0–9

Quadratic Nonresidue is 0Knowledge Provable (161)
The Asymptotic (1/2) Liar Formula (126)
The McIver–Neumann 1/2n Bound (159)
1Factorisation of Regular Graphs (80)
The 123 Conjecture (70)
Gödel's 1st Incompleteness Theorem (74)
The 1st Isomorphism Theorem (34)
Fermat's 2Squares Theorem (199)
Kepler's Conjecture in 2 dimensions (cf. 101)
Gödel's 2nd Incompleteness Theorem (75)
The 2nd Isomorphism Theorem (35)
The 3Distance Theorem (78)
The 3rd Isomorphism Theorem (253)
The 4Colour Theorem (1)
The Classification of Archimedean 4Polytopes (160)
Lagrange's 4Squares Theorem (11)
The 5 Circle Theorem (84)
Nevanlinna's 5Value Theorem (97)
The 6Circles Theorem (213)
Nonexistence of a Projective Plane of Order 10 (cf. 3)
Kuratowski's 14Set Theorem (239)
The 15 Theorem (79)
Euclid's ∞ of Primes (4)


A

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)
alKāshi'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 4Polytopes (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 ArithmeticGeometric 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

Babbitt's Theorem (106)
The Existence Theorem for Bachelor Latin Squares (176)
Bailey's Theorem on Latin Squares (53)
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)
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 Theorem on Pancylicity (cf. 230)
The Bose Equivalence Theorem in Design Theory (54)
The Heine–Borel Theorem (177)
The Borsuk–Ulam Theorem (122)
Singmaster's Binomial Multiplicity Bound (204)
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)
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

The Fundamental Theorem of the Calculus (2)
A Theorem of Anderson, Cameron and Preece on Groups of Units (243)
The Cameron–FonDerFlaass IBIS Theorem (174)
Cameron's Theorem on DistanceTransitive 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–Kovalevskaya Theorem (88)
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 CliqueIncidence Theorem (cf. 60)
The Circle Area Theorem (233)
The Descartes Circle Theorem (179)
The Five Circle Theorem (84)
Irrationality of Circumference of Unit Circle (216)
The SixCircles Theorem (213)
A Theorem on Apollonian Circle Packings (130)
The Classification of Archimedean 4Polytopes (160)
The Classification of the Semiregular Tilings (205)
Chvátal's CliqueIncidence Theorem (cf. 60)
The Diaconis–Holmes–Montgomery Coin Tossing Theorem (164)
The Merton College Theorem (20)
The FourColour Theorem (1)
Graph Colouring by Vertex Degree (70)
Thomassen's Hypergraph Colouring Theorem (cf. 120)
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)
Cook's Theorem on NPcompleteness (14)
Coolidge's Quadrilateral Area Formula (cf. 76)
The Polynomial Coprimality Theorem (116)
The Robinson–Schensted–Knuth Correspondence (143)
alKāshi's Law of Cosines (188)
The Spherical Law of Cosines (225)
Euler's Partial Fraction Cotangent Expansion (cf. 247)
The Orbit Counting Lemma (15)
The Andrews–Garvan–Dyson Crank (172)
Cardano's Cubic Formula (90)
The Bungers–Lehmer Theorem on Cyclotomic Coefficients (175) 

D

Daykin's Theorem on Zeckendorf Representability (cf. 42)
The Delsarte–Goethals–Seidel Theorem (83)
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 DistanceTransitive Graphs (46)
The Rotation Distance Bound (192)
The ThreeDistance Theorem (78)
Divergence of the Harmonic Series (cf. 245)
Netto's Conjecture (Dixon's Theorem) (49)
The DPRM Theorem (43)
The Sophomore's Dream (147)
The Andrews–Garvan–Dyson Crank (172) 

E

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 12, Prop. 7 (cf. 149)
Euclid's Book 13, concluding Remark (cf. 132)
Euclid's Infinity of Primes (4)
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)
Euler's Even Zeta Formula (238)
The InclusionExclusion 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

1Factorisation 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 TwoSquares 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 FiveValue Theorem (97)
Brouwer's Fixed Point Theorem (18)
The Cameron–FonDerFlaass IBIS Theorem (174)
The FourColour Theorem (1)
Lagrange's FourSquares 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 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

The Art Gallery Theorem (198)
Galois' Theorem on Finite Fields (58)
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 Law of Quadratic Reciprocity (29)
The Gauss–Lucas Theorem (cf. 178)
The Generalised Hexachord Theorem (93)
The ArithmeticGeometric Mean Inequality (cf. 201)
Germain's Theorem (59)
Sophie Germain's Identity (231)
The GirardNewton 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 Sumfree 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

Haken's Unknot Theorem (166)
The Asymptotic (Half) Liar Formula (126)
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)
HeathBrown's x^{3}+2y^{3} 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

The Cameron–FonDerFlaass IBIS Theorem (174)
Arrow's Impossibility Theorem (69)
Chvátal's CliqueIncidence Theorem (cf. 60)
The InclusionExclusion Principle (221)
Gödel's First Incompleteness Theorem (74)
Gödel's Second Incompleteness Theorem (75)
The ArithmeticGeometric 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)
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

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

K

Karp's Theorem (Detail) (187)
alKāshi's Law of Cosines (188)
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 ZeroKnowledge 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 14Set Theorem (239) 

L

The Robin–Lagarias Theorem (197)
Lagrange's FourSquares 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)
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)
The Lovász Local Lemma (120)
The Lagrange Property for Moufang Loops (114)
The Lucas–Lehmer Test (127)
The Lucas Test (cf. 138)
The Gauss–Lucas Theorem (cf. 178)
Lucas' Theorem (38)
The Lutz–Nagell Theorem (81)
The LYM Inequality (244) 

M

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)
Strassen's Matrix Theorem (139)
The Matrix Tree Theorem (12)
The Transversal Matroid Theorem (157)
The MaxFlow MinCut Theorem (168)
A Theorem on Maximal Sumfree Sets in Groups (214)
Kőnig's Bipartite Matching Theorem (185)
The McIver–Neumann 1/2n Bound (159)
Lin McMullin's Theorem (165)
The ArithmeticGeometric Mean Inequality (cf. 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)
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

The Lutz–Nagell Theorem (81)
Netto's Conjecture (Dixon's Theorem) (49)
The McIver–Neumann 1/2n Bound (159)
The Birkhoff–von Neumann Theorem (57)
von Neumann's Minimax Theorem (184)
Neumann's Separation Lemma (64)
Nevanlinna's FiveValue Theorem (97)
The GirardNewton 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)
Nonexistence of a Projective Plane of Order 10 (cf. 3)
The Greibach Normal Form Theorem (180)
Cook's Theorem on NPCompleteness (14)
The Law of Large Numbers (30) 

O

The Ollerenshaw–Brée Formula (129)
The OneTwoThree Conjecture (70)
Enumeration of Surjective (Onto) Functions (cf. 221)
The Orbit Counting Lemma (15)
The WellOrdering Theorem (17)
Ore's Theorem in Graph Theory (230)
The Existence Theorem for Orthogonal Diagonal Latin Squares (131) 

P

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)
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)
Euler's Polyhedral Formula (26)
The Polynomial Coprimality Theorem (116)
The Jones Knot Polynomial Theorem (240)
The Classification of Archimedean 4Polytopes (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)
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 InclusionExclusion 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)
Nonexistence of a Projective Plane of Order 10 (cf. 3)
Quadratic Nonresidue is ZeroKnowledge Provable
(161)
Ptolemy's Theorem (cf. 76)
The Pumping Lemma (105)
The Pythagorean Theorem (27)
The Spherical Pythagorean Theorem (cf. 225)


Q

The Quadratic Formula (92)
Quadratic Nonresidue is ZeroKnowledge Provable (161)
Gauss's Law of Quadratic Reciprocity (29)
Coolidge's Quadrilateral Area Formula (cf. 76)


R

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)
A Theorem of Schur on RealRootedness (148)
Gauss's Law of Quadratic Reciprocity (29)
A Theorem on Rectangular Tensegrities (140)
The Pólya–Redfield Enumeration Theorem (242)
1Factorisation 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

The Rule of Sarrus (96)
The Robinson–Schensted–Knuth Correspondence (143)
The Cantor–Bernstein–Schröder Theorem (196)
A Theorem of Schur on RealRootedness (148)
The TangentSecant 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 14Set Theorem (239)
The Robertson–Seymour Graph Minors Theorem (52)
Sharkovsky's Theorem (71)
TheTaniyama–Shimura–Weil Conjecture (cf. 9) The Eratosthenes–Legendre Sieve (207)
The Sims Conjecture (65)
Euler's Product Formula for Sine (247)
Singmaster's Binomial Multiplicity Bound (204)
The SixCircles 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 FourSquares Theorem (11)
Fermat's TwoSquares 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)
A Theorem on Maximal Sumfree Sets in Groups (214)
Lekkerkerker's Theorem on Zeckendorf Sums (cf. 42)
Enumeration of Surjective (Onto) Functions (cf. 221)
Sylvester's Catalecticant (237)
Sylvester's Law of Inertia (142)
Noether's Symmetry Theorem (86) 

T

The TangentSecant 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 ThreeDistance Theorem (78)
The OneTwoThree 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)
Miquel's Triangle Theorem (55)
Euclid's Triangular Prism (149)
A Tripartite Turán Theorem (155)
Torricelli's Trumpet (208)
The Tverberg Partition Theorem (107)
Fermat's TwoSquares Theorem (199)
The OneTwoThree Conjecture (70)
Tutte's Golden Identity (223)
The Hanani–Tutte Theorem (251) 

U

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

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

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 WellOrdering 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

HeathBrown's x^{3}+2y^{3} Theorem (cf. 202)


Y

HeathBrown's x^{3}+2y^{3} Theorem (cf. 202)


Z

Zeckendorf's Theorem (42)
Daykin's Theorem on Zeckendorf Representability (cf. 42)
Lekkerkerker's Theorem on Zeckendorf Sums (cf. 42)
Quadratic Nonresidue is ZeroKnowledge Provable
(161)
Euler's Even Zeta Formula (238)
Euler's Product Formula for ζ(s) (246) 