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

  0–9  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

 
0–9
Jump to Top 		Quadratic Nonresidue is 0-Knowledge Provable (161)
The Asymptotic (1/2) Liar Formula (126)
The McIver–Neumann 1/2-n Bound (159)
1-Factorisation of Regular Graphs (80)
The 1-2-3 Conjecture (70)
Gödel's 1st Incompleteness Theorem (74)
The 1st Isomorphism Theorem (34)
Fermat's 2-Squares Theorem (199)
Kepler's Conjecture in 2 dimensions (cf. 101)
Gödel's 2nd Incompleteness Theorem (75)
The 2nd Isomorphism Theorem (35)
The 3-Distance Theorem (78)
The 3rd Isomorphism Theorem (253)
The 4-Colour Theorem (1)
The Classification of Archimedean 4-Polytopes (160)
Lagrange's 4-Squares Theorem (11)
The 5 Circle Theorem (84)
Nevanlinna's 5-Value Theorem (97)
The 6-Circles Theorem (213)
Non-existence of a Projective Plane of Order 10 (cf. 3)
Kuratowski's 14-Set Theorem (239)
The 15 Theorem (79)
Euclid's ∞ of Primes (4)

 
A
Jump to Top 		The Abel–Hurwitz Binomial Theorem (89)
A Theorem of Melody Chan on Group Actions (51)
The Albert–Brauer–Hasse–Noether Main Theorem (158)
The Fundamental Theorem of Algebra (8)
al-Kāshi's Law of Cosines (188)
The Alternating Series Test (245)
The Analyst's Travelling Salesman Theorem (108)
A Theorem of Anderson, Cameron and Preece on Groups of Units (243)
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 Circle Area Theorem (233)
Coolidge's Quadrilateral Area Formula (cf. 76)
The Fundamental Theorem of Arithmetic (7)
The Arithmetic-Geometric Mean Inequality (cf. 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)
The Axiom of Choice (cf. 17)

 
B
Jump to Top		 Babbitt's Theorem (106)
The Existence Theorem for Bachelor Latin Squares (176)
Bailey's Theorem on Latin Squares (53)
Bertrand's Ballot Theorem (252)
The Banach–Tarski Paradox (cf. 17)
The Basel Problem (210)
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)
Bertrand's Ballot Theorem (252)
The BEST Theorem (171)
Bézout's Identity (249)
Binet's Formula (45)
The Binomial Theorem (47)
Singmaster's Binomial Multiplicity Bound (204)
The Abel–Hurwitz Binomial Theorem (89)
Kőnig's Bipartite Matching Theorem (185)
The Birkhoff–von Neumann Theorem (57)
Blichfeldt's Theorem (cf. 200)
Bondy's Subset Theorem (265)
Bondy's Theorem on Pancylicity (cf. 230)
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)
The Rotation Distance Bound (192)
Singmaster's Binomial Multiplicity Bound (204)
Schur's Commuting Matrices Bound (259)
Brahmagupta's Formula (76)
The Albert–Brauer–Hasse–Noether Main Theorem (158)
The Ollerenshaw–Brée Formula (129)
Bretschneider's Formula (cf. 76 notes)
Bregman's Theorem (112)
The Euler–Hierholzer "Bridges of Königsberg" Theorem (50)
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)
A Theorem of Anderson, Cameron and Preece on Groups of Units (243)
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 (cf. 128)
Sylvester's Catalecticant (237)
The Spherical Law of Cosines (225)
The Cauchy–Frobenius Lemma (15)
The Cauchy–Kovalevskaya Theorem (88)
Cauchy's Lemma in Number Theory (cf. 262)
Cauchy's Theorem in Group Theory (227)
Cayley's Formula (94)
Cayley's Theorem (85)
The Central Limit Theorem (8)
Centroid Formulae (cf.220)
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 Axiom of Choice (cf. 17)
The Intersecting Chords Theorem (cf. 250)
The Bruck–Ryser–Chowla Theorem on Finite Projective Planes (3)
Sokal's Theorem on Chromatic Roots (169)
Chvátal's Clique-Incidence Theorem (cf. 60)
The Circle Lemma (cf. 252)
The Circle Area Theorem (233)
The Descartes Circle Theorem (179)
The Five Circle Theorem (84)
Irrationality of Circumference of Unit Circle (216)
The Six-Circles Theorem (213)
A Theorem on Apollonian Circle Packings (130)
The Classification of Archimedean 4-Polytopes (160)
The Classification of the Semiregular Tilings (205)
Chvátal's Clique-Incidence Theorem (cf. 60)
The Diaconis–Holmes–Montgomery Coin Tossing Theorem (164)
The Merton College Theorem (20)
The Four-Colour Theorem (1)
Graph Colouring by Vertex Degree (70)
Thomassen's Hypergraph Colouring Theorem (cf. 120)
Schur's Commuting Matrices Bound (259)
The Comparison Test (cf. 245)
Jackson's Theorem on Compatible Euler Tours (190)
Kemeny's Constant (236)
Euler's Continued Fraction Correspondence (203)
Khinchin's Theorem on Continued Fractions (91)
The Contraction Mapping Theorem (145)
Minkowski's Convex Body Theorem (200)
The Convolution Theorem (95)
Turing-completeness of Conway's Game of Life (266)
Cook's Theorem on NP-completeness (14)
Coolidge's Quadrilateral Area Formula (cf. 76)
The Polynomial Coprimality Theorem (116)
The Robinson–Schensted–Knuth Correspondence (143)
al-Kāshi's Law of Cosines (188)
The Spherical Law of Cosines (225)
Euler's Partial Fraction Cotangent Expansion (cf. 247)
Countability of the Rationals (255)
The Orbit Counting Lemma (15)
Cramer's Rule (268)
The Andrews–Garvan–Dyson Crank (172)
Cardano's Cubic Formula (90)
The Bungers–Lehmer Theorem on Cyclotomic Coefficients (175)

 
D
Jump to Top 		Daykin's Theorem on Zeckendorf Representability (cf. 42)
The Delsarte–Goethals–Seidel Theorem (83)
Dunn and Pretty's Triangle-Halving Deltoid (260)
De Moivre's Theorem (152)
De Montmort's Enumeration of Derangements (cf. 136)
De Morgan's Laws (111)
De Montmort's Enumeration of Derangements (cf. 136)
The Descartes Circle Theorem (179)
The Erdős Discrepancy Problem (209)
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)
Dirac's Theorem in Graph Theory (cf. 230)
Heath's Finitely Discontinuous Function Theorem (162)
Cameron's Theorem on Distance-Transitive Graphs (46)
The Rotation Distance Bound (192)
The Three-Distance Theorem (78)
Distribution of Local Maxima in Random Samples (257)
Divergence of the Harmonic Series (cf. 245)
Netto's Conjecture (Dixon's Theorem) (49)
The DPRM Theorem (43)
The Sophomore's Dream (147)
Dunn and Pretty's Triangle-Halving Deltoid (260)
The Andrews–Garvan–Dyson Crank (172)

 
E
Jump to Top

Theorema Egregium (183)
The Happy Ending Problem (99)
The Insolvability of the Entscheidungsproblem (186)
The Pólya–Redfield Enumeration Theorem (242)
Enumeration of Surjective (Onto) Functions (cf. 221)
Archimedes' Equiareal Map Theorem (181)
The Bose Equivalence Theorem in Design Theory (54)
The Eratosthenes–Legendre Sieve (207)
The Erdős Discrepancy Problem (209)
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 1, Prop. 47 (cf. 27)
Euclid's Book 2, Prop. 12,13 (cf. 188)
Euclid's Book 3, Prop. 20,22 (cf. 63)
Euclid's Book 3, Prop. 35,36 (cf. 250)
Euclid's Book 4, Prop. 5 (cf. 76)
Euclid's Book 7, Prop. 30 (cf. 7)
Euclid's Book 7, Prop. 32 (cf. 4)
Euclid's Book 9, Prop. 20 (cf. 4)
Euclid's Book 9, Prop. 36 (cf. 128)
Euclid's Book 10, Prop. 29 (Lemma 1) (cf. 261)
Euclid's Book 12, Prop. 7 (cf. 149)
Euclid's Book 13, concluding Remark (cf. 132)
Euclid's Infinity of Primes (4)
Euclid's Pythagorean Formula (261)
Euclid's Triangular Prism (149)
The Euclid–Euler Theorem (128)
Euler's Continued Fraction Correspondence (203)
Euler's Even Zeta Formula (238)
The Euler–Hierholzer "Bridges of Königsberg" Theorem (50)
Euler's Formula (206)
Euler's Identity (36)
Euler's Partial Fraction Cotangent Expansion (cf. 247)
Euler's Partition Identity (153)
Euler's Polyhedral Formula (26)
Euler's Product Formula for Sine (247)
Euler's Product Formula for ζ(s) (246)
Jackson's Theorem on Compatible Euler Tours (190)
Theorems of Euler and Rényi on 'e' (136)
Gauss's Eureka Theorem (cf. 262)
Euler's Even Zeta Formula (238)
The Inclusion-Exclusion Principle(221)
The Existence Theorem for Bachelor Latin Squares (176)
The Existence Theorem for Orthogonal Diagonal Latin Squares (131)
Euler's Partial Fraction Cotangent Expansion (cf. 247)
Frieze's Theorem on Expected Minimum Tree Length (193)
The Riemann Explicit Formula (232)

 
F
Jump to Top 		1-Factorisation of Regular Graphs (80)
The Factor Theorem (cf. 154)
Faulhaber's Formula (222)
The Cataldi–Fermat Theorem (cf. 128)
Fermat's Last Theorem (9)
Fermat's Little Theorem (13)
Fermat's Two-Squares Theorem (199)
A Theorem on Modular Fibonacci Periodicity (235)
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)
Fisher's Inequality (228)
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)
Euler's Partial Fraction Cotangent Expansion (cf. 247)
The Friedlander–Iwaniec Theorem (202)
The Friendship Theorem (163)
Frieze's Theorem on Expected Minimum Tree Length (193)
The Cauchy–Frobenius Lemma (15)
The Marriage Theorem and The Frobenius–König Theorem (62)
Enumeration of Surjective (Onto) Functions (cf. 221)
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)
Turing-completeness of Conway's Game of Life (266)
The Large Prime Gaps Theorem (241)
The Small Prime Gaps Theorem (151)
The Andrews–Garvan–Dyson Crank (172)
A Theorem about Gaussian Moats (248)
Gauss's Eureka Theorem (cf. 262)
Gauss's Law of Quadratic Reciprocity (29)
The Gauss–Lucas Theorem (cf. 178)
The Generalised Hexachord Theorem (93)
The Arithmetic-Geometric Mean Inequality (cf. 201)
Germain's Theorem (59)
Sophie Germain's Identity (231)
The Girard–Newton Identities (182)
Girard's Theorem (37)
Giuga's Conjecture (cf. 13)
Gödel's First Incompleteness Theorem (74)
Gödel's Second Incompleteness Theorem (75)
The Delsarte–Goethals–Seidel Theorem (83)
The Goins–Maddox–Rusin Theorem on Heron Triangles (104)
Tutte's Golden Identity (223)
Goodstein's Theorem (73)
Graph Colouring by Vertex Degree (70)
Green's Theorem (224)
The Green–Tao Theorem on Primes in Arithmetic Progression (32)
Gregory's Series (cf. 170, 217)
The Greibach Normal Form Theorem (180)
A Theorem of Anderson, Cameron and Preece on Groups of Units (243)
Cauchy's Theorem in Group Theory (227)
A Theorem on Maximal Sum-free Sets in Groups (214)
A Theorem of Melody Chan on Group Actions (51)
Gruenberg's Theorem on Nilpotent Groups (82)
The Pappus–Guldin Theorems (220)

 
H
Jump to Top 		Haken's Unknot Theorem (166)
The Asymptotic (Half) Liar Formula (126)
Dunn and Pretty's Triangle-Halving Deltoid (260)
The Lecture Hall Partition Theorem (156)
The Beardwood–Halton–Hammersley Theorem (109)
The Hanani–Tutte Theorem (251)
The Handshaking Lemma (189)
The Happy Ending Problem (99)
The Hardy–Ramanujan Asymptotic Partition Formula (115)
Divergence of the Harmonic Series (cf. 245)
The Albert–Brauer–Hasse–Noether Main Theorem (158)
Heath-Brown's x3+2y3 Theorem (cf. 202)
Heath's Finitely Discontinuous Function Theorem (162)
The Heine–Borel Theorem (177)
Heron's Formula (cf. 76)
The Goins–Maddox–Rusin Theorem on Heron Triangles (104)
The Generalised Hexachord Theorem (93)
The Euler–Hierholzer "Bridges of Königsberg" Theorem (50)
A Generalised Hlawka Inequality (234)
The Diaconis–Holmes–Montgomery Coin Tossing Theorem (164)
L'Hospital's Rule (191)
Woodall's Hopping Lemma (150)
Thomassen's Hypergraph Colouring Theorem (cf. 120)
Hugh Worthington's Rule (cf. 217)
L'Huilier's Rule (cf. 76)
The Abel–Hurwitz Binomial Theorem (89)

 
I
Jump to Top 		The Cameron–Fon-Der-Flaass IBIS Theorem (174)
Arrow's Impossibility Theorem (69)
Chvátal's Clique-Incidence Theorem (cf. 60)
The Inclusion-Exclusion Principle (221)
Gödel's First Incompleteness Theorem (74)
Gödel's Second Incompleteness Theorem (75)
The Arithmetic-Geometric Mean Inequality (cf. 201)
Jensen's Inequality (201)
The LYM Inequality (244)
Sylvester's Law of Inertia (142)
Euclid's Infinity of Primes (4)
The Insolvability of the Entscheidungsproblem (186)
Integration by Parts (219)
The Intermediate Value Theorem (267)
Irrationality of Circumference of Unit Circle (216)
The First Isomorphism Theorem (34)
The Second Isomorphism Theorem (35)
The Third Isomorphism Theorem (253)
The Lagrange Interpolation Formula (124)
An Erdős–Ko–Rado Theorem on Intersecting Permutations (66)
The Friedlander–Iwaniec Theorem (202)

 
J
Jump to Top 		Jackson's Theorem on Compatible Euler Tours (190)
Jensen's Inequality (201)
The Jones Knot Polynomial Theorem (240)

 
K
Jump to Top 		Karp's Theorem (Detail) (187)
al-Kāshi's Law of Cosines (188)
Kasteleyn's Theorem (254)
Kemeny's Constant (236)
Kepler's Conjecture (101)
Kepler's Conjecture in 2 dimensions (cf. 101)
Khinchin's Theorem on Continued Fractions (91)
Kneser's Conjecture (119)
The Jones Knot Polynomial Theorem (240)
Haken's Unknot Theorem (166)
Quadratic Nonresidue is Zero-Knowledge Provable (161)
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)
Kuratowski's 14-Set Theorem (239)

 
L
Jump to Top 		The Robin–Lagarias Theorem (197)
Lagrange's Four-Squares Theorem (11, cf. 79)
The Lagrange Interpolation Formula (124)
Lagrange's Lemma (cf. 199)
The Lagrange Property for Moufang Loops (114)
Lagrange's Theorem (41)
Lambert's Formula (121)
Lamé's Theorem (87)
The Law of Large Numbers (30)
The Large Prime Gaps Theorem (241)
Fermat's Last Theorem (9)
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 Lecture Hall Partition Theorem (156)
The Eratosthenes–Legendre Sieve (207)
The Bungers–Lehmer Theorem on Cyclotomic Coefficients (175)
The Lucas–Lehmer Test (127)
Lekkerkerker's Theorem on Zeckendorf Sums (cf. 42)
L'Hospital's Rule (191)
The Asymptotic (Half) Liar Formula (126)
Liebniz's Series (cf. 137, 218)
Lieb's Square Ice Theorem (144)
Turing-completeness of Conway's Game of Life (266)
The Central Limit Theorem (8)
The Lindemann–Weierstrass Theorem (167)
Beineke's Theorem on Line Graphs (48)
Lin McMullin's Theorem (165)
Fermat's Little Theorem (13)
Wedderburn's Little Theorem (215)
Distribution of Local Maxima in Random Samples (257)
The Lagrange Property for Moufang Loops (114)
The Lovász Local Lemma (120)
The Gauss–Lucas Theorem (cf. 178)
The Lucas–Lehmer Test (127)
The Lucas Test (cf. 138)
Lucas' Theorem (38)
The Lutz–Nagell Theorem (81)
The LYM Inequality (244)

 
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)
Mantel's Theorem (cf. 155)
The Contraction Mapping Theorem (145)
The Marriage Theorem and The Frobenius–König Theorem (62)
The Stable Marriage Theorem (68)
Schur's Commuting Matrices Bound (259)
Strassen's Matrix Theorem (139)
The Matrix Tree Theorem (12)
The Transversal Matroid Theorem (157)
The Max-Flow Min-Cut Theorem (168)
Distribution of Local Maxima in Random Samples (257)
A Theorem on Maximal Sum-free Sets in Groups (214)
Kőnig's Bipartite Matching Theorem (185)
The McIver–Neumann 1/2-n Bound (159)
Lin McMullin's Theorem (165)
The Arithmetic-Geometric Mean Inequality (cf. 201)
A Theorem of Melody Chan on Group Actions (51)
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)
Morley's Miracle (56)
A Theorem about Gaussian Moats (248)
A Theorem on Modular Fibonacci Periodicity (235)
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)
Singmaster's Binomial Multiplicity Bound (204)

 
N
Jump to Top 		The Lutz–Nagell Theorem (81)
Perfect's Necklace Formula (256)
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)
Non-existence of a Projective Plane of Order 10 (cf. 3)
The Greibach Normal Form Theorem (180)
Cook's Theorem on NP-Completeness (14)
Cauchy's Lemma in Number Theory (cf. 262)
The Law of Large Numbers (30)

 
O
Jump to Top 		The Ollerenshaw–Brée Formula (129)
The One-Two-Three Conjecture (70)
Enumeration of Surjective (Onto) Functions (cf. 221)
The Orbit Counting Lemma (15)
The Well-Ordering Theorem (17)
Ore's Theorem in Graph Theory (230)
The Existence Theorem for Orthogonal Diagonal Latin Squares (131)

 
P
Jump to Top 		A Theorem on Apollonian Circle Packings (130)
The Panarboreal Formula (146)
Bondy's Theorem on Pancylicity (cf. 230)
Pappus' Theorem (44)
The Pappus–Guldin Theorems (220)
The Banach–Tarski Paradox (cf. 17)
Parameśvara's Rule (cf. 76)
The Parking Function Formula (103)
Euler's Partial Fraction Cotangent Expansion (cf. 247)
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)
Integration by Parts (219)
Pascal's Rule (39)
Perfect's Necklace Formula (256)
The Strong Perfect Graph Theorem (60)
A Theorem on Modular Fibonacci Periodicity (235)
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 Power of a Point Theorem (250)
The Pólya–Redfield Enumeration Theorem (242)
The Polygonal Number Theorem (262)
Euler's Polyhedral Formula (26)
The Polynomial Coprimality Theorem (116)
The Jones Knot Polynomial Theorem (240)
The Classification of Archimedean 4-Polytopes (160)
Poncelet's Porism (229)
The Power of a Point Theorem (250)
Praeger's Theorem on Bounded Movement (135)
Vaughan Pratt's Theorem (138)
A Theorem of Anderson, Cameron and Preece on Groups of Units (243)
Dunn and Pretty's Triangle-Halving Deltoid (260)
Euclid's Infinity of Primes (4)
The Green–Tao Theorem on Primes in Arithmetic Progression (32)
The Large Prime Gaps Theorem (241)
The Prime Number Theorem (33)
The Small Prime Gaps Theorem (151)
The Inclusion-Exclusion Principle (221)
Euclid's Triangular Prism (149)
The Total Probability Theorem (133)
The Basel Problem (210)
Euler's Product Formula for Sine (247)
Euler's Product Formula for ζ(s) (246)
Wallis's Product (137)
The Bruck–Ryser–Chowla Theorem on Finite Projective Planes (3)
Non-existence of a Projective Plane of Order 10 (cf. 3)
Quadratic Nonresidue is Zero-Knowledge Provable (161)
Ptolemy's Theorem (cf. 76)
The Pumping Lemma (105)
Euclid's Pythagorean Formula (261)
The Pythagorean Theorem (27)
The Spherical Pythagorean Theorem (cf. 225)

 
Q
Jump to Top 		The Quadratic Formula (92)
Quadratic Nonresidue is Zero-Knowledge Provable (161)
Gauss's Law of Quadratic Reciprocity (29)
Coolidge's Quadrilateral Area Formula (cf. 76)

 
R
Jump to Top 		The Erdős–Ko–Rado Theorem (195)
An Erdős–Ko–Rado Theorem on Intersecting Permutations (66)
Radon's Theorem (cf. 107)
The Hardy–Ramanujan Asymptotic Partition Formula (115)
The Ramanujan Partition Congruences (173)
Ramsey's Theorem (28)
Distribution of Local Maxima in Random Samples (257)
Countability of the Rationals (255)
A Theorem of Schur on Real-Rootedness (148)
Gauss's Law of Quadratic Reciprocity (29)
A Theorem on Rectangular Tensegrities (140)
The Pólya–Redfield Enumeration Theorem (242)
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)
Daykin's Theorem on Zeckendorf Representability (cf. 42)
The Riemann Rearrangement Theorem (218)
The Riemann Explicit Formula (232)
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 Rule of Sarrus (96)
The Goins–Maddox–Rusin Theorem on Heron Triangles (104)
The Bruck–Ryser–Chowla Theorem on Finite Projective Planes (3)

 
S
Jump to Top 		Distribution of Local Maxima in Random Samples (257)
The Rule of Sarrus (96)
Sauer's Lemma (cf. 265)
The Robinson–Schensted–Knuth Correspondence (143)
The Cantor–Bernstein–Schröder Theorem (196)
Schur's Commuting Matrices Bound (259)
A Theorem of Schur on Real-Rootedness (148)
The Tangent-Secant Theorem (cf. 250)
Gödel's Second Incompleteness Theorem (75)
The Second Isomorphism Theorem (35)
The Delsarte–Goethals–Seidel Theorem (83)
The Classification of the Semiregular Tilings (205)
Sendov's Conjecture (178)
Neumann's Separation Lemma (64)
The Alternating Series Test (245)
Divergence of the Harmonic Series (cf. 245)
Kuratowski's 14-Set Theorem (239)
The Robertson–Seymour Graph Minors Theorem (52)
Sharkovsky's Theorem (71)
TheTaniyama–Shimura–Weil Conjecture (cf. 9)
The Shoelace Formula (263)
The Eratosthenes–Legendre Sieve (207)
The Sims Conjecture (65)
Euler's Product Formula for Sine (247)
Singmaster's Binomial Multiplicity Bound (204)
The Six-Circles Theorem (213)
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)
Sophie Germain's Identity (231)
The Sophomore's Dream (147)
Sperner's Lemma (16)
Sperner's Theorem (cf. 244)
The Spherical Law of Cosines (225)
The Spherical Pythagorean Theorem (cf. 225)
Lieb's Square Ice Theorem (144)
Lagrange's Four-Squares Theorem (11)
Fermat's Two-Squares Theorem (199)
The Stable Marriage Theorem (68)
The Steinhaus Conjecture (cf. 78)
Stirling's Approximation (40)
Strassen's Matrix Theorem (139)
The Strong Perfect Graph Theorem (60)
Bondy's Subset Theorem (265)
A Theorem on Maximal Sum-free Sets in Groups (214)
Lekkerkerker's Theorem on Zeckendorf Sums (cf. 42)
Enumeration of Surjective (Onto) Functions (cf. 221)
Sylow's Theorems (258)
Sylvester's Catalecticant (237)
Sylvester's Law of Inertia (142)
Noether's Symmetry Theorem (86)

 
T
Jump to Top 		The Tangent-Secant Theorem (cf. 250)
The Taniyama–Shimura–Weil Conjecture (cf. 9)
The Green–Tao Theorem on Primes in Arithmetic Progression (32)
The Banach–Tarski Paradox (cf. 17)
Taylor's Theorem (217)
A Theorem on Rectangular Tensegrities (140)
Thales' Theorem (63)
Theaetetus' Theorem on the Platonic Solids (132)
Theorema Egregium (183)
The Third Isomorphism Theorem (253)
Thomassen's Hypergraph Colouring Theorem (cf. 120)
The Three-Distance Theorem (78)
The One-Two-Three Conjecture (70)
The Classification of the Semiregular Tilings (205)
Torricelli's Trumpet (208)
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)
The Matrix Tree Theorem (12)
Frieze's Theorem on Expected Minimum Tree Length (193)
Dunn and Pretty's Triangle-Halving Deltoid (260)
Miquel's Triangle Theorem (55)
Euclid's Triangular Prism (149)
A Tripartite Turán Theorem (155)
Torricelli's Trumpet (208)
Turing-completeness of Conway's Game of Life (266)
The Tverberg Partition Theorem (107)
Fermat's Two-Squares Theorem (199)
The One-Two-Three Conjecture (70)
Tunnell's Theorem (264)
A Tripartite Turán Theorem (155)
Tutte's Golden Identity (223)
The Hanani–Tutte Theorem (251)

 
U
Jump to Top 		The Borsuk–Ulam Theorem (122)
Cantor's Uncountability Theorem (22)
Irrationality of Circumference of Unit Circle (216)
A Theorem of Anderson, Cameron and Preece on Groups of Units (243)
Haken's Unknot Theorem (166)

 
V
Jump to Top 		The Intermediate Value Theorem (267)
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, cf. 137)
Vizing's Theorem (212)
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)
Waring's Problem (cf. 11)
The Wedderburn–Artin Theorem (123)
Wedderburn's Little Theorem (215)
The Lindemann–Weierstrass Theorem (167)
The Taniyama–Shimura–Weil Conjecture (cf. 9)
The Well-Ordering Theorem (17)
The Piff–Welsh Theorem (141)
Willans' Formula (211)
A Theorem of Erdős and Wilson on Edge Colouring (117)
Wilson's Theorem (194)
Wolstenholme's Theorem (226)
Woodall's Hopping Lemma (150)
Hugh Worthington's Rule (cf. 217)

 
X
Jump to Top 		Heath-Brown's x3+2y3 Theorem (cf. 202)

 
Y
Jump to Top 		Heath-Brown's x3+2y3 Theorem (cf. 202)

 
Z
Jump to Top 		Zeckendorf's Theorem (42)
Daykin's Theorem on Zeckendorf Representability (cf. 42)
Lekkerkerker's Theorem on Zeckendorf Sums (cf. 42)
Quadratic Nonresidue is Zero-Knowledge Provable (161)
Euler's Even Zeta Formula (238)
Euler's Product Formula for ζ(s) (246)