Historical timeline
Historical timeline
c.2000 bc | Sumerians have sexagesimal (base 60) positional numeral system |
c.1300 bc | Decimal number system (see decimal representation) recorded in China |
c.500 bc | Pythagorean school (see Pythagoras) |
c.300 bc | Euclid writes his Elements |
287 bc | Birth of Archimedes |
276 bc | Birth of Eratosthenes, who determined the Earth’s circumference |
c.262 bc | Birth of Apollonius, author of Conics |
262 bc | Archimedes shows pi lies between $3\frac{1}{7}$ and $3\frac{10}{71}$ |
c. ad 250 | Diophantus writes his Arithmetica |
c. ad 300 | Chinese remainder theorem developed |
c. ad 830 | al-Khwārizmī writes Al-Jabr, which provides the word ‘algebra’ |
c.1150 | Bhāskara solves Pell’s equation |
1202 | Fibonacci publishes his Liber Abaci |
c.1525 | Dürer writes on perspective and geometrical constructions |
1535 | Tartaglia solves the cubic equation |
1540 | Ferrari solves the quartic equation |
1545 | Cardano’s Ars Magna |
1572 | Bombelli publishes his Algebra, developing complex numbers |
1591 | Viète introduces letters for unknown variables |
1609 | Kepler publishes first two of three laws (third law 1619) |
1614 | Napier introduces logarithms |
1618 | Napier makes first reference to the number e |
1624 | Briggs publishes his tables of logarithms |
1629 | |
1632 | Galileo formulates Galilean relativity |
1636 | Fermat proves Fermat’s Little Theorem |
1637 | Descartes, and independently Fermat, introduce Cartesian coordinates |
1638 | Fermat claims, in a margin, to have a proof of Fermat’s Last Theorem |
1654 | Fermat and Pascal lay foundations of probability |
1656 | |
1664 | |
1668 | Gregory first proves Fundamental Theorem of Calculus |
1671 | Gregory discovers Taylor series |
1673 | |
1678 | |
1687 | Newton publishes his Principia |
1691 | Rolle publishes his theorem |
1696 | Brachistochrone problem posed by Jean Bernoulli |
1715 | Taylor develops Taylor series |
1722 | De Moivre states his theorem |
1727 | Euler introduces e for the base of natural logarithms |
1734 | Bishop George Berkeley publishes The Analyst, critical of the foundations of calculus |
1735 | Euler solves the Basel problem |
1736 | Euler shows Königsberg Bridge problem unsolvable |
1737 | Euler shows *e is irrational |
1738 | Daniel Bernoulli publishes Hydrodynamica |
1742 | |
1744 | Euler works on calculus of variations |
1747 | D’Alembert derives and solves the wave equation |
1748 | Euler proves the identity e^{iθ} = cosθ + isinθ |
1751 | |
1761 | Lambert shows pi is irrational |
1762 | Lagrange states the divergence theorem |
1763 | Bayes proves his theorem |
1763 | Euler generalizes Fermat’s little theorem and introduces the totient function |
1771 | Lagrange’s first version of Lagrange’s theorem |
1777 | Euler popularizes use of i for $\sqrt{-1}$ |
1788 | |
1796 | Legendre conjectures the prime number theorem |
1799 | Gauss proves the Fundamental Theorem of Algebra |
1799 | Ruffini gives an incomplete proof that quintics are not solvable by radicals |
1801 | Gauss publishes his Disquisitiones arithmeticae |
1801 | Gauss relocates Ceres by means of the least squares theorem |
1807 | Fourier series introduced |
1817 | Bolzano defines continuity and proves the intermediate value theorem |
1821 | Cauchy publishes his Cours d’analyse |
1822 | Feuerbach’s theorem of the nine-point circle |
1822 | Navier and (1842) Stokes state the Navier-Stokes equations |
1824 | Abel proves the quintic is not solvable by radicals |
1825 | Cauchy presents the Cauchy integral theorem in complex analysis |
1826 | Crelle’s Journal first published |
1828 | Green’s Theorem proved |
1828 | Gauss proves the Theorema Egregium |
1829 | Lobachevsky’s and Bolyai’s (1832) work on hyperbolic geometry |
1832 | Galois shot in duel |
1833 | |
1835 | Dirichlet proves his theorem about primes in arithmetic progressions |
1837 | Wantzel proves doubling the cube and trisecting angles impossible |
1838 | Verhulst introduces logistic equation (see logistic map) as population model |
1843 | Hamilton introduces the quaternions |
1844 | Liouville gives first example of a transcendental number |
1845 | Bertrand states his postulate |
1846 | |
1846 | |
1848 | Bonnet proves special case of Gauss-Bonnet theorem |
1850 | Kelvin writes to Stokes with details of Stokes’ Theorem |
1852 | Chebyshev proves Bertrand’s postulate |
1854 | |
1854 | Riemann presents work on the Riemann integral |
1854 | Riemann’s theorem on conditionally convergent series |
1857 | Riemann’s Theory of Abelian Functions popularizes Riemann surfaces |
1858 | Möbius introduces the Möbius band |
1858 | Cayley states the Cayley-Hamilton Theorem |
1859 | Riemann poses the Riemann hypothesis |
1861 | Weierstrass’s first lectures on epsilon-delta analysis |
1869 | Lie begins his work on Lie groups |
1870 | Weierstrass proves the isoperimetric inequality |
1871 | |
1872 | Sylow publishes his three theorems |
1873 | Maxwell publishes his equations |
1873 | Hermite proves e is transcendental |
1874 | Cantor shows there are different infinite cardinalities |
1877 | Boltzmann defines entropy |
1877 | Frobenius shows there are 3 associative division algebras |
1878 | Cantor states the continuum hypothesis |
1881 | Poincaré proves the Hairy Ball Theorem |
1882 | Lindemann proves π is transcendental |
1884 | Frege’s Grundlagen der Arithmetik |
1885 | |
1885 | |
1887 | Jordan proves Jordan Curve Theorem |
1888 | Hilbert’s basis theorem proved |
1889 | Fitzgerald and Lorentz (1892) propose the Lorentz-Fitzgerald contraction |
1889 | Jordan-Hölder Theorem proved |
1891 | Fedorov shows there are 17 wallpaper groups |
1895 | Poincaré releases his seminal Analysis Situs |
1896 | Frobenius founds representation theory |
1896 | Prime number theorem proven by Hadamard and de la Vallée-Poussin |
1897 | First International Congress of Mathematicians in Zurich |
1897 | Hensel introduces p-adic numbers |
1898 | Hurwitz shows there are four normed division algebras |
1899 | Hilbert axiomatizes Euclidean geometry |
1900 | Hilbert announces his 23 problems |
1901 | Lyapunov proves the Central Limit Theorem |
1902 | Lebesgue introduces the Lebesgue integral |
1903 | Russell’s paradox stated |
1904 | Zermelo introduces the axiom of choice |
1904 | Lorentz introduces Lorentz transformations |
1904 | Poincaré Conjecture made |
1905 | Einstein publishes his theory of special relativity |
1906 | Metric spaces defined by Fréchet |
1906 | Joukowski models lift on an aerofoil |
1906 | Markov publishes first paper on Markov chains |
1908 | Student’s (Gosset’s) t-distribution |
1908 | Zermelo lists his axioms of set theory |
1910 | Russell and Whitehead publish the first volume of Principia Mathematica |
1910 | Brouwer proves his fixed point theorem |
1910 | Lotka and later Volterra (1926) publish their predator–prey model |
1912 | Brouwer generalizes Jordan Curve Theorem to higher dimensions |
1914 | Topological spaces defined by Hausdorff |
1915 | Einstein publishes his theory of general relativity |
1915 | |
1916 | |
1918 | Hausdorff dimension (or fractal dimension) defined |
1922 | Fraenkel suggests further axioms to create Zermelo-Fraenkel axioms |
1924 | Banach-Tarski paradox published |
1925 | Morse publishes first paper on Morse theory |
1925 | Heisenberg formulates his approach to quantum theory |
1925 | Fisher publishes influential Statistical Methods for Research Workers |
1926 | Poincaré-Hopf theorem proved |
1926 | Schrödinger formulates his approach to quantum theory |
1927 | Kermack and McKendrick introduce the SIR epidemiology model |
1927 | Van der Waerden’s Theorem proved |
1927 | Noether publishes her isomorphism theorems |
1928 | |
1928 | Von Neumann’s On the Theory of Games and Strategy published, including Minimax Theorem |
1930 | Kuratowski’s Theorem proved |
1930 | Ramsey proves his theorem |
1930 | Dirac publishes The Principles of Quantum Mechanics |
1931 | |
1932 | Von Neumann’s Mathematical Foundations of Quantum Mechanics published |
1933 | Kolmogorov states the axioms of probability |
1933 | Neyman-Pearson lemma proved |
1935 | Zorn introduces his lemma (Kuratowski had earlier in 1922) |
1935 | Church provides negative answer to the decision problem |
1936 | First Fields Medals awarded |
1937 | Neyman introduces the confidence interval |
1937 | Vinogradov makes progress on Goldbach’s conjecture |
1937 | Turing writes On Computable Numbers (unaware of Church’s work) |
1938 | Gödel proves the continuum hypothesis and the axiom of choice to be consistent with Zermelo-Fraenkel axioms |
1945 | Eilenberg and Mac Lane define categories |
1945 | Cartan generalizes Stokes’ Theorem |
1947 | Dantzig publishes his simplex method |
1948 | Turing introduces LU decomposition in Rounding-off Errors in Matrix Processes |
1948 | Schwartz publishes on distributions |
1948 | Shannon’s seminal paper A Mathematical Theory of Communication published |
1949 | Weil states his influential Weil conjectures |
1950 | Hodge presents his conjecture at the 1950 ICM |
1950 | Hamming distance introduced in Error Detecting and Error Correcting Codes |
1950 | John Nash introduces Nash equilibria |
1951 | |
1951 | Huffman describes his optimal codes |
1955 | Roth’s theorem proved |
1955 | Word problem for groups proven undecidable by Novikov |
1955 | |
1963 | Lorenz attractor first described |
1963 | Atiyah-Singer Index Theorem proved |
1963 | Cohen proves axiom of choice independent of Zermelo-Fraenkel axioms and continuum hypothesis independent of ZFC axioms |
1965 | Birch-Swinnerton-Dyer conjecture made |
1966 | Robinson introduces hyperreals |
1967 | Langlands conjectures made |
1968 | Thom begins his work on catastrophe theory |
1973 | Chen makes progress on Goldbach conjecture |
1974 | First Penrose tilings discovered |
1974 | Deligne proves Weil conjectures |
1975 | Mandelbrot coins the term fractal |
1975 | Szemerédi’s theorem proved |
1976 | Four Colour Theorem proven by Appel and Haken using computers |
1976 | May finds chaos in discrete logistic equation (see logistic map) |
1976 | Lakatos’s Proofs and Refutations published posthumously |
1978 | Mandelbrot set first defined |
1978 | Donald Knuth introduces TeX |
1978 | RSA cryptography developed |
1983 | Faltings proves the Mordell conjecture |
1983 | Donaldson shows exotic differentiable structures exist in 4D |
1984 | Jones introduces his polynomial knot invariant |
1985 | Bieberbach conjecture proved by de Branges |
1985 | abc conjecture stated |
1995 | Wiles proves Fermat’s Last Theorem |
1998 | Hales proves the Kepler conjecture. Finally accepted 2017 |
2000 | Millennium Prize problems announced |
2002 | Catalan’s conjecture proved by Mih်ilescu |
2003 | Perelman proves the Poincaré Conjecture |
2004 | Green-Tao theorem proved |
2013 | Zhang makes advances on the twin prime conjecture |
2014 | Miriam Mirzakhani wins Fields Medal |