 CE
Euler's Introduction to Analysis of the Infinite
Leonhard Euler publishes Introductio in analysin infinitorum, systematically treating algebraic functions and curves, influencing algebraic geometry. #algebra #curves
By Jakob Emanuel Handmann - This file was derived from: Leonhard Euler.jpg Edited by: Bammesk Original source: Kunstmuseum Basel, Public domain, https://commons.wikimedia.org/w/index.php?curid=113056351
1769 CE
Lagrange's Symmetric Functions
Joseph-Louis Lagrange studies symmetric functions, important for the algebra underlying algebraic geometry. #algebra #history
By Unknown author - File:Joseph_Louis_Lagrange.jpg, CC0, https://commons.wikimedia.org/w/index.php?curid=155608232
1827 CE
Plücker's Formulae for Plane Curves
Julius Plücker publishes his work on analytic geometry, deriving formulas (Plücker formulas) relating invariants of plane algebraic curves. #algebra #geometry
By Rudolf Hoffmann (Lithograph), nach einer Photographie von Schafgans in Bonn. - [1]; transferred from en.wikipedia; description page was here 10:04, 15 June 2004 Magnus Manske 728x909 (133,849 bytes), Public domain, https://commons.wikimedia.org/w/index.php?curid=813547
1839 CE
Salmon's Treatise on Higher Plane Curves
Irish mathematician George Salmon publishes a comprehensive treatise on algebraic curves, systematizing the subject and introducing many theorems. #algebra #curves
By Werner & Son - Cassell's universal portrait gallery: https://archive.org/stream/cassellsuniversa00londiala#page/468/mode/2up, Public domain, https://commons.wikimedia.org/w/index.php?curid=31269581
1844 CE
Grassmann's Linear Algebra
Hermann Grassmann publishes 'Die lineale Ausdehnungslehre', developing vector spaces and exterior algebra, foundational for modern algebraic geometry. #algebra #geometry
By Unknown author - From the beginning of vol. 1 of Grassmann's collected works (1894), Public domain, https://commons.wikimedia.org/w/index.php?curid=174414110
1854 CE
Riemann's Foundations of Algebraic Geometry
Bernhard Riemann introduces the concept of Riemann surfaces and uses topological methods to study algebraic curves, fundamentally transforming algebraic geometry. #geometry #algebra
By Unknown author - http://www.sil.si.edu/digitalcollections/hst/scientific-identity/explore.htm according to the German Wikipedia., Public domain, https://commons.wikimedia.org/w/index.php?curid=27383
1870 CE
Clebsch and Gordan on Algebraic Curves
Alfred Clebsch and Paul Gordan apply invariant theory to algebraic curves, developing the theory of plane curves and their classification. #algebra #curves
By Unknown author - Unknown source, Public domain, https://commons.wikimedia.org/w/index.php?curid=928786
1882 CE
Dedekind and Weber's Algebraic Functions
Richard Dedekind and Heinrich Weber develop a purely algebraic theory of algebraic functions, linking algebraic geometry with number theory. #algebra #numbertheory
By Unknown (Mondadori Publishers) - https://www.gettyimages.co.uk/detail/news-photo/portrait-of-the-german-mathematician-richard-dedekind-1900s-news-photo/141551154, Public domain, https://commons.wikimedia.org/w/index.php?curid=41284791
1885 CE
Poincaré's Analytic Functions
Henri Poincaré develops uniformization of Riemann surfaces and studies algebraic curves via automorphic functions. #algebra #curves
By Unknown author - Popular Science Monthly Volume 82, Public domain, https://commons.wikimedia.org/w/index.php?curid=20644432
1893 CE
Max Noether's Contributions to Algebraic Geometry
Max Noether, father of Emmy Noether, publishes fundamental results on algebraic curves and surfaces, including the Riemann-Roch theorem generalization. #algebra #curves
By University of Heidelberg - http://www.ub.uni-heidelberg.de/helios/fachinfo/www/math/edd/uni-archiv/noether.htm, Public domain, https://commons.wikimedia.org/w/index.php?curid=167770415
1900 CE
Hilbert's Problem on Schubert Calculus
David Hilbert poses the 15th problem, asking for a rigorous foundation for Schubert's enumerative calculus, spurring developments in algebraic geometry. #algebra #geometry
1913 CE
Emmy Noether's Invariant Theory
Emmy Noether publishes her work on invariant theory under Albert Einstein, laying algebraic foundations for modern algebraic geometry. #algebra #women
By Unknown authorUnknown author Publisher: Mathematical Association of America [3], Brooklyn Museum [4], Agnes Scott College [5], [6] - Emmy Noether (1882-1935), Archived, Public domain, https://commons.wikimedia.org/w/index.php?curid=158126186
1926 CE
Zariski's Algebraic Foundations
Oscar Zariski begins his work on algebraic geometry over arbitrary fields, introducing Zariski topology and the concept of normal varieties. #algebra #geometry
By George Bergman - https://opc.mfo.de/detail?photo_id=6262, GFDL 1.2, https://commons.wikimedia.org/w/index.php?curid=6090840
1930 CE
van der Waerden's Modern Algebra
Bartel Leendert van der Waerden publishes 'Moderne Algebra', systematically using algebraic structures and influencing the development of algebraic geometry. #algebra #history
By Böhm, W. Ernst - This image is from the collection of the ETH-Bibliothek and has been published on Wikimedia Commons as part of a cooperation with Wikimedia CH. Corrections and additional information are welcome., CC BY-SA 4.0, https://commons.wikimedia.org/w/index.php?curid=103244960
1946 CE
André Weil's Foundations of Algebraic Geometry
André Weil publishes 'Foundations of Algebraic Geometry', establishing a rigorous foundation using abstract algebra, and later formulates the Weil conjectures. #algebra #geometry
By Konrad Jacobs - opc.mfo.de/detail?would like to publish=1&photo id=8654, CC BY-SA 2.0 de, https://commons.wikimedia.org/w/index.php?curid=163826140
1954 CE
Kodaira's Vanishing Theorem
Kunihiko Kodaira proves the vanishing theorem for algebraic varieties, a key tool in classifying complex manifolds and algebraic geometry. #geometry #algebra
By Konrad Jacobs, MFO - https://opc.mfo.de/detail?photoID=2327, CC BY-SA 2.0 de, https://commons.wikimedia.org/w/index.php?curid=3899822
1955 CE
Serre's FAC (Faisceaux Algébriques Cohérents)
Jean-Pierre Serre publishes 'Faisceaux Algébriques Cohérents', applying sheaf theory to algebraic geometry, introducing coherent sheaves. #algebra #geometry
By Mediterranean Institute for the Mathematical Sciences - Extracted from https://www.youtube.com/watch?v=wXCo54RuP1s&t=1502s, CC BY 3.0, https://commons.wikimedia.org/w/index.php?curid=110894720
1958 CE
Grothendieck's Revolution: Scheme Theory
Alexander Grothendieck begins developing the theory of schemes, profoundly transforming algebraic geometry by unifying topology, algebra, and geometry. #algebra #geometry
By Konrad Jacobs, Erlangen, Copyright by MFO / Original uploader was AEDP at it.wikipedia - Cutted from File:Alexander_Grothendieck.jpg, CC BY-SA 4.0, https://commons.wikimedia.org/w/index.php?curid=154118951
1960 CE
Serre's GAGA Principle
Jean-Pierre Serre publishes 'Géométrie algébrique et géométrie analytique', establishing an equivalence between complex algebraic varieties and complex analytic spaces. #algebra #geometry
1961 CE
Grothendieck's EGA
Alexander Grothendieck begins publishing EGA, laying out the foundations of scheme theory in monumental detail. #algebra #geometry
1963 CE
Hironaka's Resolution of Singularities
Heisuke Hironaka proves that algebraic varieties over fields of characteristic zero can be resolved, eliminating singularities, a landmark in algebraic geometry. #algebra #singularities
By 日本学士院 - https://www.japan-acad.go.jp/japanese/members/4/hironaka_heisuke.html, CC BY 4.0, https://commons.wikimedia.org/w/index.php?curid=143448854
1964 CE
Buchberger's Gröbner Bases Algorithm
Bruno Buchberger introduces Gröbner bases in his PhD thesis, providing a computational tool for solving polynomial equations, revolutionizing computational algebraic geometry. #algebra #computation
1970 CE
Mumford's Geometric Invariant Theory
David Mumford publishes 'Geometric Invariant Theory', providing methods to construct moduli spaces of algebraic curves and other objects. #algebra #geometry
By George Bergman - https://opc.mfo.de/detail?photo_id=13740, GFDL 1.2, https://commons.wikimedia.org/w/index.php?curid=25005390
1972 CE
Deligne Proves Weil Conjectures
Pierre Deligne completes the proof of the Weil conjectures using étale cohomology, a profound achievement linking algebraic geometry and number theory. #algebra #numbertheory
By "copyright C. J. Mozzochi, Princeton N.J" - http://www.mozzochi.org/deligne60/Deligne1/_DSC0017.jpg, Attribution, https://commons.wikimedia.org/w/index.php?curid=110967143
1983 CE
Faltings Proves Mordell Conjecture
Gerd Faltings proves the Mordell conjecture, showing that genus >1 curves have only finitely many rational points, a major result in arithmetic geometry. #algebra #numbertheory
By Renate Schmid - https://opc.mfo.de/detail?photoID=7513, CC BY-SA 2.0 de, https://commons.wikimedia.org/w/index.php?curid=187216638
1984 CE
Mori's Minimal Model Program
Shigefumi Mori launches the minimal model program (MMP) for classifying algebraic varieties, earning a Fields Medal for his work on threefolds. #algebra #geometry
By 大臣官房人事課 - 令和3年度 文化勲章受章者：文部科学省, CC BY 4.0, https://commons.wikimedia.org/w/index.php?curid=112412706
1990 CE
Mirror Symmetry in Algebraic Geometry
Physicists and mathematicians discover mirror symmetry, linking algebraic geometry of Calabi-Yau manifolds and enumerative geometry. #algebra #physics )
1993 CE
Wiles Proves Fermat's Last Theorem
Andrew Wiles proves Fermat's Last Theorem using advanced algebraic geometry, including modularity of elliptic curves, a historic breakthrough. #algebra #numbertheory
By "copyright C. J. Mozzochi, Princeton N.J" - http://www.mozzochi.org/deligne60/Deligne1/_DSC0024.jpg, Attribution, https://commons.wikimedia.org/w/index.php?curid=2635913
1994 CE
Taylor and Wiles Complete Proof
Richard Taylor and Andrew Wiles fill the gap in the original proof, confirming Fermat's Last Theorem and linking elliptic curves to Galois representations. #algebra #numbertheory )
By George Bergman - https://opc.mfo.de/detail?photo_id=13009, GFDL 1.2, https://commons.wikimedia.org/w/index.php?curid=18070147
2000 CE
Tropical Geometry Emerges
Tropical geometry, a piecewise-linear analogue of algebraic geometry, develops as a tool for solving problems in enumerative geometry. #algebra #geometry
By Kilom691 - Own work, CC BY-SA 4.0, https://commons.wikimedia.org/w/index.php?curid=41071159
2002 CE
Lafforgue's Langlands Correspondence
Laurent Lafforgue proves the Langlands correspondence for function fields using algebraic geometry, particularly moduli stacks of shtukas. #algebra #numbertheory
By Institut des Hautes Études Scientifiques (IHÉS) - Issu de https://www.youtube.com/watch?v=YQthqp5gplc, CC BY 3.0, https://commons.wikimedia.org/w/index.php?curid=50468182
2009 CE
Ngô Bảo Châu Proves Fundamental Lemma
Ngô Bảo Châu proves the fundamental lemma in the Langlands program using geometric methods and the Hitchin fibration, earning a Fields Medal. #algebra #geometry
By Nguyentrongphu - Own work, CC BY-SA 4.0, https://commons.wikimedia.org/w/index.php?curid=169783860
2012 CE
Scholze Introduces Perfectoid Spaces
Peter Scholze introduces perfectoid spaces, a new concept in arithmetic geometry that simplifies many proofs in number theory and algebraic geometry. #algebra #numbertheory
By George Bergman - https://commons.wikimedia.org/wiki/File:Peter_Scholze_2014_Berkeley_(version_2).jpg, CC BY-SA 4.0, https://commons.wikimedia.org/w/index.php?curid=180277069