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Timeline of mathematics

   * 2450 BC - Egypt, first systematic method for the approximative
     calculation of the circle on the basis of the Sacred Triangle 3-4-5,
   * 1650 BC - Rhind Mathematical Papyrus, copy of a lost scroll from around
     1850 BC, a great and still widely misunderstood synopsis of early
     geometry and mathematics.
   * 530 BC - Pythagoras studies propositional geometry and vibrating lyre
     strings; his group discovers the irrationality of the square root of
   * 370 BC - Eudoxus states the method of exhaustion for area
   * 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,
   * 260 BC - Archimedes computes π to two decimal places using inscribed
     and circumscribed polygons and computes the area under a parabolic
   * 225 BC - Apollonius of Perga writes On Conic Sections and names the
     ellipse, parabola, and hyperbola,
   * 200 BC ?240 BC - Eratosthenes uses his sieve algorithm to isolate prime
     numbers and finds the number of primes is infinite,
   * 140 BC - Hipparchus develops the bases of trigonometry,
   * 250 - Diophantus uses symbols for unknown numbers in terms of the
     syncopated algebra,
   * 250 - Diophantus writes Arithmetica the first systematic treatise on
   * 450 - Tsu Ch'ung-Chih and Tsu Kng-Chih compute π to six decimal
   * 550 - Hindu mathematicians give zero a numeral representation in a
     positional notation system,
   * 628 - Brahmagupta writes Brahma- sphuta- siddhanta,
   * 750 - Al-Khawarzimi - 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
   * 975 - Al-Batani - Extended the Indian concepts of sine and cosine to
     other trigonometrical ratios, like tangent, secant and their
     reciprocals. Derived the formula: sin α = tan α /  (1+tan2
     α) and cos α = 1 / (1 + tan2 α).
   * 1020 - Abul Wafa - 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 Ahmed Nasawi - Develops the division of days into 24 hours,
     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. Invented the second
     and third degree of quadratic equations.
   * 1202 - Leonardo Fibonacci demonstrates the utility of Arabic numerals
     in his Book of the Abacus,
   * 1424 - Ghiyath al-Kashi - computes π to sixteen decimal places using
     inscribed and circumscribed polygons,
   * 1520 - Scipione dal Ferro develops a method for solving cubic
   * 1535 - Niccolo Tartaglia develops a method for solving cubic equations,
   * 1540 - Lodovico Ferrari solves the quartic equation,
   * 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 - Ren Descartes discovers analytic geometry,
   * 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
   * 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 invents his 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
     inverse-tangent function,
   * 1673 - Gottfried Leibniz invents his 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'Hpital 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 inverse-tangent 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 first-order ordinary differential equations,
   * 1736 - Leonhard Euler solves the problem of the Seven bridges of
     Knigsberg, 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 presents a method for constructing a
     heptadecagon using only a compass and straightedge and also shows that
     only polygons with certain numbers of sides can be constructed,
   * 1796 - Adrien-Marie 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 that every polynomial equation has a
     solution among the complex numbers,
   * 1805 - Adrien-Marie 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 - Simon-Denis Poisson carries out integrations along paths in the
     complex plane,
   * 1817 - Bernard Bolzano presents the intermediate value theorem---a
     continuous function which is negative at one point and positive at
     another point must be zero for at least one point in between,
   * 1822 - Augustin-Louis 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 - Augustin-Louis Cauchy presents the Cauchy integral theorem for
     general integration paths -- he assumes the function being integrated
     has a continuous derivative,
   * 1825 - Augustin-Louis Cauchy introduces the theory of residues in
     complex analysis,
   * 1825 - Johann Peter Gustav Lejeune Dirichlet and Adrien-Marie Legendre
     prove Fermat's last theorem for n = 5,
   * 1825 - Andr-Marie Ampre discovers Stokes' theorem,
   * 1828 - George Green proves Green's theorem,
   * 1829 - Nikolai Ivanovich Lobachevsky publishes his work on hyperbolic
     non-Euclidean geometry,
   * 1831 - Mikhail Vasilievich Ostrogradsky rediscovers and gives the first
     proof of the divergence theorem of earlier described by Lagrange, Gauss
     and Green,
   * 1832 - variste 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,
   * 1841 - Karl Weierstrass discovers but does not publish the Laurent
     expansion theorem,
   * 1843 - Pierre-Alphonse Laurent discovers and presents the Laurent
     expansion theorem,
   * 1843 - William Hamilton discovers the calculus of quaternions and
     deduces that they are non-commutative,
   * 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 four-dimensional space,
   * 1858 - August Ferdinand Mbius invents the Mbius 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 self-consistency 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 formulates set theory and uses his diagonal
     argument to show that the set of all real numbers is uncountably
     infinite but the set of all algebraic numbers is countably infinite,
   * 1878 - Charles Hermite solves the general quintic equation by means of
     elliptic and modular functions
   * 1882 - Carl Louis 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 Valle-Poussin independently
     prove the prime number theorem,
   * 1899 - Georg Cantor discovers a contradiction in his set theory,
   * 1899 - David Hilbert presents a set of self-consistent 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 - lie Cartan develops the exterior derivative,
   * 1903 - Carle David Tolme Runge presents a fast Fourier Transform
   * 1903 - Edmund Georg Hermann Landau gives considerably simpler proof of
     the prime number theorem,
   * 1908 - Ernst Zermelo axiomizes set theory, thus avoiding Cantor's
   * 1908 - Josip Plemelj solves the Riemman 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 fixed-point
   * 1912 - Josip Plemelj publishes simplified proof for the Fermat's last
     theorem for exponent n = 5,
   * 1914 - Srinivasa Aaiyangar Ramanujan publishes Modular Equations and
     Approximations to π,
   * 1919 - Viggo Brun defines Brun's constant B2 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
   * 1931 - Kurt Gdel proves his incompleteness theorem which shows that
     every axiomatic system for mathematics is either incomplete or
   * 1931 - Georges De Rham develops theorem in cohomology and
     characteristic classes,
   * 1933 - Karol Borsuk and Stanislaw Ulam present the Borsuk-Ulam
     antipodal-point theorem,
   * 1933 - Andrey Nikolaevich Kolmogorov publishes his book Basic notions
     of the calculus of variations (Grundbegriffe der
     Wahrscheinlichkeitsrechnung) which contains an axiomatization of
     probability based on measure theory,
   * 1940 - Kurt Gdel shows that neither the continuum hypothesis nor the
     axiom of choice can be disproven from the standard axioms of set
   * 1942 - G.C. Danielson and Cornelius Lanczos develop a Fast Fourier
     Transform algorithm,
   * 1943 - Kenneth Levenberg proposes a method for nonlinear least squares
   * 1948 - John von Neumann mathematically studies self-reproducing
   * 1949 - John von Neumann computes π to 2,037 decimal places using
   * 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 Reed-Solomon
     error-correcting code,
   * 1961 - Daniel Shanks and John Wrench compute π to 100,000 decimal
     places using an inverse-tangent identity and an IBM-7090 computer,
   * 1962 - Donald Marquardt proposes the Levenberg-Marquardt 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
     Fermi-Pasta-Ulam 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
   * 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 Atiyah-Singer index
     theorem about the index of elliptic operators,
   * 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
   * 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 SX-2 supercomputer to compute π to 134 million
     decimal places,
   * 1991 - Alain Connes and John W. Lott develop non-commutative geometry,
   * 1994 - Andrew Wiles proves part of the Taniyama-Shimura conjecture and
     thereby proves Fermat's last theorem,
   * 1999 - the full Taniyama-Shimura 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 Indian
     Institute of Technology (IIT), Kanpur, India, present a 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
     64-node supercomputer,
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