250 BCE
Archimedes' Method of Exhaustion
Archimedes uses method of exhaustion to compute areas and volumes, anticipating integral calculus. #mathematics #history
Chronological Storyline (45 Milestones)
263 CE
Liu Hui's Method of Exhaustion
Liu Hui uses method of exhaustion to compute π and volume of solids, anticipating integral calculus. #mathematics #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
480 CE
Zu Chongzhi Approximates π
Chinese mathematician Zu Chongzhi computes π between 3.1415926 and 3.1415927 using Liu Hui's algorithm. #mathematics #China
By 三猎 - Own work, CC BY-SA 4.0, https://commons.wikimedia.org/w/index.php?curid=54922069
1000 CE
Alhazen's Summation of Powers
Alhazen (Ibn al-Haytham) derives formula for sum of fourth powers, using a method akin to integration. #mathematics #Islam
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
1150 CE
Bhaskara II on Derivatives
Bhaskara II gives early ideas of differential calculus and mean value theorem. #mathematics #India
By Unknown author - Own work, Public domain, https://commons.wikimedia.org/w/index.php?curid=150275955
1400 CE
Madhava Series for Sine
Madhava of Sangamagrama discovers infinite series for sine and arctangent, anticipating calculus. #mathematics #India
1585 CE
Stevin Introduces Decimal Fractions
Simon Stevin publishes De Thiende, introducing decimal fractions and facilitating real number representation. #mathematics #Netherlands
By Unknown author - Digitool Leiden University Library, http://digitalcollections.universiteitleiden.nl, Public domain, https://commons.wikimedia.org/w/index.php?curid=72690
1614 CE
Napier's Logarithms
John Napier publishes Mirifici Logarithmorum Canonis Descriptio, introducing logarithms to simplify calculations. #mathematics #Scotland
By Unknown author - https://www.nationalgalleries.org/art-and-artists/3383, Public domain, https://commons.wikimedia.org/w/index.php?curid=154916365
1635 CE
Cavalieri's Method of Indivisibles
Bonaventura Cavalieri develops method of indivisibles, a precursor to integral calculus. #mathematics #Italy
By Christopher Grattoni - demonstrations.wolfram.com, CC BY 4.0, https://commons.wikimedia.org/w/index.php?curid=145384849
1665 CE
Newton's Fluxions
Isaac Newton develops his method of fluxions, the foundation of differential calculus. #mathematics #England
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
1668 CE
Gregory's Series
James Gregory discovers infinite series for arctan and other functions. #mathematics #Scotland )
By John Scougal - https://artuk.org/discover/artworks/james-gregory-16381675-ma-frs-196636, Public domain, https://commons.wikimedia.org/w/index.php?curid=168216215
1684 CE
Leibniz Publishes Calculus
Gottfried Wilhelm Leibniz publishes Nova Methodus, first paper on differential calculus. #mathematics #Germany
By Christoph Bernhard Francke - Herzog Anton Ulrich-Museum, online, Public domain, https://commons.wikimedia.org/w/index.php?curid=53159699
1713 CE
Bernoulli's Law of Large Numbers
Jacob Bernoulli publishes Ars Conjectandi, containing law of large numbers, foundational for measure theory. #mathematics #Switzerland
By Niklaus Bernoulli (1662-1716) - [2] [3], Public domain, https://commons.wikimedia.org/w/index.php?curid=266673
1748 CE
Euler's Introductio
Leonhard Euler publishes Introductio in analysin infinitorum, systematizing real analysis. #mathematics #Switzerland
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
1772 CE
Lagrange's Contributions
Joseph-Louis Lagrange contributes to calculus of variations and foundations of analysis. #mathematics #France
By Unknown author - File:Joseph_Louis_Lagrange.jpg, CC0, https://commons.wikimedia.org/w/index.php?curid=155608232
1817 CE
Bolzano's Intermediate Value Theorem
Bernard Bolzano proves intermediate value theorem with rigorous analysis foundations. #mathematics #CzechRepublic
By Unknown author, Public domain, https://commons.wikimedia.org/w/index.php?curid=73300
1821 CE
Cauchy's Epsilon-Delta
Augustin-Louis Cauchy introduces rigorous epsilon-delta definitions in Cours d'Analyse. #mathematics #France
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
1822 CE
Fourier Series
Joseph Fourier publishes Théorie analytique de la chaleur, expanding functions in trigonometric series. #mathematics #France
By Lucas Vieira - File:Fourier transform time and frequency domains (small).gif, CC0, https://commons.wikimedia.org/w/index.php?curid=28399050
1826 CE
Abel's Binomial Theorem
Niels Henrik Abel generalizes binomial theorem and works on convergence of series. #mathematics #Norway
By Johan Gørbitz - Originally uploaded to English wikipedia by en:User:Pladask, http://www.math.uio.no/div/abelkonkurransen/, Public domain, https://commons.wikimedia.org/w/index.php?curid=90392
1829 CE
Dirichlet Function
Peter Gustav Lejeune Dirichlet defines the Dirichlet function, a pathological example in real analysis. #mathematics #Germany
1854 CE
Riemann Integral
Bernhard Riemann formalizes the Riemann integral in his Habilitation thesis. #mathematics #Germany
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
Dedekind Cuts
Richard Dedekind publishes Stetigkeit und irrationale Zahlen, defining real numbers via Dedekind cuts. #mathematics #Germany
By Melikamp - Own work, CC BY-SA 4.0, https://commons.wikimedia.org/w/index.php?curid=147735710
1872 CE
Weierstrass's Nowhere Differentiable Function
Karl Weierstrass presents a continuous but nowhere differentiable function, challenging intuition. #mathematics #Germany
By Eeyore22 - Own work, Public domain, https://commons.wikimedia.org/w/index.php?curid=5075959
1874 CE
Cantor's Denumerability
Georg Cantor proves the uncountability of reals and develops set theory. #mathematics #Germany
By Unknown author - https://www.math.cmu.edu/~rcristof/pdf/Cantor_pubblicato.pdf and they had it from https://photos.aip.org/history-programs/niels-bohr-library/photos/cantor-georg-a1, Public domain, https://commons.wikimedia.org/w/index.php?curid=74820875
1898 CE
Borel's Measure
Émile Borel introduces Borel sets and measure theory in Leçons sur la théorie des fonctions. #mathematics #France
By Agence de presse Mondial Photo-Presse - Bibliothèque nationale de France, Public domain, https://commons.wikimedia.org/w/index.php?curid=15265004
1902 CE
Lebesgue Integral
Henri Lebesgue publishes his theory of integration and measure in Intégrale, longueur, aire. #mathematics #France
By Unknown author, Public domain, https://commons.wikimedia.org/w/index.php?curid=336482
1905 CE
Fatou's Lemma
Pierre Fatou proves Fatou's lemma in the context of Lebesgue integration. #mathematics #France
1906 CE
Egorov's Theorem
Dmitri Egorov proves Egorov's theorem on uniform convergence almost everywhere. #mathematics #Russia
1907 CE
Fubini's Theorem
Guido Fubini proves Fubini's theorem for iterated integrals. #mathematics #Italy
1909 CE
Riesz Representation Theorem
Frigyes Riesz proves representation theorem for linear functionals on continuous functions. #mathematics #Hungary
1913 CE
Radon-Nikodym Theorem
Johann Radon publishes the Radon-Nikodym theorem generalizing derivatives of measures. #mathematics #Austria
1914 CE
Carathéodory Extension
Constantin Carathéodory develops Carathéodory's extension theorem for measures. #mathematics #Greece
1915 CE
Luzin's Theorem
Nikolai Luzin proves Luzin's theorem on measurability of functions. #mathematics #Russia
1918 CE
Hausdorff Measure
Felix Hausdorff introduces Hausdorff measure and dimension for fractal sets. #mathematics #Germany
1920 CE
Hahn-Banach Theorem
Hans Hahn and Stefan Banach establish the Hahn-Banach theorem in functional analysis. #mathematics #Poland
1932 CE
Banach's Book on Linear Operators
Stefan Banach publishes Théorie des opérations linéaires, founding functional analysis. #mathematics #Poland
By nieznany/unknown - Warszawski Kalendarz Ilustrowany 1967, Wydawnictwo Warszawskiego Tygodnika "Stolica", Warszawa 1966, p. 152, Public domain, https://commons.wikimedia.org/w/index.php?curid=19058077
1933 CE
Kolmogorov Axioms
Andrey Kolmogorov axiomatizes probability theory using measure theory. #mathematics #Russia
By Konrad Jacobs - https://opc.mfo.de/detail?photoID=7493, CC BY-SA 2.0 de, https://commons.wikimedia.org/w/index.php?curid=11829175
1933 CE
Haar Measure
Alfréd Haar introduces Haar measure on locally compact groups. #mathematics #Hungary
1937 CE
Stone-Weierstrass Theorem
Marshall Stone generalizes Weierstrass approximation theorem. #mathematics #USA
1944 CE
Itô Calculus
Kiyoshi Itô develops stochastic integral and calculus. #mathematics #Japan
By Shiyu Ji - Own work, CC BY-SA 4.0, https://commons.wikimedia.org/w/index.php?curid=53067749
1954 CE
Kolmogorov's Extension Theorem
Andrey Kolmogorov extends measure theory to stochastic processes. #mathematics #Russia
1960 CE
Non-Standard Analysis
Abraham Robinson develops non-standard analysis using hyperreal numbers. #mathematics #USA
By Christoph Bernhard Francke - Herzog Anton Ulrich-Museum Braunschweig, Public domain, https://commons.wikimedia.org/w/index.php?curid=57268659
1966 CE
Malliavin Calculus
Paul Malliavin introduces stochastic calculus of variations. #mathematics #France
1978 CE
Geometric Measure Theory
Ennio De Giorgi and others develop geometric measure theory. #mathematics #Italy
1999 CE
Bourgain's Breakthroughs
Jean Bourgain makes breakthroughs in harmonic analysis and PDEs. #mathematics #Belgium
By George Bergman - This image has been extracted from another file, CC BY-SA 4.0, https://commons.wikimedia.org/w/index.php?curid=74881233