250 BCE
Archimedes Develops Exhaustion Method
Archimedes of Syracuse uses the method of exhaustion to compute areas and volumes, anticipating integral calculus. #calculus #history
Chronological Storyline (32 Milestones)
499 CE
Aryabhata Tables Sine Differences
Indian mathematician Aryabhata provides sine difference tables, a precursor to differentiation. #indianmathematics #calculus
By Cpjha13 - Own work, CC BY-SA 4.0, https://commons.wikimedia.org/w/index.php?curid=49883192
1020 CE
Ibn al-Haytham Sums Powers
Ibn al-Haytham (Alhazen) derives formulas for sums of powers, contributing to integral calculus. #islamicgoldenage #calculus
By Adolph Boÿ, engraved by Jeremias Falck. Used as the frontispiece to Johannes Hevelius, Selenographia, 1647 - https://www.loc.gov/resource/rbctos.2017rosen1321/?sp=9&r=0.059,0.617,0.327,0.182,0, Public domain, https://commons.wikimedia.org/w/index.php?curid=165125519
1400 CE
Madhava Discovers Power Series
Madhava of Sangamagrama develops infinite series expansions for trigonometric functions, laying groundwork for calculus. #indianmathematics #calculus
1635 CE
Bonaventura Cavalieri Publishes Geometry of Indivisibles
Cavalieri introduces the method of indivisibles, a step toward integral calculus. #calculus #history
By Christopher Grattoni - demonstrations.wolfram.com, CC BY 4.0, https://commons.wikimedia.org/w/index.php?curid=145384849
1637 CE
Fermat Uses Adequality
Pierre de Fermat develops a method of adequality for finding tangents and maxima, a precursor to differentiation. #calculus #history
By Unknown author - https://web.archive.org/web/20191028044928/http://www-groups.dcs.st-and.ac.uk/~history/PictDisplay/Fermat.html, Public domain, https://commons.wikimedia.org/w/index.php?curid=36804
1666 CE
Newton Develops Fluxions
Isaac Newton begins work on his method of fluxions, an early form of differential calculus. #calculus #newton
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
1684 CE
Leibniz Publishes First Calculus Paper
Gottfried Wilhelm Leibniz publishes 'Nova Methodus pro Maximis et Minimis', introducing differential calculus notation. #calculus #leibniz
By Christoph Bernhard Francke - Herzog Anton Ulrich-Museum, online, Public domain, https://commons.wikimedia.org/w/index.php?curid=53159699
1687 CE
Newton Publishes Principia
Isaac Newton's Principia Mathematica uses calculus concepts to describe motion and gravitation. #calculus #physics
By The original uploader was Zhaladshar at English Wikisource. - Transferred from en.wikisource to Commons. (previous image from another copy) Internet Archive (current image from the Bern Dibner copy), Public domain, https://commons.wikimedia.org/w/index.php?curid=2681838
1696 CE
L'Hôpital's Rule Published
Guillaume de L'Hôpital publishes the first calculus textbook, containing L'Hôpital's rule for limits. #calculus #history
1734 CE
Berkeley Criticizes Calculus
George Berkeley publishes 'The Analyst', criticizing the logical foundations of calculus, spurring rigor. #calculus #philosophy
By George Berkeley - https://archive.org/details/theanalystoradis00berkuoft/page/n3/mode/2up, Public domain, https://commons.wikimedia.org/w/index.php?curid=181022569
1748 CE
Euler Publishes Introductio in Analysin Infinitorum
Leonhard Euler's work systematizes calculus and introduces many modern notations. #calculus #euler
By Cronholm144 at English Wikipedia - Transferred from en.wikipedia to Commons., CC BY-SA 3.0, https://commons.wikimedia.org/w/index.php?curid=3128774
1755 CE
Euler Publishes Institutiones Calculi Differentialis
Euler formalizes differential calculus with foundations in infinite series. #calculus #euler
By Leonhard Euler - http://doi.org/10.3931/e-rara-3788 (e-rara.ch), Public domain, https://commons.wikimedia.org/w/index.php?curid=69561606
1768 CE
Lagrange Uses Functional Approach
Joseph-Louis Lagrange attempts to base calculus on algebraic functions, introducing the term 'derivative'. #calculus #history
By Unknown author - File:Joseph_Louis_Lagrange.jpg, CC0, https://commons.wikimedia.org/w/index.php?curid=155608232
1797 CE
Lagrange Publishes Théorie des Fonctions Analytiques
Lagrange's treatise seeks to put calculus on a rigorous algebraic foundation, influencing later analysis. #calculus #history
1821 CE
Cauchy Develops Rigorous Limits
Augustin-Louis Cauchy publishes Cours d'Analyse, defining limits, continuity, and derivatives with epsilon-delta rigor. #calculus #analysis
By Augustin Louis Cauchy - screenshot of https://archive.org/details/bub_gb_OlxT3B6EjykC/page/n5/mode/2up, CC0, https://commons.wikimedia.org/w/index.php?curid=94855343
1823 CE
Cauchy Defines Definite Integral
Cauchy gives the first rigorous definition of the definite integral as a limit of sums. #calculus #analysis
By Public domain - Library of Congress Prints and Photographs Division. From an illustration in: Das neunzehnte Jahrhundert in Bildnissen / Karl Werckmeister, ed. Berlin : Kunstverlag der photographische gesellschaft, 1840, vol. V, no. 581., Public domain, https://commons.wikimedia.org/w/index.php?curid=7059486
1854 CE
Riemann Integrals Introduced
Bernhard Riemann introduces the Riemann integral, formalizing integration of arbitrary functions. #calculus #analysis
By Brad219 - Own work created using Inkscape 1.3. Redrawn from original PNG source authored by KSmrq, CC0, https://commons.wikimedia.org/w/index.php?curid=150414772
1872 CE
Weierstrass Presents Continuous Non-Differentiable Function
Karl Weierstrass shocks the mathematical world with a function that is everywhere continuous but nowhere differentiable. #calculus #analysis
By Eeyore22 - Own work, Public domain, https://commons.wikimedia.org/w/index.php?curid=5075959
1881 CE
Gibbs Develops Vector Calculus
Josiah Willard Gibbs publishes elements of vector analysis, simplifying equations in physics. #calculus #vectors
By Unknown. Uploaded by Serge Lachinov (обработка для wiki) - Frontispiece of The Scientific Papers of J. Willard Gibbs, in two volumes, eds. H. A. Bumstead and R. G. Van Name, (London and New York: Longmans, Green, and Co., 1906), Public domain, https://commons.wikimedia.org/w/index.php?curid=7919387
1887 CE
Poincaré Foundes Algebraic Topology
Henri Poincaré's work on topology uses calculus concepts, influencing differential geometry. #calculus #topology
By Unknown author - Popular Science Monthly Volume 82, Public domain, https://commons.wikimedia.org/w/index.php?curid=20644432
1902 CE
Lebesgue Introduces Measure Theory
Henri Lebesgue develops the Lebesgue integral, generalizing Riemann integration. #calculus #analysis
By ~~helix84 15:43, 27 November 2006 (UTC) - own work, based on en:Image:Integral-area-under-curve.png, Public domain, https://commons.wikimedia.org/w/index.php?curid=1409775
1908 CE
Zermelo-Fraenkel Set Theory Axiomatized
Set theory foundation for calculus is axiomatized, providing logical basis for analysis. #calculus #foundations
By Konrad Jacobs - https://opc.mfo.de/detail?photo_id=8666, CC BY-SA 2.0 de, https://commons.wikimedia.org/w/index.php?curid=6092305
1930 CE
Schwartz Develops Distribution Theory
Laurent Schwartz creates distribution theory, extending calculus to generalized functions. #calculus #analysis )
1945 CE
Whitney Formulates Differentiable Manifolds
Hassler Whitney's embedding theorem advances differential geometry. #calculus #geometry
1960 CE
Nonstandard Analysis Introduced
Abraham Robinson introduces nonstandard analysis, using infinitesimals rigorously. #calculus #history
By Christoph Bernhard Francke - Herzog Anton Ulrich-Museum Braunschweig, Public domain, https://commons.wikimedia.org/w/index.php?curid=57268659
1970 CE
Morse Theory Developed
Marston Morse's theory connects calculus to topology, critical for modern geometry. #calculus #topology
1980 CE
Chaos Theory and Calculus
Edward Lorenz and others apply calculus to nonlinear dynamics, founding chaos theory. #calculus #chaos
By Wikimol, Dschwen - Own work based on: images Lorenz system r28 s10 b2-6666.png by Wikimol and Lorenz attractor.svg by Dschwen, CC BY-SA 3.0, https://commons.wikimedia.org/w/index.php?curid=495592
1990 CE
Computational Calculus Emerges
Advances in numerical methods and computer algebra systems make calculus computation widespread. #calculus #computational
1998 CE
Calculus Reform Movement in Education
The 'Calculus Reform' movement emphasizes conceptual understanding and technology use. #calculus #education
2010 CE
Fractional Calculus Gains Prominence
Fractional calculus, with derivatives of non-integer order, finds applications in physics and engineering. #calculus #fractional
2016 CE
Deep Learning and Automatic Differentiation
Automatic differentiation principles, rooted in calculus, become central to training neural networks. #calculus #machinelearning