300 BCE
Eudoxus of Cnidus Develops Method of Exhaustion
Eudoxus formalizes the method of exhaustion for computing areas and volumes by inscribing polygons, laying a geometric foundation for integral calculus. #math #history
Chronological Storyline (44 Milestones)
250 BCE
Archimedes Uses Infinitesimals
Archimedes computes the area under a parabola and the volume of a sphere using infinitesimal techniques, anticipating integral calculus. #math #history
By Domenico Fetti - http://archimedes2.mpiwg-berlin.mpg.de/archimedes_templates/popup.htm, Public domain, https://commons.wikimedia.org/w/index.php?curid=146592
263 CE
Liu Hui Improves π Approximation
Chinese mathematician Liu Hui develops a recursive polygon algorithm to approximate π, demonstrating early limit concepts. #math #history
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
500 CE
Zu Chongzhi Calculates π Precisely
Zu Chongzhi computes π between 3.1415926 and 3.1415927 using polygon methods, a record for centuries. #math #history
By 三猎 - Own work, CC BY-SA 4.0, https://commons.wikimedia.org/w/index.php?curid=54922069
965 CE
Alhazen's Problem on Volume
Ibn al-Haytham (Alhazen) attempts to find the volume of a paraboloid using a method analogous to integration, influencing later European calculus. #math #history
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
1070 CE
Omar Khayyam's Geometric Calculus
Omar Khayyam develops algebraic methods for solving cubic equations and uses geometric techniques resembling integration to find areas. #math #history
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
1400 CE
Madhava's Infinite Series for Trig Functions
Madhava of Sangamagrama discovers power series expansions for sine, cosine, and arctangent, founding the Kerala school of calculus. #math #history
1500 CE
Kerala School Synthesizes Calculus Ideas
Indian mathematicians of the Kerala school, including Nilakantha Somayaji, develop calculus-like methods for series and integration, predating Newton and Leibniz. #math #history
By ChandlerMinh - Own work, CC BY-SA 4.0, https://commons.wikimedia.org/w/index.php?curid=92927231
1635 CE
Cavalieri's Principle of Indivisibles
Bonaventura Cavalieri publishes Geometria Indivisibilibus, introducing indivisibles to compute areas and volumes, a precursor to integral calculus. #math #history
By Christopher Grattoni - demonstrations.wolfram.com, CC BY 4.0, https://commons.wikimedia.org/w/index.php?curid=145384849
1637 CE
Descartes Links Algebra and Geometry
René Descartes' La Géométrie establishes analytic geometry, enabling algebraic treatment of curves and providing a foundation for calculus. #math #history
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
1655 CE
Fermat's Method of Finding Tangents
Pierre de Fermat develops a method for finding tangents to curves using a technique similar to differentiation, anticipating the derivative concept. #math #history
1666 CE
Newton's Fluxions and Fluents
Isaac Newton begins developing his calculus of fluxions (derivatives) and fluents (integrals), applying it to physics and motion. #math #history
1670 CE
Seki Takakazu's Similar Developments in Japan
Japanese mathematician Seki Takakazu independently develops calculus-like methods for solving problems in geometry and algebra, contributing to wasan tradition. #math #history
By upload by AMorozov - Gakken, Public domain, https://commons.wikimedia.org/w/index.php?curid=710154
1684 CE
Leibniz Publishes Differential Calculus
Gottfried Wilhelm Leibniz publishes 'Nova Methodus pro Maximis et Minimis', presenting differential calculus notation (dx, dy) and rules. #math #history
By G. W. Leibniz - https://archive.org/details/s1id13206500/page/467/mode/1up, Public domain, https://commons.wikimedia.org/w/index.php?curid=140197496
1687 CE
Newton's Principia Mathematica
Isaac Newton's Philosophiæ Naturalis Principia Mathematica uses calculus concepts to describe universal gravitation and laws of motion, revolutionizing science. #math #history
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
Bernoulli Family Contributions
Johann and Jacob Bernoulli extend calculus, solving the brachistochrone problem and developing the calculus of variations. #math #history
1696 CE
L'Hôpital's Rule Published
Guillaume de l'Hôpital publishes Analyse des Infiniment Petits, containing the rule for evaluating limits with indeterminate forms (attributed to Johann Bernoulli). #math #history
1715 CE
Brook Taylor Derives Taylor Series
Brook Taylor publishes Methodus Incrementorum Directa et Inversa, introducing the Taylor series expansion for functions. #math #history
By IkamusumeFan - Own work, CC BY-SA 3.0, https://commons.wikimedia.org/w/index.php?curid=27865201
1734 CE
Euler's Notation for e and π
Leonhard Euler introduces the notation e for Euler's number and popularizes π, standardizing symbols crucial for calculus. #math #history
1748 CE
Euler's Introductio in analysin infinitorum
Leonhard Euler's seminal textbook systematically treats functions, series, and calculus, establishing notation and concepts like e and π. #math #history
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
1760 CE
Lagrange's Calculus of Variations
Joseph-Louis Lagrange develops the calculus of variations, introducing the Euler-Lagrange equation and variational methods. #math #history
1781 CE
Laplace's Mécanique Céleste
Pierre-Simon Laplace applies calculus to celestial mechanics, developing the Laplace equation and potential theory. #math #history
1797 CE
Lagrange's Theory of Functions
Lagrange publishes Théorie des fonctions analytiques, attempting to base calculus on algebraic foundations without infinitesimals. #math #history
1821 CE
Cauchy's Cours d'analyse
Augustin-Louis Cauchy formalizes limits, continuity, and convergence in Cours d'analyse, providing a rigorous foundation for calculus. #math #history
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
1822 CE
Fourier's Théorie analytique de la chaleur
Joseph Fourier publishes his work on heat conduction, introducing Fourier series and expansion of functions in trigonometric series. #math #history
1823 CE
Cauchy's Definition of the Definite Integral
Cauchy defines the definite integral as a limit of sums, providing a rigorous foundation for integration. #math #history
By KSmrq - self-made using text editor, CC BY-SA 3.0, https://commons.wikimedia.org/w/index.php?curid=2268147
1850 CE
Riemann's Theory of Complex Functions
Bernhard Riemann's work on complex analysis, including the Cauchy-Riemann equations, connects complex differentiation to calculus. #math #history
By Cauchy-Riemann.png: Keenan Crane vector version: VectorVoyager - This file was derived from: Cauchy-Riemann.png:, CC BY-SA 4.0, https://commons.wikimedia.org/w/index.php?curid=127954258
1854 CE
Riemann's Definition of the Integral
Bernhard Riemann presents the Riemann integral definition in his habilitation thesis, formalizing integration of arbitrary functions. #math #history
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
1861 CE
Weierstrass Epsilon-Delta Definition of Limit
Karl Weierstrass provides the modern ε-δ definition of limits, rigorously establishing the foundation of differential calculus. #math #history
1872 CE
Weierstrass Constructs Continuous Everywhere, Differentiable Nowhere Function
Weierstrass presents an example of a function that is continuous but not differentiable at any point, expanding understanding of calculus. #math #history
By Eeyore22 - Own work, Public domain, https://commons.wikimedia.org/w/index.php?curid=5075959
1874 CE
Cantor's Set Theory and Transfinite Numbers
Georg Cantor develops set theory, which later influences measure theory and integration, including the concept of cardinality. #math #history
By Cepheus - Own work, Public domain, https://commons.wikimedia.org/w/index.php?curid=1234767
1880 CE
Frege's Foundations of Arithmetic
Gottlob Frege's Begriffsschrift introduces logical foundations for mathematics, influencing later rigor in analysis. #math #history
By Unknown author - digitized version at https://gallica.bnf.fr/ark:/12148/bpt6k65658c, Public domain, https://commons.wikimedia.org/w/index.php?curid=2669038
1887 CE
Poincaré's Qualitative Theory of Differential Equations
Henri Poincaré introduces the qualitative theory of differential equations, using topology to study their behavior. #math #history
1902 CE
Lebesgue Integration Theory
Henri Lebesgue introduces measure theory and the Lebesgue integral, generalizing Riemann integration and enabling wider integrability. #math #history
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
1904 CE
Zermelo's Axiom of Choice and Set Theory
Ernst Zermelo's axiom of choice is debated, affecting the foundations of analysis and integration. #math #history
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
1918 CE
Wiener's Generalized Harmonic Analysis
Norbert Wiener develops generalized harmonic analysis, applying integration theory to stochastic processes and communication. #math #history
By Garry Olsh - Own work, CC0, https://commons.wikimedia.org/w/index.php?curid=148383228
1930 CE
Distribution Theory by Laurent Schwartz
Laurent Schwartz develops distribution theory, extending the concept of derivative to generalized functions like the Dirac delta. #math #history )
1933 CE
Kolmogorov's Axiomatization of Probability
Andrey Kolmogorov publishes Foundations of the Theory of Probability, using measure theory to ground probability in calculus. #math #history
By Ainali - Own work, CC BY-SA 3.0, https://commons.wikimedia.org/w/index.php?curid=3141713
1945 CE
Schwartz's Théorie des Distributions
Laurent Schwartz publishes Théorie des distributions, formalizing distribution theory for calculus and partial differential equations. #math #history
1960 CE
Robinson's Non-Standard Analysis
Abraham Robinson introduces non-standard analysis, rigorously reviving infinitesimals within a hyperreal number system. #math #history
By Christoph Bernhard Francke - Herzog Anton Ulrich-Museum Braunschweig, Public domain, https://commons.wikimedia.org/w/index.php?curid=57268659
1966 CE
Bishop's Constructive Analysis
Errett Bishop publishes Foundations of Constructive Analysis, offering a constructive approach to calculus without the law of excluded middle. #math #history
1970 CE
Non-Standard Analysis Refinements
Abraham Robinson's non-standard analysis gains traction, providing a rigorous framework for infinitesimals used in calculus. #math #history
1990 CE
Computer Algebra Systems and Calculus
Software like Mathematica and Maple enable symbolic differentiation and integration, revolutionizing calculus education and research. #math #history
2000 CE
Calculus Reform Movement
Educational initiatives emphasize conceptual understanding, technology use, and applications, reshaping calculus teaching. #math #history