Home›Theorems›All TheoremsBrowse ByAll TheoremsReference and ClassificationDevelopingProved mathematical results, statements with an accepted proof within the mathematical community. Belongs here: theorems, grouped below by the branch of mathematics the result belongs to. Does not belong here: unproved claims, filed as conjectures, even ones widely believed true.All TheoremsConnectionsSourcesComments (0)Reader Challenges (0)All TheoremsFilter Results907 entriesBranchAllAlgebra (51)Algebraic Geometry (12)Algebraic Number Theory (15)Algebraic Topology (11)Analysis (68)Analytic Number Theory (8)Approximation Theory (1)Arithmetic (3)Calculus (4)Calculus of Variations (1)Category Theory (4)Coding Theory (1)Combinatorics (37)Commutative Algebra (7)Complex Analysis (20)Computability Theory (9)Computational Complexity Theory (11)Differential Equations (6)Differential Geometry (5)Differential Topology (7)Discrete Geometry (9)Dynamical Systems (3)Ergodic Theory (1)Field Theory (2)Functional Analysis (8)Galois Theory (2)Game Theory (27)Geometric Topology (1)Geometry (90)Graph Theory (47)Group Theory (5)Harmonic Analysis (5)Information Theory (2)Knot Theory (1)Lie Theory (3)Linear Algebra (15)Logic and Foundations (44)Mathematical Biology (1)Mathematical Physics (63)Measure Theory (4)Model Theory (6)Number Theory (103)Numerical Analysis (1)Operator Theory (2)Optimization (6)Order Theory (2)Potential Theory (1)Probability and Statistics (57)Proof Theory (3)Real Analysis (12)Representation Theory (6)Ring Theory (2)Set Theory (11)Topology (27)Trigonometry (4)Universal Algebra (1)Topic AreaAllAdditive Number Theory (14)Algebraic Geometry (6)Algebraic Number Theory (20)Algebraic Topology (15)Analytic Number Theory (19)Approximation Theory (7)Category Theory (1)Class Field Theory (19)Classical Euclidean Geometry (27)Classical Mechanics and Dynamics (16)Combinatorial Number Theory (9)Complex Analysis (29)Computability and Complexity Theory (24)Congruences and Modular Arithmetic (13)Convex Analysis (7)Convex and Discrete Geometry (16)Decision Theory and Utility (6)Differential Equations (8)Differential Geometry (7)Diophantine Equations (30)Economic Theory (20)Electromagnetism, Optics and Continuum Mechanics (16)Enumerative, Additive and Algebraic Combinatorics (22)Equilibria, Bargaining and Cooperative Games (10)Field Theory and Galois Theory (4)Fixed-Point Theorems (4)Fourier and Harmonic Analysis (10)Functional Analysis (20)General and Universal Algebra (4)General Topology (5)Geometric and Differential Topology (17)Graph Theory (42)Group Theory (12)International Trade Theory (5)Lie Algebras and Representation Theory (11)Linear Algebra and Matrix Theory (18)Mathematical Logic and Model Theory (28)Mathematical Statistics and Estimation (13)Measure Theory and Integration (10)Mechanism Design (5)Polyhedra and Polytopes (5)Polynomials and Elementary Algebra (20)Prime Number Distribution (13)Probability Theory (32)Projective Geometry (5)Proof Theory and Methods of Proof (8)Quadratic Forms and Reciprocity (7)Quantum Mechanics and Quantum Field Theory (22)Ramsey Theory and Extremal Combinatorics (14)Real Analysis (45)Relativity and Gravitation (6)Ring Theory and Commutative Algebra (16)Set Theory (12)Social Choice and Voting Theory (7)Statistical Mechanics and Thermodynamics (9)Stochastic Processes and Martingales (11)Triangle and Circle Geometry (40)ProvedAll520 BCE (1)300 BCE (2)200 BCE (1)60 (1)150 (1)340 (1)1247 (1)1591 (1)1637 (1)1640 (1)1643 (1)1648 (1)1654 (1)1666 (2)1672 (1)1678 (1)1679 (1)1680 (1)1687 (1)1691 (1)1713 (1)1715 (1)1725 (1)1731 (1)1733 (1)1735 (1)1736 (2)1737 (1)1738 (1)1743 (1)1746 (1)1747 (1)1748 (2)1749 (1)1750 (1)1751 (1)1758 (1)1763 (2)1768 (1)1770 (2)1771 (1)1775 (1)1779 (1)1783 (1)1785 (1)1796 (1)1797 (2)1799 (3)1801 (4)1804 (1)1807 (2)1808 (1)1810 (1)1813 (2)1817 (2)1821 (2)1822 (2)1823 (2)1824 (1)1826 (4)1827 (2)1829 (2)1830 (2)1833 (1)1834 (2)1837 (2)1839 (1)1840 (1)1842 (2)1844 (2)1845 (1)1847 (2)1848 (1)1850 (2)1851 (1)1852 (3)1854 (1)1855 (2)1857 (1)1860 (2)1861 (1)1862 (2)1867 (1)1869 (1)1870 (2)1871 (1)1872 (3)1873 (1)1874 (3)1875 (1)1876 (3)1877 (2)1878 (6)1881 (1)1882 (1)1883 (1)1884 (3)1885 (4)1886 (2)1887 (1)1889 (1)1890 (5)1891 (3)1892 (2)1893 (1)1894 (1)1895 (4)1896 (2)1897 (2)1898 (2)1899 (4)1900 (3)1901 (1)1903 (2)1904 (4)1905 (2)1906 (2)1907 (6)1908 (1)1909 (6)1910 (3)1911 (5)1912 (2)1913 (3)1914 (2)1915 (3)1916 (3)1917 (1)1918 (3)1919 (2)1921 (3)1922 (4)1923 (2)1924 (2)1925 (2)1926 (5)1927 (13)1928 (7)1929 (7)1930 (11)1931 (9)1932 (3)1933 (8)1934 (8)1935 (8)1936 (9)1937 (8)1938 (4)1939 (5)1940 (5)1941 (6)1942 (3)1943 (3)1944 (5)1945 (2)1946 (3)1947 (4)1948 (6)1949 (5)1950 (7)1951 (11)1952 (4)1953 (9)1954 (6)1955 (8)1956 (6)1957 (5)1958 (5)1959 (4)1960 (7)1961 (11)1962 (3)1963 (7)1964 (6)1965 (7)1966 (6)1967 (6)1968 (4)1969 (6)1970 (5)1971 (2)1972 (5)1973 (7)1974 (3)1975 (11)1976 (5)1977 (2)1978 (3)1979 (3)1980 (1)1982 (6)1983 (5)1984 (1)1985 (2)1986 (3)1987 (1)1988 (2)1989 (1)1990 (1)1991 (2)1993 (1)1994 (2)1995 (1)1997 (5)1998 (2)2000 (1)2001 (1)2002 (3)2003 (4)2004 (2)2006 (1)2011 (1)2016 (1)2019 (2)Proved ByAllAbraham de Moivre (3)Abraham Seidenberg (2)Abraham Wald (2)Adrien-Marie Legendre (1)Alan Baker (1)Alan Turing (3)Albert Muchnik (1)Aleksandr Khinchin (1)Aleksandr Lyapunov (1)Alexander Gelfond (1)Alexander Grothendieck (1)Alexander Ostrowski (1)Alexandru Froda (1)Alexis Claude Clairaut (1)Alfred Tarski (4)Allan Gibbard (2)Alonzo Church (1)Andrew M. Gleason (1)Andrew Wiles (4)Andrey Kolmogorov (4)André Weil (1)Archimedes (1)Arthur Cayley (4)Augustin-Louis Cauchy (17)Augustus De Morgan (1)Barry Mazur (1)Bartel Leendert van der Waerden (1)Ben Green (1)Beppo Levi (1)Bernard Bolzano (2)Bernard Dwork (1)Bernard Malgrange (1)Bernhard Riemann (6)Bertram Kostant (1)Blaise Pascal (2)Brook Taylor (1)Bruno Courcelle (1)Bryan Birch (1)Camille Jordan (4)Carl Anton Bretschneider (1)Carl Friedrich Gauss (12)Carl Gustav Jacob Jacobi (1)Carl Ludwig Siegel (4)Carl Runge (1)Carl Wilhelm Oseen (1)Carlo Severini (1)Charles Hermite (1)Charles-Jean de la Vallee Poussin (1)Claude Berge (3)Claude Chevalley (1)Constantin Carathéodory (3)David Blackwell (2)David Hilbert (8)Donald A. Martin (1)Dov Gabbay (1)Dénes Kőnig (1)Désiré André (1)Edgar H. Brown (1)Eduard Helly (2)Edward Charles Titchmarsh (2)Edward John Routh (1)Edward Witten (1)Edwin Hewitt (1)Egon Pearson (1)Emanuel Lasker (1)Emanuel Sperner (2)Emil Artin (5)Emil Post (1)Emmy Noether (6)Endre Szemerédi (5)Enrico Betti (1)Enrico Bombieri (1)Ernst Kummer (1)Ernst Leonard Lindelöf (2)Ernst Specker (1)Ernst Steinitz (3)Ernst Witt (2)Ernst Zermelo (3)Euclid (5)Eugene Wigner (1)Eugenio Elia Levi (1)Evert Willem Beth (1)Felix Hausdorff (1)Ferdinand Georg Frobenius (3)Francesco Paolo Cantelli (3)Frank Morley (1)Frank P. Ramsey (1)Franz Mertens (1)Franz Rellich (1)François Budan de Boislaurent (1)François Viète (1)Friedrich Bessel (1)Frigyes Riesz (3)Gabriel Cramer (1)Garrett Birkhoff (1)Gaspard Monge (1)Gaston Darboux (2)Georg Alexander Pick (1)Georg Cantor (3)George David Birkhoff (3)George Gabriel Stokes (1)George Pólya (3)George Udny Yule (1)Georgy Voronoy (1)Gerd Faltings (1)Gerhard Gentzen (2)Gerhard Ringel (1)Giovanni Ceva (1)Giovanni Girolamo Saccheri (1)Giuseppe Vitali (2)Gottfried Wilhelm Leibniz (1)Gotthold Eisenstein (1)Gottlob Frege (1)Graham Higman (1)Grigori Perelman (2)Guido Fubini (2)Gustav Herglotz (2)Gustav Kirchhoff (1)Gérard Debreu (2)Gösta Mittag-Leffler (1)Hans Freudenthal (1)Hans Hahn (2)Hans Rademacher (1)Hans-Egon Richert (1)Hao Huang (1)Harald Bohr (1)Harald Cramér (4)Hassler Whitney (3)Heinrich Martin Weber (1)Heinrich Maschke (1)Heinrich Tietze (1)Heinz Hopf (1)Helmut Hasse (3)Helmut Maier (1)Henri Lebesgue (3)Henri Poincaré (7)Herbert Robbins (1)Herbert Seifert (1)Herman Müntz (1)Hermann Minkowski (2)Hermann Schwarz (2)Hermann Weyl (3)Heron of Alexandria (1)Hugo Steinhaus (1)Irvin S. Cohen (1)Isaac Namioka (1)Isaac Newton (3)Issai Schur (2)Ivan Niven (1)Ivan Vinogradov (3)Ivar Fredholm (1)J. Barkley Rosser (1)J. H. C. Whitehead (1)J. W. T. Youngs (1)Jacob Bernoulli (3)Jacques Charles François Sturm (1)Jacques Hadamard (2)Jacques Herbrand (2)Jakob Levitzki (1)Jakob Steiner (4)James Joseph Sylvester (1)Johann Radon (2)John Conway (2)John G. Thompson (1)John Milnor (1)John Nash (3)John von Neumann (2)Jon Barwise (1)Joseph Bertrand (2)Joseph Fourier (1)Joseph Kruskal (2)Joseph L. Doob (2)Joseph Liouville (2)Joseph R. Shoenfield (1)Joseph Wedderburn (1)Joseph Wolstenholme (1)Joseph-Louis Lagrange (5)Joseph-Émile Barbier (1)Julius Petersen (3)Juliusz Schauder (1)Jun-iti Nagata (1)Karl Menger (1)Karl von Staudt (1)Karl Weierstrass (8)Karol Borsuk (1)Kazimierz Kuratowski (2)Ken Ribet (1)Kenneth Appel (1)Kenneth Arrow (1)Kiyosi Itô (1)Klaus Wagner (2)Kurt Gödel (4)Kurt Heegner (1)Kurt Mahler (3)L. E. J. Brouwer (3)Laurent Clozel (1)Laurent Lafforgue (1)Lazare Carnot (1)Lennart Carleson (1)Leonhard Euler (13)Leonid Levin (1)Leopold Kronecker (2)Leopold Löwenheim (1)Leopold Vietoris (1)Lipót Fejér (1)Lloyd Shapley (3)Louis Mordell (1)Louis Poinsot (1)Ludwig Boltzmann (1)Ludwig Sylow (1)László Lovász (1)Marc-Antoine Parseval (1)Marcel Riesz (1)Mark Krein (1)Mark Satterthwaite (2)Marquis de Condorcet (1)Martin Kutta (1)Max Born (1)Max Zorn (1)Menelaus of Alexandria (1)Michael Atiyah (1)Michael Freedman (1)Michael Harris (1)Michel Plancherel (1)Mikhail Gromov (1)Moritz Pasch (1)Neil Robertson (3)Nicholas Shepherd-Barron (1)Nicolaas Govert de Bruijn (2)Nicolaas Kuiper (1)Niels Henrik Abel (6)Nikolai Chebotaryov (1)Olga Bondareva (1)Olga Taussky-Todd (1)Oskar Perron (1)Otto Schreier (2)Otto Szász (1)Pafnuty Chebyshev (3)Pappus of Alexandria (1)Patrick Michael Grundy (1)Paul Erdos (12)Paul Lévy (1)Paul Seymour (3)Pavel Urysohn (2)Per Lindström (1)Percy Alexander MacMahon (1)Percy John Heawood (1)Peter Gustav Lejeune Dirichlet (6)Philip Hall (1)Philipp Furtwängler (1)Pierre de Fermat (4)Pierre Fatou (1)Pierre Ossian Bonnet (1)Pierre Varignon (1)Pierre Wantzel (1)Pierre-Simon Laplace (3)Pietro Mengoli (1)Preda Mihăilescu (1)Pythagoras (1)Pál Turán (2)Qin Jiushao (1)R. Leonard Brooks (1)René Descartes (2)René Fréchet (2)Reuben Goodstein (1)Richard Bellman (1)Richard Taylor (1)Robert Aumann (1)Robert Lawson Vaught (1)Robert M. Solovay (2)Robert P. Dilworth (1)Robert Simson (3)Robert Tijdeman (1)Roger Lyndon (1)Roger Penrose (1)Roland Sprague (1)Ronald Fisher (4)Rudolf Clausius (1)Salomon Bochner (1)Samuel Earnshaw (1)Samuel Eilenberg (1)Sarvadaman Chowla (1)Semyon Aranovich Gershgorin (1)Serge Lang (1)Sergei Bernstein (1)Shimshon Amitsur (1)Shizuo Kakutani (1)Simon B. Kochen (2)Simon Donaldson (1)Siméon Denis Poisson (1)Solomon Lefschetz (1)Sophie Germain (1)Sophus Lie (2)Srinivasa Ramanujan (2)Stanisław Świerczkowski (1)Stefan Banach (4)Stephen Cole Kleene (2)Stephen Cook (2)Stephen Smale (2)Sumner Byron Myers (1)Teiji Takagi (1)Terence Tao (1)Thabit ibn Qurra (1)Theodor Schneider (1)Theodore Motzkin (1)Thomas Bayes (1)Thomas Clausen (1)Thomas Hales (1)Thoralf Skolem (1)Tibor Gallai (1)Vadim G. Vizing (1)Vera T. Sós (1)Viggo Brun (2)W. T. Tutte (5)Wacław Sierpiński (1)Walter Feit (1)Wassily Hoeffding (3)Wei-Liang Chow (1)Wilhelm Ackermann (1)Wilhelm Blaschke (1)Wilhelm Grunwald (1)Wilhelm Specht (1)Willi Rinow (1)William Allen Whitworth (1)William Burnside (1)William Gemmell Cochran (1)William Lawvere (1)William Rowan Hamilton (1)William Vallance Douglas Hodge (1)Wolfgang Haken (1)Wolfgang Krull (5)Yuri Linnik (1)Zsolt Baranyai (1)Édouard Goursat (2)Édouard Lucas (1)Élie Cartan (2)Émile Picard (2)Étienne Bézout (2)Évariste Galois (1)Øystein Ore (1)Named AfterAllAdrien-Marie Legendre (1)Alan Turing (1)Andrew Wiles (1)Andrey Kolmogorov (3)Andrey Markov (1)Arthur Cayley (2)Augustin-Louis Cauchy (2)Bernhard Riemann (1)Bryan Birch (1)Carl Friedrich Gauss (2)David Hilbert (5)Emmy Noether (3)Ernst Zermelo (2)Euclid (2)Georg Cantor (2)Isaac Newton (2)John Nash (1)Joseph-Louis Lagrange (2)Kurt Gödel (2)Leonhard Euler (6)Niels Henrik Abel (5)Pierre de Fermat (4)Sophie Germain (1)Statement FormAllCharacterization Theorem (262)Classification Theorem (20)Existence Theorem (211)Identity or Equation (212)Impossibility Theorem (45)Inequality (164)Uniqueness Theorem (44)Show ResultsBrowseCompareSelect all 100Nash-Williams FormulaCombinatorics and Graph TheoryNernst's TheoremMathematical PhysicsNewton's IdentitiesAlgebraNewton's Theorem (Quadrilateral)GeometryNeyman-Pearson LemmaProbability and StatisticsNicomachus's TheoremCombinatorics and Graph TheoryNielsen-Schreier TheoremAlgebraNine-Point Circle TheoremGeometryNiven's TheoremNumber TheoryNo Free Lunch TheoremProbability and StatisticsNo-Cloning TheoremMathematical PhysicsNoether Normalization LemmaAlgebraNoether's Isomorphism TheoremsAlgebraNoether's Second TheoremMathematical PhysicsNoether's TheoremMathematical PhysicsNo-Hair TheoremMathematical PhysicsNo-Trade TheoremGame TheoryOdd Number TheoremMathematical PhysicsOkishio's TheoremGame TheoryOmitting Types TheoremLogic and FoundationsOnsager Reciprocal RelationsMathematical PhysicsOpen Mapping Theorem (Complex Analysis)AnalysisOpen Mapping Theorem (Functional Analysis)AnalysisOptical TheoremMathematical PhysicsOptional Stopping TheoremProbability and StatisticsOre's TheoremCombinatorics and Graph TheoryOstrowski's TheoremNumber TheoryPappus's TheoremGeometryParallel Axis TheoremMathematical PhysicsParis-Harrington TheoremLogic and FoundationsParseval's TheoremAnalysisPascal's TheoremGeometryPasch's TheoremGeometryPataraia's TheoremLogic and FoundationsPCP TheoremLogic and FoundationsPeano Existence TheoremAnalysisPell's EquationNumber TheoryPenrose-Hawking Singularity TheoremsMathematical PhysicsPentagonal Number TheoremNumber TheoryPerfect Graph TheoremCombinatorics and Graph TheoryPerpendicular Axis TheoremMathematical PhysicsPerron-Frobenius TheoremAlgebraPetersen-Morley TheoremGeometryPetersen's TheoremCombinatorics and Graph TheoryPeter-Weyl TheoremAlgebraPhragmen-Lindelof PrincipleAnalysisPicard TheoremAnalysisPicard-Lindelof TheoremAnalysisPick's TheoremGeometryPitot TheoremGeometryPlanar Separator TheoremCombinatorics and Graph TheoryPlancherel TheoremAnalysisPoincare ConjectureTopologyPoincare Duality TheoremTopologyPoincare LemmaTopologyPoincare Recurrence TheoremMathematical PhysicsPoincare-Bendixson TheoremAnalysisPoincare-Birkhoff-Witt TheoremAlgebraPoincare-Hopf TheoremTopologyPoisson Summation FormulaAnalysisPokhozhaev's IdentityAnalysisPolya Enumeration TheoremCombinatorics and Graph TheoryPolya-Vinogradov InequalityNumber TheoryPomeranchuk's TheoremMathematical PhysicsPompeiu's TheoremGeometryPoncelet's Closure TheoremGeometryPoncelet-Steiner TheoremGeometryPoppy-Seed Bagel TheoremAnalysisPost's TheoremLogic and FoundationsPoynting's TheoremMathematical PhysicsPrigogine's TheoremMathematical PhysicsPrime Number TheoremNumber TheoryPrimitive Element TheoremAlgebraPrincipal Axis TheoremAlgebraPrincipal Ideal TheoremNumber TheoryProbabilistic MethodCombinatorics and Graph TheoryProof by ExhaustionLogic and FoundationsProof by Infinite DescentNumber TheoryProof of Fermat's Last Theorem for Specific ExponentsNumber TheoryProof that 22/7 Exceeds PiNumber TheoryProof That e Is IrrationalNumber TheoryProof that Pi is IrrationalNumber TheoryProof Without WordsLogic and FoundationsProofs of Quadratic ReciprocityNumber TheoryProth's TheoremNumber TheoryPtolemy's TheoremGeometryPythagorean TheoremGeometryPythagorean Trigonometric IdentityAnalysisRabin's Calibration TheoremProbability and StatisticsRademacher's TheoremAnalysisRadon-Nikodym TheoremAnalysisRadon's TheoremGeometryRamanujan-Nagell EquationNumber TheoryRamanujan-Nagell TheoremNumber TheoryRamsey's TheoremCombinatorics and Graph TheoryRank-Nullity TheoremAlgebraRao-Blackwell TheoremProbability and StatisticsRational Root TheoremAlgebraRauch Comparison TheoremGeometryReeh-Schlieder TheoremMathematical Physics← Previous1…5678910Next →ConnectionsShowing the first 400 of 908 connections.SourcesMacTutor History of Mathematics Archivetier 1University of St Andrews, School of Mathematics and StatisticsContains: Central Limit TheoremContains: Bayes' TheoremView the SourceWikipedia: Noether's Theoremtier 2Wikimedia FoundationContains: Noether's TheoremView the SourceWikipedia: Cayley's Theoremtier 2Wikimedia FoundationContains: Cayley's TheoremView the SourceComments (0)No comments yet. Be the first to share a thought.Sign in to join the discussion.Reader Challenges (0)No disputes yet. Spotted an error or a better source? Open the first one.Sign in to dispute this or suggest a correction.