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Theorem List (Alphabetical)

This version of the complete list of theorems is given alphabetically by keyword. Thus Albert–Brauer–Hasse–Noether Main Theorem will appear under A for Albert, B for Brauer, H for Hasse, N for Noether and M for Main (but not T for Theorem).

Clicking on a theorem will open its description page (pdf). Numbers in parentheses following an entry link back to the corresponding entry in the main theorem listing.

  A  B   C   D  E   F   G  H   I   J  K   L   M  N   O   P  Q   R   S  T   U   V  W   X   Y  Z

 
A
Jump to Top 		The Abel–Hurwitz Binomial Theorem (89)
The Albert–Brauer–Hasse–Noether Main Theorem (158)
The Fundamental Theorem of Algebra (8)
al-Kāshi's Law of Cosines (188)
The Analyst's Travelling Salesman Theorem (108)
The Andrews–Garvan–Dyson Crank (172)
A Theorem on Apollonian Circle Packings (130)
The Classification of Archimedean 4-Polytopes (160)
Archimedes' Equiareal Map Theorem (181)
The Fundamental Theorem of Arithmetic (7)
The Green–Tao Theorem on Primes in Arithmetic Progression (32)
Arrow's Impossibility Theorem (69)
The Wedderburn–Artin Theorem (123)
The Asymptotic (Half) Liar Formula (126)
The Hardy–Ramanujan Asymptotic Partition Formula (115)

 
B
Jump to Top		 Babbitt's Theorem (106)
The Existence Theorem for Bachelor Latin Squares (176)
Bailey's Theorem on Latin Squares (53)
Bayes' Theorem (10)
The Beardwood–Halton–Hammersley Theorem (109)
Beineke's Theorem on Line Graphs (48)
Benford's Law (31)
The BEST Theorem (171)
Binet's Formula (45)
The Binomial Theorem (47)
The Abel–Hurwitz Binomial Theorem (89)
Kőnig's Bipartite Matching Theorem (185)
The Birkhoff–von Neumann Theorem (57)
The Bose Equivalence Theorem in Design Theory (54)
The Heine–Borel Theorem (177)
The Borsuk–Ulam Theorem (122)
Praeger's Theorem on Bounded Movement (135)
Brahmagupta's Formula (76)
The Albert–Brauer–Hasse–Noether Main Theorem (158)
The Ollerenshaw–Brée Formula (129)
Bregman's Theorem (112)
Brouwer's Fixed Point Theorem (18)
The Bruck–Ryser–Chowla Theorem on Finite Projective Planes (3)
Brun's Theorem (21)
The Bungers–Lehmer Theorem on Cyclotomic Coefficients (175)

 
C
Jump to Top 		The Fundamental Theorem of the Calculus (2)
The Cameron–Fon-Der-Flaass IBIS Theorem (174)
Cameron's Theorem on Distance-Transitive Graphs (46)
Cantor's Theorem (23)
Cantor's Uncountability Theorem (22)
Cardano's Cubic Formula (90)
Cartwright's Theorem (98)
Catalan's Conjecture (Mihăilescu's Theorem) (118)
The Cauchy–Kovalevskaya Theorem (88)
Cayley's Formula (94)
Cayley's Theorem (85)
The Central Limit Theorem (8)
The Design of the Century (100)
A Theorem of Melody Chan on Group Actions (51)
The Change of Variables Theorem (134)
The Chinese Remainder Theorem (5)
The Bruck–Ryser–Chowla Theorem on Finite Projective Planes (3)
Sokal's Theorem on Chromatic Roots (169)
A Theorem on Apollonian Circle Packings (130)
The Five Circle Theorem (84)
The Descartes Circle Theorem (179)
The Classification of Archimedean 4-Polytopes (160)
The Diaconis–Holmes–Montgomery Coin Tossing Theorem (164)
Graph Colouring by Vertex Degree (70)
Khinchin's Theorem on Continued Fractions (91)
The Contraction Mapping Theorem (145)
The Convolution Theorem (95)
Cook's Theorem on NP-completeness (14)
The Polynomial Coprimality Theorem (116)
The Robinson–Schensted–Knuth Correspondence (143)
al-Kāshi's Law of Cosines (188)
The Andrews–Garvan–Dyson Crank (172)
Cardano's Cubic Formula (90)
The Bungers–Lehmer Theorem on Cyclotomic Coefficients (175)

 
D
Jump to Top 		The Delsarte–Goethals–Seidel Theorem (83)
De Moivre's Theorem (152)
De Morgan's Laws (111)
The Descartes Circle Theorem (179)
The Design of the Century (100)
The Bose Equivalence Theorem in Design Theory (54)
The Diaconis–Holmes–Montgomery Coin Tossing Theorem (164)
The Existence Theorem for Orthogonal Diagonal Latin Squares (131)
Dilworth's Theorem (19)
The Three-Distance Theorem (78)
Cameron's Theorem on Distance-Transitive Graphs (46)
Netto's Conjecture (Dixon's Theorem) (49)
The DPRM Theorem (43)
The Sophomore's Dream (147)
The Andrews–Garvan–Dyson Crank (172)

 
E
Jump to Top

Theorema Egregium (183)
The Happy Ending Problem (99)
The Insolvability of the Entscheidungsproblem (186)
Archimedes' Equiareal Map Theorem (181)
The Bose Equivalence Theorem in Design Theory (54)
An Erdős–Ko–Rado Theorem on Intersecting Permutations (66)
A Theorem of Erdős and Wilson on Edge Colouring (117)
The Euclid–Euler Theorem (128)
Euclid's Infinity of Primes (4)
Euclid's Triangular Prism (149)
Euler's Formula (26)
The Euler–Hierholzer "Bridges of Königsberg" Theorem (50)
Euler's Identity (36)
Euler's Partition Identity (153)
Theorems of Euler and Rényi on 'e' (136)
The Existence Theorem for Bachelor Latin Squares (176)
The Existence Theorem for Orthogonal Diagonal Latin Squares (131)

 
F
Jump to Top 		1-Factorisation of Regular Graphs (80)
Fermat's Last Theorem (9)
Fermat's Little Theorem (13)
The Fifteen Theorem (79)
Galois' Theorem on Finite Fields (58)
Heath's Finitely Discontinuous Function Theorem (162)
The Bruck–Ryser–Chowla Theorem on Finite Projective Planes (3)
The First Isomorphism Theorem (34)
Gödel's First Incompleteness Theorem (74)
The Five Circle Theorem (84)
Nevanlinna's Five-Value Theorem (97)
Brouwer's Fixed Point Theorem (18)
The Cameron–Fon-Der-Flaass IBIS Theorem (174)
The Four-Colour Theorem (1)
Lagrange's Four Squares Theorem (11)
The Friendship Theorem (163)
The Marriage Theorem and The Frobenius–König Theorem (62)
The Fundamental Theorem of Algebra (6)
The Fundamental Theorem of Arithmetic (7)
The Fundamental Theorem of the Calculus (2)

 
G
Jump to Top 		Galois' Theorem on Finite Fields (58)
The Small Prime Gaps Theorem (151)
The Andrews–Garvan–Dyson Crank (172)
Gauss's Law of Quadratic Reciprocity (29)
The Generalised Hexachord Theorem (93)
Germain's Theorem (59)
The Girard-Newton Identities (182)
Girard's Theorem (37)
Gödel's First Incompleteness Theorem (74)
Gödel's Second Incompleteness Theorem (75)
Goodstein's Theorem (73)
The Delsarte–Goethals–Seidel Theorem (83)
The Goins–Maddox–Rusin Theorem on Heron Triangles (104)
Graph Colouring by Vertex Degree (The Green–Tao Theorem on Primes in Arithmetic Progression (32)
The Greibach Normal Form Theorem (180)
A Theorem of Melody Chan on Group Actions (51)
Gruenberg's Theorem on Nilpotent Groups (82)

 
H
Jump to Top 		Haken's Unknot Theorem (166)
The Asymptotic (Half) Liar Formula (126)
The Beardwood–Halton–Hammersley Theorem (109)
The Happy Ending Problem (99)
The Hardy–Ramanujan Asymptotic Partition Formula (115)
The Albert–Brauer–Hasse–Noether Main Theorem (158)
Heath's Finitely Discontinuous Function Theorem (162)
The Heine–Borel Theorem (177)
The Goins–Maddox–Rusin Theorem on Heron Triangles (104)
The Generalised Hexachord Theorem (93)
The Euler–Hierholzer "Bridges of Königsberg" Theorem (50)
The Diaconis–Holmes–Montgomery Coin Tossing Theorem (164)
Woodall's Hopping Lemma (150)
The Abel–Hurwitz Binomial Theorem (89)

 
I
Jump to Top 		The Cameron–Fon-Der-Flaass IBIS Theorem (174)
Arrow's Impossibility Theorem (69)
Gödel's First Incompleteness Theorem (74)
Gödel's Second Incompleteness Theorem (75)
Sylvester's Law of Inertia (142)
The Insolvability of the Entscheidungsproblem (186)
The First Isomorphism Theorem (34)
The Second and Third Isomorphism Theorems (35)
The Lagrange Interpolation Formula (124)
An Erdős–Ko–Rado Theorem on Intersecting Permutations (66)

 
J
Jump to Top

 
K
Jump to Top 		Karp's Theorem (Detail) Conjecture (187)
Kepler's Conjecture (101)
Khinchin's Theorem on Continued Fractions (91)
Kneser's Conjecture (119)
The Robinson–Schensted–Knuth Correspondence (143)
An Erdős–Ko–Rado Theorem on Intersecting Permutations (66)
The Euler–Hierholzer "Bridges of Königsberg" Theorem (50)
Kőnig's Bipartite Matching Theorem (185)
The Marriage Theorem and The Frobenius–Kőnig Theorem (62)
The Cauchy–Kovalevskaya Theorem (88)
Kuratowski's Theorem (24)

 
L
Jump to Top 		Lagrange's Four Squares Theorem (11)
The Lagrange Interpolation Formula (124)
The Lagrange Property for Moufang Loops (114)
Lagrange's Theorem (41)
Lambert's Formula (121)
Lamé's Theorem (87)
Bailey's Theorem on Latin Squares (53)
The Existence Theorem for Bachelor Latin Squares (176)
The Existence Theorem for Orthogonal Diagonal Latin Squares (131)
Sylvester's Law of Inertia (142)
The Law of Large Numbers (30)
The Lecture Hall Partition Theorem (156)
The Bungers–Lehmer Theorem on Cyclotomic Coefficients (175)
The Asymptotic (Half) Liar Formula (126)
Lieb's Square Ice Theorem (144)
The Lindemann–Weierstrass Theorem (167)
Beineke's Theorem on Line Graphs (48)
Lin McMullin's Theorem (165)
The Lovász Local Lemma (120)
The Lucas–Lehmer Test (127)
Lucas' Theorem (38)
The Lutz–Nagell Theorem (81)

 
M
Jump to Top 		Machin's Formula (170)
MacWilliams' Identity (72)
The Goins–Maddox–Rusin Theorem on Heron Triangles (104)
The Albert–Brauer–Hasse–Noether Main Theorem (158)
The Contraction Mapping Theorem (145)
The Marriage Theorem and The Frobenius–König Theorem (62)
The Stable Marriage Theorem (68)
Strassen's Matrix Theorem (139)
The Matrix Tree Theorem (12)
The Transversal Matroid Theorem (157)
The Max-Flow Min-Cut Theorem (168)
Kőnig's Bipartite Matching Theorem (185)
The McIver–Neumann 1/2-n Bound (159)
Lin McMullin's Theorem (165)
The Merton College Theorem (20)
Catalan's Conjecture (Mihăilescu's Theorem) (118)
von Neumann's Minimax Theorem (184)
The Robertson–Seymour Graph Minors Theorem (52)
Miquel's Triangle Theorem (55)
De Moivre's Theorem (152)
The Diaconis–Holmes–Montgomery Coin Tossing Theorem (164)
De Morgan's Laws (111)
Morley's Miracle (56)
The Lagrange Property for Moufang Loops (114)
Moufang's Theorem (61)
Praeger's Theorem on Bounded Movement (135)

 
N
Jump to Top 		The Lutz–Nagell Theorem (81)
Netto's Conjecture (Dixon's Theorem) (49)
The McIver–Neumann 1/2-n Bound (159)
The Birkhoff–von Neumann Theorem (57)
von Neumann's Minimax Theorem (184)
Neumann's Separation Lemma (64)
Nevanlinna's Five-Value Theorem (97)
The Girard-Newton Identities (182)
Gruenberg's Theorem on Nilpotent Groups (82)
Noether's Symmetry Theorem (86)
The Albert–Brauer–Hasse–Noether Main Theorem (158)
The Skolem–Noether Theorem (125)
The Greibach Normal Form Theorem (180)
Cook's Theorem on NP-Completeness (14)

 
O
Jump to Top 		The Ollerenshaw–Brée Formula (129)
The Orbit Counting Lemma (15)
The Existence Theorem for Orthogonal Diagonal Latin Squares (131)

 
P
Jump to Top 		A Theorem on Apollonian Circle Packings (130)
The Panarboreal Formula (146)
Pappus' Theorem (44)
The Parking Function Formula (103)
The Hardy–Ramanujan Asymptotic Partition Formula (115)
Euler's Partition Identity (153)
The Lecture Hall Partition Theorem (156)
The Ramanujan Partition Congruences (173)
The Tverberg Partition Theorem (107)
Pascal's Rule (39)
The Strong Perfect Graph Theorem (60)
An Erdős–Ko–Rado Theorem on Intersecting Permutations (66)
Pick's Theorem (77)
The Piff–Welsh Theorem (141)
Theaetetus' Theorem on the Platonic Solids (132)
The Polynomial Coprimality Theorem (116)
The Classification of Archimedean 4-Polytopes (160)
Praeger's Theorem on Bounded Movement (135)
Vaughan Pratt's Theorem (138)
The Small Prime Gaps Theorem (151)
The Prime Number Theorem (33)
The Green–Tao Theorem on Primes in Arithmetic Progression (32)
Euclid's Triangular Prism (149)
The Total Probability Theorem (133)
Wallis's Product (137)
The Bruck–Ryser–Chowla Theorem on Finite Projective Planes (3)
The Pumping Lemma (105)
The Pythagorean Theorem (27)

 
Q
Jump to Top 		The Quadratic Formula (92)
Quadratic Nonresidue is Zero-Knowledge Provable (161)
Gauss's Law of Quadratic Reciprocity (29)

 
R
Jump to Top 		An Erdős–Ko–Rado Theorem on Intersecting Permutations (66)
The Hardy–Ramanujan Asymptotic Partition Formula (115)
The Ramanujan Partition Congruences (173)
Ramsey's Theorem (28)
A Theorem of Schur on Real-Rootedness (148)
A Theorem on Rectangular Tensegrities (140)
1-Factorisation of Regular Graphs (80)
Reidemeister's Theorem (67)
The Remainder Theorem (154)
Theorems of Euler and Rényi on 'e' (136)
The Robbins Problem (110)
The Robertson–Seymour Graph Minors Theorem (52)
The Robinson–Schensted–Knuth Correspondence (143)
The Goins–Maddox–Rusin Theorem on Heron Triangles (104)
The Bruck–Ryser–Chowla Theorem on Finite Projective Planes (3)

 
S
Jump to Top 		The Rule of Sarrus (96)
The Robinson–Schensted–Knuth Correspondence (143)
A Theorem of Schur on Real-Rootedness (148)
Gödel's Second Incompleteness Theorem (75)
The Second and Third Isomorphism Theorems (35)
The Delsarte–Goethals–Seidel Theorem (83)
Sendov's Conjecture (178)
Neumann's Separation Lemma (64)
The Robertson–Seymour Graph Minors Theorem (52)
Sharkovsky's Theorem (71)
Sims' Conjecture (65)
The Skolem–Noether Theorem (125)
The Small Prime Gaps Theorem (151)
Sokal's Theorem on Chromatic Roots (169)
Theaetetus' Theorem on the Platonic Solids (132)
The Sophomore's Dream (147)
Sperner's Lemma (16)
Lieb's Square Ice Theorem (144)
The Stable Marriage Theorem (68)
Stirling's Approximation (40)
Strassen's Matrix Theorem (139)
The Strong Perfect Graph Theorem (60)
Sylvester's Law of Inertia (142)
Noether's Symmetry Theorem (142)

 
T
Jump to Top 		The Green–Tao Theorem on Primes in Arithmetic Progression (32)
A Theorem on Rectangular Tensegrities (140)
Thales' Theorem (63)
Theaetetus' Theorem on the Platonic Solids (132)
Theorema Egregium (183)
The Second and Third Isomorphism Theorems (35)
The Three-Distance Theorem (78)
The Total Probability Theorem (133)
The Transversal Matroid Theorem (157)
The Analyst's Travelling Salesman Theorem (108)
Miquel's Triangle Theorem (55)
Euclid's Triangular Prism (149)
A Tripartite Turán Theorem (155)
The Tverberg Partition Theorem (107)

 
U
Jump to Top 		The Borsuk–Ulam Theorem (122)
Cantor's Uncountability Theorem (22)
Haken's Unknot Theorem (166)

 
V
Jump to Top 		van der Waerden's Conjecture (113)
The Change of Variables Theorem (134)
Vaughan Pratt's Theorem (138)
Graph Colouring by Vertex Degree (70)
Viète's Formula (102)
The Birkhoff–von Neumann Theorem (57)
von Neumann's Minimax Theorem (184)

 
W
Jump to Top 		Wagner's Theorem (25)
Wallis's Product (137)
van der Waerden's Conjecture (113)
The Wedderburn–Artin Theorem (123)
The Well-Ordering Theorem (17)
A Theorem of Erdős and Wilson on Edge Colouring (117)
The Lindemann–Weierstrass Theorem (167)
The Piff–Welsh Theorem (141)
Woodall's Hopping Lemma (150)

 
X
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Y
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Z
Jump to Top 		Zeckendorf's Theorem (42)
Quadratic Nonresidue is Zero-Knowledge Provable (161)

Theorem of the Day is maintained by Robin Whitty. Comments or suggestions are welcomed by me.
All text and images and associated .pdf files © Robin Whitty, 2005–2012, except where otherwise acknowledged. See FAQ for more.