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17세기

1600s - Putumana Somayaji writes the "Paddhati", which presents a detailed discussion of various trigonometric series
1614 - John Napier discusses Napierian logarithms in Mirifici Logarithmorum Canonis Descriptio,
1617 - Henry Briggs discusses decimal logarithms in Logarithmorum Chilias Prima,
1618 - John Napier publishes the first references to e in a work on logarithms.
1619 - René Descartes discovers analytic geometry (Pierre de Fermat claimed that he also discovered it independently),
1619 - Johannes Kepler discovers two of the Kepler-Poinsot polyhedra.
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,
1636 - Muhammad Baqir Yazdi jointly discovered the pair of amicable numbers 9,363,584 and 9,437,056 along with Descartes (1636).인용 오류: <ref> 태그가 잘못되었습니다;

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1637 - Pierre de Fermat claims to have proven Fermat's Last Theorem in his copy of Diophantus' Arithmetica,
1637 - First use of the term imaginary number by René Descartes; it was meant to be derogatory.
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 develops his version of infinitesimal 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 develops a series expansion for the inverse-tangent function (originally discovered by Madhava)
1673 - Gottfried Leibniz also develops his version of infinitesimal calculus,
1675 - Isaac Newton invents an algorithm for the computation of functional roots,
1680s - Gottfried Leibniz works on symbolic logic,
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,

18세기

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 formula 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,
1735 - Leonhard Euler solves the Basel problem, relating an infinite series to π,
1736 - Leonhard Euler solves the problem of the Seven bridges of Königsberg, in effect creating graph theory,
1739 - Leonhard Euler solves the general homogeneous 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 17-gon can be constructed using only a compass and straightedge
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 the fundamental theorem of algebra (every polynomial equation has a solution among the complex numbers),
1799 - Paolo Ruffini partially proves the Abel–Ruffini theorem that quintic or higher equations cannot be solved by a general formula,

19세기

1801 - Disquisitiones Arithmeticae, Carl Friedrich Gauss's number theory treatise, is published in Latin
1805 - Adrien-Marie Legendre introduces the method of least squares for fitting a curve to a given set of observations,
1806 - Louis Poinsot discovers the two remaining Kepler-Poinsot polyhedra.
1806 - Jean-Robert Argand publishes proof of the Fundamental theorem of algebra and the Argand diagram,
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 - Siméon-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 the Abel–Ruffini theorem 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, and he 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 - André-Marie Ampère discovers Stokes' theorem,
1828 - George Green proves Green's theorem,
1829 - Bolyai, Gauss, and Lobachevsky invent hyperbolic non-Euclidean 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 - 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 is now called Boolean algebra,
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 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 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 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 Jean de la Vallée-Poussin independently prove the prime number theorem,
1896 - Hermann Minkowski presents Geometry of numbers,
1887 - 12월 22일, 라마누잔 탄생(라마누잔의 수학)
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.

20세기

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.
1905 - Einstein's theory of special relativity.
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 fixed-point 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 complex theorems without proofs to G. H. Hardy,
1914 - Srinivasa Aaiyangar Ramanujan publishes Modular Equations and Approximations to π,
1916 - Einstein's theory of general relativity.
1910s - Srinivasa Aaiyangar Ramanujan develops over 3000 theorems, including properties of highly composite numbers, the partition function and its asymptotics, and mock theta functions. He also makes major breakthroughs and discoveries in the areas of gamma functions, modular forms, divergent series, hypergeometric series and prime number theory
1919 - Viggo Brun defines Brun's constantB₂ for twin primes,
1920 - 4월 26일 라마누잔 사망
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 theorems 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 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 self-reproducing 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 - H. S. M. Coxeter et al. publish the complete list of uniform polyhedron,
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 S. 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,
1963 - meteorologist and mathematician Edward Norton Lorenz published solutions for a simplified mathematical model of atmospheric turbulence - generally known as chaotic behaviour and strange attractors or Lorenz Attractor - also the Butterfly Effect,
1965 - Iranian mathematician Lotfi Asker Zadeh founded fuzzy set theory as an extension of the classical notion of set and he founded the field of Fuzzy Mathematics,
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,
1966 - Abraham Robinson presents Non-standard analysis.
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,
1973 - Lotfi Zadeh founded the field of fuzzy logic,
1975 - Benoît Mandelbrot publishes 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 - 유한단순군의 분류 완료
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 페르마의 마지막 정리 증명
1998 - Thomas Callister Hales (almost certainly) 케플러의 추측 증명
1999 - the full Taniyama-Shimura conjecture is proved,
2000 - the Clay Mathematics Institute proposes the seven Millennium Prize Problems of unsolved important classic mathematical questions.

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