Timeline of mathematics
From Academic Kids

A timeline of pure and applied mathematics
 ca. 35000 BC to 20000 BC  Africa & France, earliest known prehistoric attempts to quantify time (references: [1] (http://www.tacomacc.edu/home/jkellerm/Papers/Menses/Menses.htm), [2] (http://www.math.buffalo.edu/mad/AncientAfrica/lebombo.html), [3] (http://www.math.buffalo.edu/mad/AncientAfrica/ishango.html))
 ca. 3100 BC  Egypt, earliest known decimal system allows indefinite counting by way of introducing new symbols, [4] (http://www.math.buffalo.edu/mad/AncientAfrica/mad_ancient_egyptpapyrus.html#berlin)
 2800 BC  The Lo Shu Square, the unique normal magic square of order three, was discovered in China
 2700 BC  Egypt, precision surveying
 2600 BC  Indus Valley Civilization, earliest use of decimal fractions in a uniform system of ancient weights and measures, and also negative numbers (see Negative Number: History)
 2400 BC  Egypt, precise Astronomical Calendar, used even in the Middle Ages for its mathematical regularity
 1800 BC  Moscow Mathematical Papyrus, generalized formula for finding volume of frustrums, [5] (http://www.math.buffalo.edu/mad/AncientAfrica/mad_ancient_egyptpapyrus.html#berlin)
 1800 BC  Berlin Papyrus, shows that the ancient Egyptians knew how to solve 2nd order algebraic equations: [6] (http://www.math.buffalo.edu/mad/AncientAfrica/mad_ancient_egyptpapyrus.html#berlin).
 1650 BC  Rhind Mathematical Papyrus, copy of a lost scroll from around 1850 BC, the scribe Ahmes presents first known approximate value of π at 3.16, the first attempt at squaring the circle, earliest known use of a sort of cotangent, and knowledge of solving first order linear equations.
 530 BC  Pythagoras studies propositional geometry and vibrating lyre strings; his group discovers the irrationality of the square root of two,
 370 BC  Eudoxus states the method of exhaustion for area determination,
 350 BC  Aristotle discusses logical reasoning in Organon,
 300 BC  Euclid in his Elements studies geometry as an axiomatic system, proves the infinitude of prime numbers and presents the Euclidean algorithm; he states the law of reflection in Catoptrics, and he proves the fundamental theorem of arithmetic
 260 BC  Archimedes computes π to two decimal places using inscribed and circumscribed polygons and computes the area under a parabolic segment,
 ca. 250 BC  late Olmecs had already begun to use a true zero (a shell glyph) several centuries before Ptolemy in the New World. See 0 (number).
 240 BC  Eratosthenes uses his sieve algorithm to quickly isolate prime numbers,
 225 BC  Apollonius of Perga writes On Conic Sections and names the ellipse, parabola, and hyperbola,
 140 BC  Hipparchus develops the bases of trigonometry,
 about 200s  Ptolemy of Alexandria wrote the Almagest,
 250  Diophantus uses symbols for unknown numbers in terms of the syncopated algebra, and he writes Arithmetica, the first systematic treatise on algebra,
 450  Zu Chongzhi computes π to seven decimal places,
 550  Hindu mathematicians give zero a numeral representation in a positional notation system,
 628  Brahmagupta writes Brahma sphuta siddhanta,
 750  AlKhawarizmi  Considered father of modern algebra. First mathematician to work on the details of 'Arithmetic and Algebra of inheritance' besides the systematisation of the theory of linear and quadratic equations.
 895  Thabit ibn Qurra  The only surviving fragment of his original work contains a chapter on the solution and properties of cubic equations.
 975  AlBatani  Extended the Indian concepts of sine and cosine to other trigonometrical ratios, like tangent, secant and their inverse functions. Derived the formula: sin α = tan α / (1+tan² α) and cos α = 1 / (1 + tan² α).
 1020  Abul Wáfa  Gave this famous formula: sin (α + β) = sin α cos β + sin β cos α. Also discussed the quadrature of the parabola and the volume of the paraboloid.
 1030  Ali Ahmad Nasawi  Divides hours into 60 minutes and minutes into 60 seconds.
 1070  Omar Khayyam begins to write Treatise on Demonstration of Problems of Algebra and classifies cubic equations.
 1202  Leonardo Fibonacci demonstrates the utility of Arabic numerals in his Book of the Abacus,
 1303  Zhu Shijie publishes Precious Mirror of the Four Elements, which contains ancient method of arranging binomial coefficients in a triangle.
 1424  Ghiyath alKashi  computes π to sixteen decimal places using inscribed and circumscribed polygons,
 1520  Scipione dal Ferro develops a method for solving "depressed" cubic equations (cubic equations without an x^{2} term), but does not publish,
 1535  Niccolo Tartaglia independently develops a method for solving depressed cubic equations but also does not publish,
 1539  Gerolamo Cardano learns Tartaglia's method for solving depressed cubics and discovers a method for depressing cubics, thereby creating a method for solving all cubics,
 1540  Lodovico Ferrari solves the quartic equation,
 1544  Michael Stifel publishes "Arithmetica integra",
 1596  Ludolf van Ceulen computes π to twenty decimal places using inscribed and circumscribed polygons,
 1614  John Napier discusses Napierian logarithms in Mirifici Logarithmorum Canonis Descriptio,
 1617  Henry Briggs discusses decimal logarithms in Logarithmorum Chilias Prima,
 1619  René Descartes discovers analytic geometry (Pierre de Fermat claimed that he also discovered it independently),
 1629  Pierre de Fermat develops a rudimentary differential calculus,
 1634  Gilles de Roberval shows that the area under a cycloid is three times the area of its generating circle,
 1637  Pierre de Fermat claims to have proven Fermat's last theorem in his copy of Diophantus' Arithmetica,
 1654  Blaise Pascal and Pierre de Fermat create the theory of probability,
 1655  John Wallis writes Arithmetica Infinitorum,
 1658  Christopher Wren shows that the length of a cycloid is four times the diameter of its generating circle,
 1665  Isaac Newton works on the fundamental theorem of calculus and invents his version of calculus,
 1668  Nicholas Mercator and William Brouncker discover an infinite series for the logarithm while attempting to calculate the area under a hyperbolic segment,
 1671  James Gregory discovers the series expansion for the inversetangent function,
 1673  Gottfried Leibniz independently invents his version of calculus,
 1675  Isaac Newton invents an algorithm for the computation of functional roots,
 1691  Gottfried Leibniz discovers the technique of separation of variables for ordinary differential equations,
 1693  Edmund Halley prepares the first mortality tables statistically relating death rate to age,
 1696  Guillaume de L'Hôpital states his rule for the computation of certain limits,
 1696  Jakob Bernoulli and Johann Bernoulli solve brachistochrone problem, the first result in the calculus of variations,
 1706  John Machin develops a quickly converging inversetangent series for π and computes π to 100 decimal places,
 1712  Brook Taylor develops Taylor series,
 1722  Abraham De Moivre states De Moivre's theorem connecting trigonometric functions and complex numbers,
 1724  Abraham De Moivre studies mortality statistics and the foundation of the theory of annuities in Annuities on Lives,
 1730  James Stirling publishes The Differential Method,
 1733  Giovanni Gerolamo Saccheri studies what geometry would be like if Euclid's fifth postulate were false,
 1733  Abraham de Moivre introduces the normal distribution to approximate the binomial distribution in probability,
 1734  Leonhard Euler introduces the integrating factor technique for solving firstorder ordinary differential equations,
 1736  Leonhard Euler solves the problem of the Seven bridges of Königsberg, in effect creating graph theory,
 1739  Leonhard Euler solves the general homogenous linear ordinary differential equation with constant coefficients,
 1742  Christian Goldbach conjectures that every even number greater than two can be expressed as the sum of two primes, now known as Goldbach's conjecture,
 1748  Maria Gaetana Agnesi discusses analysis in Instituzioni Analitiche ad Uso della Gioventu Italiana,
 1761  Thomas Bayes proves Bayes' theorem,
 1762  Joseph Louis Lagrange discovers the divergence theorem,
 1789  Jurij Vega improves Machin's formula and computes π to 140 decimal places,
 1794  Jurij Vega publishes Thesaurus Logarithmorum Completus,
 1796  Carl Friedrich Gauss proves that the regular 17gon can be constructed using only a compass and straightedge
 1796  AdrienMarie Legendre conjectures the prime number theorem,
 1797  Caspar Wessel associates vectors with complex numbers and studies complex number operations in geometrical terms,
 1799  Carl Friedrich Gauss proves the fundamental theorem of algebra (every polynomial equation has a solution among the complex numbers),
 1801  Disquisitiones Arithmeticae, Carl Friedrich Gauss's number theory treatise, is published in Latin
 1805  AdrienMarie Legendre introduces the method of least squares for fitting a curve to a given set of observations,
 1807  Joseph Fourier announces his discoveries about the trigonometric decomposition of functions,
 1811  Carl Friedrich Gauss discusses the meaning of integrals with complex limits and briefly examines the dependence of such integrals on the chosen path of integration,
 1815  SiméonDenis Poisson carries out integrations along paths in the complex plane,
 1817  Bernard Bolzano presents the intermediate value theorema continuous function which is negative at one point and positive at another point must be zero for at least one point in between,
 1822  AugustinLouis Cauchy presents the Cauchy integral theorem for integration around the boundary of a rectangle in the complex plane,
 1824  Niels Henrik Abel partially proves that the general quintic or higher equations cannot be solved by a general formula involving only arithmetical operations and roots,
 1825  AugustinLouis Cauchy presents the Cauchy integral theorem for general integration paths  he assumes the function being integrated has a continuous derivative, and he introduces the theory of residues in complex analysis,
 1825  Johann Peter Gustav Lejeune Dirichlet and AdrienMarie Legendre prove Fermat's last theorem for n = 5,
 1825  AndréMarie Ampère discovers Stokes' theorem,
 1828  George Green proves Green's theorem,
 1829  Nikolai Ivanovich Lobachevsky publishes his work on hyperbolic nonEuclidean geometry,
 1831  Mikhail Vasilievich Ostrogradsky rediscovers and gives the first proof of the divergence theorem earlier described by Lagrange, Gauss and Green,
 1832  Évariste Galois presents a general condition for the solvability of algebraic equations, thereby essentially founding group theory and Galois theory,
 1832  Peter Dirichlet proves Fermat's last theorem for n = 14,
 1835  Peter Dirichlet proves Dirichlet's theorem about prime numbers in arithmetical progressions,
 1837  Pierre Wantsel proves that doubling the cube and trisecting the angle are impossible with only a compass and straightedge, as well as the full completion of the problem of constructability of regular polygons
 1841  Karl Weierstrass discovers but does not publish the Laurent expansion theorem,
 1843  PierreAlphonse Laurent discovers and presents the Laurent expansion theorem,
 1843  William Hamilton discovers the calculus of quaternions and deduces that they are noncommutative,
 1847  George Boole formalizes symbolic logic in The Mathematical Analysis of Logic, defining what are now called Boolean algebras,
 1849  George Gabriel Stokes shows that solitary waves can arise from a combination of periodic waves,
 1850  Victor Alexandre Puiseux distinguishes between poles and branch points and introduces the concept of essential singular points,
 1850  George Gabriel Stokes rediscovers and proves Stokes' theorem,
 1854  Bernhard Riemann introduces Riemannian geometry,
 1854  Arthur Cayley shows that quaternions can be used to represent rotations in fourdimensional space,
 1858  August Ferdinand Möbius invents the Möbius strip,
 1859  Bernhard Riemann formulates the Riemann hypothesis which has strong implications about the distribution of prime numbers,
 1870  Felix Klein constructs an analytic geometry for Lobachevski's geometry thereby establishing its selfconsistency and the logical independence of Euclid's fifth postulate,
 1873  Charles Hermite proves that e is transcendental,
 1873  Georg Frobenius presents his method for finding series solutions to linear differential equations with regular singular points,
 1874  Georg Cantor shows that the set of all real numbers is uncountably infinite but the set of all algebraic numbers is countably infinite. Contrary to widely held beliefs, his method was not his famous diagonal argument, which he published three years later. (Nor did he formulate set theory at this time.)
 1878  Charles Hermite solves the general quintic equation by means of elliptic and modular functions
 1882  Ferdinand von Lindemann proves that π is transcendental and that therefore the circle cannot be squared with a compass and straightedge,
 1882  Felix Klein invents the Klein bottle,
 1895  Diederik Korteweg and Gustav de Vries derive the KdV equation to describe the development of long solitary water waves in a canal of rectangular cross section,
 1895  Georg Cantor publishes a book about set theory containing the arithmetic of infinite cardinal numbers and the continuum hypothesis,
 1896  Jacques Hadamard and Charles de La ValléePoussin independently prove the prime number theorem,
 1896  Hermann Minkowski presents Geometry of numbers,
 1899  Georg Cantor discovers a contradiction in his set theory,
 1899  David Hilbert presents a set of selfconsistent geometric axioms in Foundations of Geometry,
 1900  David Hilbert states his list of 23 problems which show where some further mathematical work is needed,
 1901  Élie Cartan develops the exterior derivative,
 1903  Carle David Tolme Runge presents a fast Fourier Transform algorithm,
 1903  Edmund Georg Hermann Landau gives considerably simpler proof of the prime number theorem,
 1908  Ernst Zermelo axiomizes set theory, thus avoiding Cantor's contradictions,
 1908  Josip Plemelj solves the Riemann problem about the existence of a differential equation with a given monodromic group and uses Sokhotsky  Plemelj formulae,
 1912  Luitzen Egbertus Jan Brouwer presents the Brouwer fixedpoint theorem,
 1912  Josip Plemelj publishes simplified proof for the Fermat's last theorem for exponent n = 5,
 1913  Srinivasa Aaiyangar Ramanujan sends a long list of theorems without proofs to G. H. Hardy.
 1914  Srinivasa Aaiyangar Ramanujan publishes Modular Equations and Approximations to π,
 1919  Viggo Brun defines Brun's constant B_{2} for twin primes,
 1928  John von Neumann begins devising the principles of game theory and proves the minimax theorem,
 1930  Casimir Kuratowski shows that the three cottage problem has no solution,
 1931  Kurt Gödel proves his incompleteness theorem which shows that every axiomatic system for mathematics is either incomplete or inconsistent,
 1931  Georges de Rham develops theorem in cohomology and characteristic classes,
 1933  Karol Borsuk and Stanislaw Ulam present the BorsukUlam antipodalpoint theorem,
 1933  Andrey Nikolaevich Kolmogorov publishes his book Basic notions of the calculus of probability (Grundbegriffe der Wahrscheinlichkeitsrechnung) which contains an axiomatization of probability based on measure theory,
 1940  Kurt Gödel shows that neither the continuum hypothesis nor the axiom of choice can be disproven from the standard axioms of set theory,
 1942  G.C. Danielson and Cornelius Lanczos develop a Fast Fourier Transform algorithm,
 1943  Kenneth Levenberg proposes a method for nonlinear least squares fitting,
 1948  John von Neumann mathematically studies selfreproducing machines,
 1949  John von Neumann computes π to 2,037 decimal places using ENIAC,
 1950  Stanislaw Ulam and John von Neumann present cellular automata dynamical systems,
 1953  Nicholas Metropolis introduces the idea of thermodynamic simulated annealing algorithms,
 1955  Enrico Fermi, John Pasta, and Stanislaw Ulam numerically study a nonlinear spring model of heat conduction and discover solitary wave type behavior,
 1960  C. A. R. Hoare invents the quicksort algorithm,
 1960  Irving Reed and Gustave Solomon present the ReedSolomon errorcorrecting code,
 1961  Daniel Shanks and John Wrench compute π to 100,000 decimal places using an inversetangent identity and an IBM7090 computer,
 1962  Donald Marquardt proposes the LevenbergMarquardt nonlinear least squares fitting algorithm,
 1963  Paul Cohen uses his technique of forcing to show that neither the continuum hypothesis nor the axiom of choice can be proven from the standard axioms of set theory,
 1963  Martin Kruskal and Norman Zabusky analytically study the FermiPastaUlam heat conduction problem in the continuum limit and find that the KdV equation governs this system,
 1965  Martin Kruskal and Norman Zabusky numerically study colliding solitary waves in plasmas and find that they do not disperse after collisions,
 1965  James Cooley and John Tukey present an influential Fast Fourier Transform algorithm,
 1966  E.J. Putzer presents two methods for computing the exponential of a matrix in terms of a polynomial in that matrix,
 1967  Robert Langlands formulates the influential Langlands program of conjectures relating number theory and representation theory,
 1968  Michael Atiyah and Isadore Singer prove the AtiyahSinger index theorem about the index of elliptic operators,
 1975  Benoit Mandelbrot published Les objets fractals, forme, hasard et dimension,
 1976  Kenneth Appel and Wolfgang Haken use a computer to prove the Four color theorem,
 1983  Gerd Faltings proves the Mordell conjecture and thereby shows that there are only finitely many whole number solutions for each exponent of Fermat's last theorem,
 1983  the classification of finite simple groups, a collaborative work involving some hundred mathematicians and spanning thirty years, is completed,
 1985  Louis de Branges de Bourcia proves the Bieberbach conjecture,
 1987  Yasumasa Kanada, David Bailey, Jonathan Borwein, and Peter Borwein use iterative modular equation approximations to elliptic integrals and a NEC SX2 supercomputer to compute π to 134 million decimal places,
 1991  Alain Connes and John W. Lott develop noncommutative geometry,
 1994  Andrew Wiles proves part of the TaniyamaShimura conjecture and thereby proves Fermat's last theorem,
 1998  Thomas Hales (almost certainly) proves the Kepler conjecture,
 1999  the full TaniyamaShimura conjecture is proved.
 2000  the Clay Mathematics Institute establishes the seven Millennium Prize Problems of unsolved important classic mathematical questions,
 2002  Manindra Agrawal, Nitin Saxena, and Neeraj Kayal of IIT Kanpur present an unconditional deterministic polynomial time algorithm to determine whether a given number is prime,
 2002  Yasumasa Kanada, Y. Ushiro, Hisayasu Kuroda, Makoto Kudoh and a team of nine more compute π to 1241 billion digits using a Hitachi 64node supercomputer,
 2004  Richard Arenstorf provides proofs of twin prime conjecture and HardyLittlewood conjecture which contain an error in Lemma 8, discovered by Michel Balazard,
Note
 This article is based on a timeline developed by Niel Brandt (1994) who has given permission for its use in Wikipedia. (See Talk:Timeline of mathematics.)it:Cronologia della matematica