수학사 연표

17세기

1600s - Putumana Somayaji writes the "Paddhati", which presents a detailed discussion of various trigonometric series
1614 -존 네이피어가 Mirifici Logarithmorum Canonis Descriptio에서 네이피어 로그의 개념을 논함
1617 - Henry Briggs discusses decimal logarithms in Logarithmorum Chilias Prima,
1618 - 네이피어가 로그와 관련한 작업을 통하여 자연상수에 대한 첫번째 출판을 함
1619 - 페르마가 해석기하학을 독립적으로 발견했음을 주장함
1619 - Johannes Kepler discovers two of the Kepler-Poinsot polyhedra.
1629 - 페르마가 기초적인 미분학을 발전시킴
1634 - Gilles de Roberval 사이클로이드 아래의 면적이 기본원의 세 배임을 증명
1636 - Muhammad Baqir Yazdi jointly discovered the pair of amicable numbers 9,363,584 and 9,437,056 along with Descartes (1636)
1637 - 데카르트가 방법서설을 출판, 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 - 파스칼과 페르마가 확률론을 창시
1655 - 존 월리스가 Arithmetica Infinitorum를 저술
1658 - Christopher Wren 사이클로이드의 길이가 기본원의 네 배임을 증명
1665 - 뉴턴이 미적분학의 기본정리를 연구하고 미적분학을 발전시킴
1668 - Nicholas Mercator and William Brouncker discover an infinite series for the logarithm while attempting to calculate the area under a hyperbolic segment,
1671 - 제임스 그레고리가 아크탄젠트함수의 급수표현을 발견(그레고리-라이프니츠 급수) (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 - 자콥 베르누이와 요한 베르누이가 최단강하곡선 문제를 해결함. the first result in the calculus of variations,

18세기

1706 - 마친, 마친(Machin)의 공식을 활용하여 파이값 100자리까지 계산
1712 - Brook Taylor develops Taylor series,
1722 - 드 무아브르의 정리, 복소수와 정다각형 발견
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 - 드무아브르가 정규분포의 확률밀도함수를 통해 이항분포의 근사식을 얻음. 드무아브르-라플라스 중심극한정리 참조.
1734 - Leonhard Euler introduces the integrating factor technique for solving first-order ordinary differential equations,
1735 - 오일러가 바젤 문제를 해결함 오일러와 바젤문제(완전제곱수의 역수들의 합)
1736 - Leonhard Euler solves the problem of the Seven bridges of Königsberg, in effect creating graph theory,
1739 - 오일러가 상수계수 선형미분방정식의 일반해를 구함
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 - 가우스가 정17각형의 작도 문제를 해결함.
1796 - 르장드르가 소수정리를 추측함.
1797 - Caspar Wessel associates vectors with complex numbers and studies complex number operations in geometrical terms,
1799 - 가우스가 대수학의 기본정리를 증명함
1799 - Paolo Ruffini partially proves the Abel–Ruffini theorem that quintic or higher equations cannot be solved by a general formula,

19세기

1801 - 가우스가 Disquisitiones Arithmeticae를 출판함.
1805 - 르장드르가 최소자승의 법칙을 도입함.
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 - 푸리에가 함수의 삼각함수로의 분해를 발표
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 -코쉬가 복소함수론에서 사각형의 둘레를 따라 적분한데 대한 코쉬정리를 발표함
1824 - 아벨이 일반적인 5차 이상의 방정식의 근의 공식이 없음을 증명함. 5차방정식의 근의 공식과 아벨의 증명 참조
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 - 디리클레와 르장드르가 n = 5인 경우에 대해 페르마의 마지막 정리를 증명
1825 - André-Marie Ampère 가 스토크스 정리를 발견
1828 - 조지 그린(George Green)이 그린 정리 를 증명함
1829 - 볼리아이, 가우스, 로바체프스키가 쌍곡기하학을 발견
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 - 디리클레가 n = 14인 경우의 페르마의 마지막 정리를 증명
1837 - 디리클레가 등차수열의 소수분포에 관한 디리클레 정리를 증명
1837 - 피에르 완첼(Pierre Wantsel)이 두배의 부피를 갖는 정육면체(The duplication of the cube)과 각의 3등분(The trisection of an angle) 문제가 자와 컴파스로 해결불가능임을 증명, 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 - 해밀턴이 사원수 를 발견함
1844 - 리우빌이 초월수인 리우빌 수를 구성함
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 - 리만이 리만기하학을 소개
1854 - Arthur Cayley shows that quaternions can be used to represent rotations in four-dimensional space,
1858 - 뫼비우스가 뫼비우스의 띠를 발견
1859 - 리만이 리만가설을 발표
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 자연상수 e는 초월수
임으
1873 - 프로베니우스(Georg Frobenius)가 정규특이점(regular singular points)을 가지는 선형미분방정식의 급수해 찾는 방법을 소개함
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
- 오차방정식과 정이십면체
1882 - 린데만이 파이는 초월수임을 증명하고 따라서 원이 자와 컴파스로 작도 불가능함을 증명
1882 - 펠릭스 클라인이 클라인씨의 병을 발견
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 [1]아인슈타인 특수상대성 이론 발표
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 - 라마누잔이 'Modular Equations and Approximations to π'를 출판
- 라마누잔과 파이 항목 참조
1916 아인슈타인 일반상대성 이론 발표
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 - 폰노이만이 에니악을 이용하여 파이를 소수점 2,037 자리까지 계산함
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. 베이커의 정리.
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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