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Historical timeline

Source:
The Concise Oxford Dictionary of Mathematics

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 317 and 31071

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

Fermat develops methods to find tangents (published 1636)

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

Wallis’ product

1664

Newton begins his work on calculus

1668

Gregory first proves Fundamental Theorem of Calculus

1671

Gregory discovers Taylor series

1673

Leibniz develops his theory of calculus, publishes 1684

1678

Hooke’s Law

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

Goldbach makes his conjecture in a letter to Euler

1744

Euler works on calculus of variations

1747

D’Alembert derives and solves the wave equation

1748

Euler proves the identity eiθ‎ = cosθ‎ + isinθ‎

1751

Euler formula VE + F = 2 for polyhedra

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 1

1788

Lagrange publishes his equations in mechanics

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

Hamiltonian mechanics

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

Liouville popularizes Galois’ work

1846

Chebyshev proves weak law of large numbers

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

Cayley gives axioms for an abstract group

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

Dedekind defines rings, fields, and modules

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

Weierstrass proves Weierstrass’ Approximation Theorem

1885

Tait publishes table of knots up to 10 crossings

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

Noether’s theorem

1916

Bieberbach conjecture made

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

Alexander introduces his polynomial knot invariant

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

Gödel’s Incompleteness Theorem

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

Arrow’s Impossibility Theorem

1951

Huffman describes his optimal codes

1955

Roth’s theorem proved

1955

Word problem for groups proven undecidable by Novikov

1955

Taniyama-Shimura conjecture made

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