Theorem of the Day  

 

  

Home

 

 

Resources Centre

 

 

Gallery Shop

  

 

Visitors' Book

 

  

Acknowledgements 

 

 

Other listings
Main Theorem List
Subject Listings
Theorems by Women Mathematicians  
Index of Mathematicians
Bibliography

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 '⊆' means the theorem is formally stated as or within a differently named theorem description).

  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 Arithmetic-Geometric Mean Inequality (⊆201)
The Green–Tao Theorem on Primes in Arithmetic Progression (32)
Arrow's Impossibility Theorem (69)
The Art Gallery Theorem (198)
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 Cantor–Bernstein–Schröder Theorem (196)
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)
Blichfeldt's Theorem (⊆200)
The Bose Equivalence Theorem in Design Theory (54)
The Heine–Borel Theorem (177)
The Borsuk–Ulam Theorem (122)
The Rotation Distance Bound (192)
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)
The Cantor–Bernstein–Schröder Theorem (196)
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 Cataldi–Fermat Theorem (⊆128)
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)
The Four-Colour Theorem (1)
Graph Colouring by Vertex Degree (70)
Jackson's Theorem on Compatible Euler Tours (190)
Khinchin's Theorem on Continued Fractions (91)
The Contraction Mapping Theorem (145)
Minkowski's Convex Body Theorem (200)
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)
Cameron's Theorem on Distance-Transitive Graphs (46)
The Rotation Distance Bound (192)
The Three-Distance Theorem (78)
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)
The Erdős–Ko–Rado Theorem (195)
An Erdős–Ko–Rado Theorem on Intersecting Permutations (66)
A Theorem of Erdős and Wilson on Edge Colouring (117)
Euclid's Book 2, Prop. 12,13 (⊆188)
Euclid's Book 9, Prop. 20 (⊆4)
Euclid's Book 9, Prop. 36 (⊆128)
Euclid's Book 12, Prop. 7 (⊆149)
Euclid's Book 13, concluding Remark (⊆132)
Euclid's Infinity of Primes (4)
Euclid's Triangular Prism (149)
Euler's Polyhedral Formula (26)
The Euclid–Euler Theorem (128)
Euler's Identity (36)
Euler's Partition Identity (153)
Jackson's Theorem on Compatible Euler Tours (190)
The Euler–Hierholzer "Bridges of Königsberg" Theorem (50)
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)
Frieze's Theorem on Expected Minimum Tree Length (193)

 
F
Jump to Top 		1-Factorisation of Regular Graphs (80)
The Factor Theorem (⊆154)
The Cataldi–Fermat Theorem (⊆128)
Fermat's Last Theorem (9)
Fermat's Little Theorem (13)
Fermat's Two-Squares Theorem (199)
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)
Frieze's Theorem on Expected Minimum Tree Length (193)
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 		The Art Gallery Theorem (198)
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)
The Arithmetic-Geometric Mean Inequality (⊆201)
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 (70)
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 Handshaking Lemma (189)
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)
L'Hospital's Rule (191)
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)
The Arithmetic-Geometric Mean Inequality (⊆201)
Jensen's Inequality (201)
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 		Jackson's Theorem on Compatible Euler Tours (190)
Jensen's Inequality (201)

 
K
Jump to Top 		Karp's Theorem (Detail) (187)
al-Kāshi's Law of Cosines (188)
Kepler's Conjecture (101)
Khinchin's Theorem on Continued Fractions (91)
Kneser's Conjecture (119)
The Robinson–Schensted–Knuth Correspondence (143)
The Erdős–Ko–Rado Theorem (195)
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 		The Robin–Lagarias Theorem (197)
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 Lucas–Lehmer Test (127)
The Asymptotic (Half) Liar Formula (126)
Lieb's Square Ice Theorem (144)
The Central Limit Theorem (8)
The Lindemann–Weierstrass Theorem (167)
Beineke's Theorem on Line Graphs (48)
Lin McMullin's Theorem (165)
L'Hospital's Rule (191)
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 Arithmetic-Geometric Mean Inequality (⊆201)
The Merton College Theorem (20)
Catalan's Conjecture (Mihăilescu's Theorem) (118)
von Neumann's Minimax Theorem (184)
Frieze's Theorem on Expected Minimum Tree Length (193)
Minkowski's Convex Body Theorem (200)
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)
Euler's Polyhedral Formula (26)
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 		The Erdős–Ko–Rado Theorem (195)
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)
The Chinese Remainder Theorem (5)
Theorems of Euler and Rényi on 'e' (136)
The Robin–Lagarias Theorem (197)
The Robbins Problem (110)
The Robertson–Seymour Graph Minors Theorem (52)
The Robinson–Schensted–Knuth Correspondence (143)
The Rotation Distance Bound (192)
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)
The Cantor–Bernstein–Schröder Theorem (196)
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)
Lagrange's Four-Squares Theorem (11)
Fermat's Two-Squares Theorem (199)
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)
Jackson's Theorem on Compatible Euler Tours (190)
The Transversal Matroid Theorem (157)
The Analyst's Travelling Salesman Theorem (108)
Frieze's Theorem on Expected Minimum Tree Length (193)
Miquel's Triangle Theorem (55)
Euclid's Triangular Prism (149)
A Tripartite Turán Theorem (155)
The Tverberg Partition Theorem (107)
Fermat's Two-Squares Theorem (199)

 
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 		van der Waerden's Conjecture (113)
Wagner's Theorem (25)
Wallis's Product (137)
The Wedderburn–Artin Theorem (123)
The Lindemann–Weierstrass Theorem (167)
The Well-Ordering Theorem (17)
The Piff–Welsh Theorem (141)
A Theorem of Erdős and Wilson on Edge Colouring (117)
Wilson's Theorem (194)
Woodall's Hopping Lemma (150)

 
X
Jump to Top

 
Y
Jump to Top

 
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, 2005–2013, except where otherwise acknowledged. See FAQ for more.