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The Whole Jolly Lot (now enriched withPrime Curios)    

The list is presented here in reverse chronological order, so that new additions will appear at the top. This is not the order in which the theorem of the day is picked which is more designed to mix up the different areas of mathematics and the level of abstractness or technicality involved. The way that the list of theorems is indexed is described here.

Every theorem number is linked to its entry in the delightful 'Prime Curios!' compendium at The Prime Pages. For good measure I have highlighted primes in red. Click on any number and be beguiled (don't forget to look at the theorem too!)

All files are pdf pdf file icon, mostly between 100 and 300 Kbytes in size. Some of the theorems have matching Java applets: these will open in the same window and will usually prompt for permission before running. Some theorem descriptions depend on colour for their effect; monochrome alternatives are provided as indicated.

A QED following a theorem indicates that the description includes a (sketch) proof of the theorem.

A tricolore French indicates that a separate French version is available.


250   The Power of a Point Theorem

249   Bézout's Identity

248   A Theorem about Gaussian Moats

247   Euler's Product Formula for Sine QED

246   Euler's Product Formula for ζ(s) QED

245   The Alternating Series Test

244   The LYM Inequality QED

243   A Theorem of Anderson, Cameron and Preece on Groups of Units

242   The Pólya–Redfield Enumeration Theorem

241   The Large Prime Gaps Theorem (Notes icon a Theorem under construction!)

240   The Jones Knot Polynomial Theorem

239   Kuratowski's 14-Set Theorem

238   Euler's Even Zeta Formula

237   Sylvester's Catalecticant

236   Kemeny's Constant

235   A Theorem on Modular Fibonacci Periodicity

234   A Generalised Hlawka Inequality

233   The Circle Area Theorem

232   The Riemann Explicit Formula

231   Sophie Germain's Identity QED

230   Ore's Theorem in Graph Theory    French Le Théorème d'Ore en Théorie des Graphes QED

229   Poncelet's Porism    French Le Porisme de Poncelet

228   Fisher's Inequality QED

227   Cauchy's Theorem in Group Theory QED

226   Wolstenholme's Theorem

225   The Spherical Law of Cosines

224   Green's Theorem

223   Tutte's Golden Identity

222   Faulhaber's Formula

221   The Inclusion-Exclusion Principle

220   The Pappus–Guldin Theorems

219   Integration by Parts

218   The Riemann Rearrangement Theorem

217   Taylor's Theorem

216   Irrationality of Circumference of Unit Circle

215   Wedderburn's Little Theorem

214   A Theorem on Maximal Sum-free Sets in Groups

213   The 6-Circles Theorem

212   Vizing's Theorem

211   Willans' Formula QED

210   The Basel Problem QED

209   The Erdős Discrepancy Problem (Notes icon a Theorem under construction!)

208   Toricelli's Trumpet QED

207   The Eratosthenes-Legendre Sieve QED

206   Euler's Formula QED

205   The Classification of the Semiregular Tilings

204   Singmaster's Binomial Multiplicity Bound QED (Notes icon a Theorem under construction!)

203   Euler's Continued Fraction Correspondence

202   The Friedlander–Iwaniec Theorem

201   Jensen's Inequality

200   Minkowski's Convex Body Theorem QED

199   Fermat's Two-Squares Theorem QED

198   The Art Gallery Theorem QED

197   The Robin–Lagarias Theorem

196   The Cantor–Bernstein–Schröder Theorem QED

195   The Erdős–Ko–Rado Theorem QED

194   Wilson's Theorem QED

193   Frieze's Theorem on Expected Minimum Tree Length

192   The Rotation Distance Bound

191   L'Hospital's Rule

190   Jackson's Theorem on Compatible Euler Tours (or colour-free)

189   The Handshaking Lemma QED

188   al-Kāshi's Law of Cosines

187   Karp's Theorem (Detail) QED

186   The Insolvability of the Entscheidungsproblem QED

185   Kőnig's Bipartite Matching Theorem

184   von Neumann's Minimax Theorem

183   Theorema Egregium

182   The Girard-Newton Identities

181   Archimedes' Equiareal Map Theorem

180   The Greibach Normal Form Theorem

179   The Descartes Circle Theorem

178   Sendov's Conjecture (Notes icon a Theorem under construction!)

177   The Heine–Borel Theorem QED

176   The Existence Theorem for Bachelor Latin Squares

175   The Bungers–Lehmer Theorem on Cyclotomic Coefficients

174   The Cameron–Fon-Der-Flaass IBIS Theorem

173   The Ramanujan Partition Congruences

172   The Andrews–Garvan–Dyson Crank

171   The BEST Theorem

170   Machin's Formula

169   Sokal's Theorem on Chromatic Roots

168   The Max-Flow Min-Cut Theorem

167   The Lindemann–Weierstrass Theorem

166   Haken's Unknot Theorem

165   Lin McMullin's Theorem

164   The Diaconis–Holmes–Montgomery Coin Tossing Theorem

163   The Friendship Theorem

162   Heath's Finitely Discontinuous Function Theorem

161   Quadratic Nonresidue is Zero-Knowledge Provable QED

160   The Classification of Archimedean 4-Polytopes

159   The McIver–Neumann 1/2-n Bound

158   The Albert–Brauer–Hasse–Noether Main Theorem

157   The Transversal Matroid Theorem

156   The Lecture Hall Partition Theorem

155   A Tripartite Turán Theorem

154   The Remainder Theorem QED

153   Euler's Partition Identity QED

152   De Moivre's Theorem

151   The Small Prime Gaps Theorem

150   Woodall's Hopping Lemma

149   Euclid's Triangular Prism QED

148   A Theorem of Schur on Real-Rootedness

147   The Sophomore's Dream

146   The Panarboreal Formula

145   The Contraction Mapping Theorem QED

144   Lieb's Square Ice Theorem

143   The Robinson–Schensted–Knuth Correspondence QED

142   Sylvester's Law of Inertia

141   The Piff–Welsh Theorem

140   A Theorem on Rectangular Tensegrities

139   Strassen's Matrix Theorem QED (Notes icon a Theorem under construction!)

138   Vaughan Pratt's Theorem

137   Wallis's Product

136   Theorems of Euler and Rényi on 'e'

135   Praeger's Theorem on Bounded Movement

134   The Change of Variables Theorem

133   The Total Probability Theorem

132   Theaetetus' Theorem on the Platonic Solids

131   The Existence Theorem for Orthogonal Diagonal Latin Squares

130   A Theorem on Apollonian Circle Packings

129   The Ollerenshaw–Brée Formula

128   The Euclid–Euler Theorem

127   The Lucas–Lehmer Test

126   The Asymptotic (Half) Liar Formula

125   The Skolem–Noether Theorem

124   The Lagrange Interpolation Formula QED

123   The Wedderburn–Artin Theorem

122   The Borsuk–Ulam Theorem

121   Lambert's Formula

120   The Lovász Local Lemma

119   Kneser's Conjecture

118   Catalan's Conjecture (Mihăilescu's Theorem)

117   A Theorem of Erdős and Wilson on Edge Colouring

116   The Polynomial Coprimality Theorem

115   The Hardy–Ramanujan Asymptotic Partition Formula

114   The Lagrange Property for Moufang Loops

113   van der Waerden's Conjecture

112   Bregman's Theorem

111   De Morgan's Laws QED

110   The Robbins Problem

109   The Beardwood–Halton–Hammersley Theorem

108   The Analyst's Travelling Salesman Theorem

107   The Tverberg Partition Theorem

106   Babbitt's Theorem

105   The Pumping Lemma

104   The Goins–Maddox–Rusin Theorem on Heron Triangles

103   The Parking Function Formula QED

102   Viète's Formula

101   Kepler's Conjecture (Notes icon a Theorem under construction!)

100   The Design of the Century

99     The Happy Ending Problem QED

98     Cartwright's Theorem

97     Nevanlinna's Five-Value Theorem

96     The Rule of Sarrus QED

95     The Convolution Theorem

94     Cayley's Formula

93     The Generalised Hexachord Theorem

92     The Quadratic Formula QED

91     Khinchin's Theorem on Continued Fractions

90     Cardano's Cubic Formula

89     The Abel–Hurwitz Binomial Theorem

88     The Cauchy–Kovalevskaya Theorem

87     Lamé's Theorem QED

86     Noether's Symmetry Theorem

85     Cayley's Theorem

84     The Five Circle Theorem (matching Java applet)

83     The Delsarte–Goethals–Seidel Theorem

82     Gruenberg's Theorem on Nilpotent Groups

81     The Lutz–Nagell Theorem

80     1-Factorisation of Regular Graphs (Notes icon a Theorem under construction!) Colour-free version here.

79     The Fifteen Theorem

78     The Three-Distance Theorem

77     Pick's Theorem

76     Brahmagupta's Formula

75     Gödel's Second Incompleteness Theorem

74     Gödel's First Incompleteness Theorem

73     Goodstein's Theorem

72     MacWilliams' Identity

71     Sharkovsky's Theorem

70     The 1-2-3 Conjecture (Notes icon a Theorem under construction!) (previously listed as "Graph Colouring by Vertex Degree")

69     Arrow's Impossibility Theorem

68     The Stable Marriage Theorem

67     Reidemeister's Theorem

66     An Erdős–Ko–Rado Theorem on Intersecting Permutations

65     Sims' Conjecture

64     Neumann's Separation Lemma

63     Thales' Theorem

62     The Marriage Theorem and The Frobenius–Kőnig Theorem

61     Moufang's Theorem

60     The Strong Perfect Graph Theorem

59     Germain's Theorem

58     Galois' Theorem on Finite Fields

57     The Birkhoff–von Neumann Theorem

56     Morley's Miracle (matching Java applet)

55     Miquel's Triangle Theorem (matching Java applet)

54     The Bose Equivalence Theorem in Design Theory (600KB — a smaller version is here)

53     Bailey's Theorem on Latin Squares (or colour-free)

52     The Robertson–Seymour Graph Minors Theorem

51     A Theorem of Melody Chan on Group Actions

50     The Euler–Hierholzer "Bridges of Königsberg" Theorem

49     Netto's Conjecture (Dixon's Theorem) (or colour-free)

48     Beineke's Theorem on Line Graphs

47     The Binomial Theorem

46     Cameron's Theorem on Distance-Transitive Graphs

45     Binet's Formula

44     Pappus' Theorem (matching Java applet)

43     The DPRM Theorem

42     Zeckendorf's Theorem

41     Lagrange's Theorem

40     Stirling's Approximation

39     Pascal's Rule QED

38     Lucas' Theorem

37     Girard's Theorem QED

36     Euler's Identity QED

35     The Second and Third Isomorphism Theorems

34     The First Isomorphism Theorem

33     The Prime Number Theorem

32     The Green–Tao Theorem on Primes in Arithmetic Progression

31     Benford's Law

30     The Law of Large Numbers

29     Gauss's Law of Quadratic Reciprocity

28     Ramsey's Theorem

27     The Pythagorean Theorem

26     Euler's Polyhedral Formula QED

25     Wagner's Theorem

24     Kuratowski's Theorem

23     Cantor's Theorem QED

22     Cantor's Uncountability Theorem QED

21     Brun's Theorem

20     The Merton College Theorem

19     Dilworth's Theorem ( an older version with a snooker illustration)

18     Brouwer's Fixed Point Theorem

17     The Well-Ordering Theorem

16     Sperner's Lemma QED

15     The Orbit Counting Lemma

14     Cook's Theorem on NP-completeness

13     Fermat's Little Theorem

12     The Matrix Tree Theorem

11     Lagrange's Four-Squares TheoremPoster version

10     Bayes' Theorem

9       Fermat's Last Theorem

8       The Central Limit Theorem

7       The Fundamental Theorem of Arithmetic

6       The Fundamental Theorem of Algebra

5       The Chinese Remainder Theorem QED

4       Euclid's Infinity of Primes QED

3       The Bruck–Ryser–Chowla Theorem on Finite Projective Planes

2       The Fundamental Theorem of the Calculus

1       The Four-Colour Theorem

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