Theorem of the Day  

Complete Theorem Listing

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.

All files are pdf , mostly between 100 and 300 Kbytes in size.

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

A Notes link takes you to accompanying notes (e.g. expert commentary or references to source articles). Uses MathJax which takes a while to load and is unpredictable on handheld devices.

A list of theorems which may eventually feature in this list is given here, of value mostly because I record web links to relevant material.

Alternative versions of theorem descriptions are available as indicated:

• monochrome versions, where theorem illustrations depend on colour for their effect;
• poster versions supress clickable icons and add a more visible theoremoftheday logo
• translations from the original English (may have some variation in content). People who helped with translation are acknowledged here and on individual theorem pages by their initials next to a symbol

1. Moessner's Magic    Notes
2. Wolstenholme's Inequality    Notes
3. The Catalan–Euler–Segner Bijection    Notes
4. Cramer's Rule    Notes
5. The Intermediate Value Theorem    Notes
6. Turing-completeness of Conway's Game of Life    Notes
7. Bondy's Subset Theorem   Notes  French version
8. Tunnell's Theorem    Notes
9. The Shoelace Formula    Notes
10. The Polygonal Number Theorem    QED   Notes
11. Euclid's Pythagorean Formula   Notes  French version
12. Dunn and Pretty's Triangle-Halving Deltoid   Notes
13. Schur's Commuting Matrices Bound   Notes
14. Sylow's Theorems   Notes
15. Distribution of Local Maxima in Random Samples   Notes
16. Moreau's Necklace Formula   Notes
17. Countability of the Rationals    QED   Notes
18. Kasteleyn's Theorem   Notes
19. The Third Isomorphism Theorem   Notes
20. Bertrand's Ballot Theorem    QED   Notes
21. The Hanani–Tutte Theorem   Notes   Poster
22. The Power of a Point Theorem     QED   Notes
23. Bézout's Identity     QED   Notes  Poster
24. A Theorem about Gaussian Moats    Notes
25. Euler's Product Formula for Sine    QED  Notes
26. Euler's Product Formula for ζ(s)     QED   Notes
27. The Alternating Series Test    Notes
28. The LYM Inequality   QED    Notes
29. A Theorem of Anderson, Cameron and Preece on Groups of Units   Notes
30. The Pólya–Redfield Enumeration Theorem   Notes
31. The Large Prime Gaps Theorem ( a Theorem under construction!)   Notes
32. The Jones Knot Polynomial Theorem   Notes
33. Kuratowski's 14-Set Theorem   Notes
34. Euler's Even Zeta Formula   Notes
35. Sylvester's Catalecticant   Notes
36. Kemeny's Constant   Notes
37. A Theorem on Modular Fibonacci Periodicity    QED   Notes
38. A Generalised Hlawka Inequality   Notes
39. The Circle Area Theorem    QED   Notes   Poster  Greek Poster
40. The Riemann Explicit Formula   Notes
41. Sophie Germain's Identity    QED   Notes
42. Ore's Theorem in Graph Theory  QED   Notes  French version 
43. Poncelet's Porism   Notes  French version
44. Fisher's Inequality    QED   Notes
45. Cauchy's Theorem in Group Theory   QED   Notes  French version
46. Wolstenholme's Theorem   Notes
47. The Spherical Law of Cosines   Notes
48. Green's Theorem   Notes
49. Tutte's Golden Identity    Notes  Poster
50. Faulhaber's Formula   Notes
51. The Inclusion-Exclusion Principle   Notes
52. The Pappus–Guldin Theorems   Notes
53. Integration by Parts   Notes
54. The Riemann Rearrangement Theorem    QED   Notes
55. Taylor's Theorem   Notes
56. Irrationality of Circumference of Unit Circle    QED   Notes
57. Wedderburn's Little Theorem   Notes
58. A Theorem on Maximal Sum-free Sets in Groups   Notes
59. The 6-Circles Theorem   Notes
60. Vizing's Theorem   Notes
61. Willans' Formula   QED   Notes
62. The Basel Problem   QED   Notes
63. The Erdős Discrepancy Problem ( a Theorem under construction!)   Notes
64. Toricelli's Trumpet   QED   Notes  French version
65. The Eratosthenes-Legendre Sieve   QED   Notes
66. Euler's Formula   QED   Notes
67. The Classification of the Semiregular Tilings   Notes
68. Singmaster's Binomial Multiplicity Bound ( a Theorem under construction!)  QED   Notes
69. Euler's Continued Fraction Correspondence    Notes
70. The Friedlander–Iwaniec Theorem    Notes
71. Jensen's Inequality    Notes
72. Minkowski's Convex Body Theorem   QED   Notes
73. Fermat's Two-Squares Theorem   QED   Notes
74. The Art Gallery Theorem   QED   Notes
75. The Robin–Lagarias Theorem   Notes
76. The Cantor–Bernstein–Schröder Theorem   QED   Notes
77. The Erdős–Ko–Rado Theorem   QED   Notes
78. Wilson's Theorem   QED   Notes
79. Frieze's Theorem on Expected Minimum Tree Length   Notes
80. The Rotation Distance Bound   Notes
81. L'Hospital's Rule   Notes
82. Jackson's Theorem on Compatible Euler Tours   Notes    monochrome
83. The Handshaking Lemma   QED   Notes
84. al-Kāshi's Law of Cosines   Notes
85. Karp's Theorem (Detail)   QED   Notes
86. The Insolvability of the Entscheidungsproblem   QED   Notes
87. Kőnig's Bipartite Matching Theorem   Notes
88. von Neumann's Minimax Theorem   Notes
89. Theorema Egregium   Notes
90. The Girard–Newton Identities   Notes
91. Archimedes' Equiareal Map Theorem   Notes
92. The Greibach Normal Form Theorem   Notes
93. The Descartes Circle Theorem   Notes
94. Sendov's Conjecture ( a Theorem under construction!)   Notes
95. The Heine–Borel Theorem   QED   Notes
96. The Existence Theorem for Bachelor Latin Squares   Notes
97. The Bungers–Lehmer Theorem on Cyclotomic Coefficients   Notes
98. The Cameron–Fon-Der-Flaass IBIS Theorem   Notes
99. The Ramanujan Partition Congruences   Notes
100. The Andrews–Garvan–Dyson Crank   Notes
101. The BEST Theorem    Notes  Poster
102. Machin's Formula   Notes
103. Sokal's Theorem on Chromatic Roots   Notes
104. The Max-Flow Min-Cut Theorem   Notes
105. The Lindemann–Weierstrass Theorem   Notes
106. Haken's Unknot Theorem   Notes
107. Lin McMullin's Theorem   Notes
108. The Diaconis–Holmes–Montgomery Coin Tossing Theorem   Notes
109. The Friendship Theorem   Notes
110. Heath's Finitely Discontinuous Function Theorem   Notes
111. Quadratic Nonresidue is Zero-Knowledge Provable   QED   Notes
112. The Classification of Archimedean 4-Polytopes   Notes
113. The McIver–Neumann 1/2-n Bound   Notes
114. The Albert–Brauer–Hasse–Noether Main Theorem   Notes
115. The Transversal Matroid Theorem   Notes
116. The Lecture Hall Partition Theorem   Notes
117. A Tripartite Turán Theorem   Notes
118. The Remainder Theorem   QED   Notes
119. Euler's Partition Identity   QED   Notes
120. De Moivre's Theorem   Notes
121. The Small Prime Gaps Theorem   Notes
122. Woodall's Hopping Lemma   Notes
123. Euclid's Triangular Prism   QED   Notes
124. A Theorem of Schur on Real-Rootedness   Notes
125. The Sophomore's Dream   Notes
126. The Panarboreal Formula   Notes
127. The Contraction Mapping Theorem   QED   Notes
128. Lieb's Square Ice Theorem   Notes
129. The Robinson–Schensted–Knuth Correspondence   QED   Notes
130. Sylvester's Law of Inertia   Notes
131. The Piff–Welsh Theorem   Notes
132. A Theorem on Rectangular Tensegrities   Notes
133. Strassen's Matrix Theorem ( a Theorem under construction!) QED    Notes
134. Vaughan Pratt's Theorem   Notes
135. Wallis's Product   Notes
136. Theorems of Euler and Rényi on 'e'   Notes
137. Praeger's Theorem on Bounded Movement   Notes
138. The Change of Variables Theorem   Notes
139. The Total Probability Theorem   Notes
140. Theaetetus' Theorem on the Platonic Solids   Notes
141. The Existence Theorem for Orthogonal Diagonal Latin Squares   Notes
142. A Theorem on Apollonian Circle Packings   Notes
143. The Ollerenshaw–Brée Formula   Notes
144. The Euclid–Euler Theorem   Notes
145. The Lucas–Lehmer Test   Notes
146. The Asymptotic (Half) Liar Formula   Notes
147. The Skolem–Noether Theorem   Notes
148. The Lagrange Interpolation Formula   QED   Notes
149. The Wedderburn–Artin Theorem   Notes
150. The Borsuk–Ulam Theorem   Notes
151. Lambert's Formula   Notes
152. The Lovász Local Lemma   Notes
153. Kneser's Conjecture   Notes
154. Catalan's Conjecture (Mihăilescu's Theorem)   Notes  Spanish version
155. A Theorem of Erdős and Wilson on Edge Colouring   Notes
156. The Polynomial Coprimality Theorem   Notes
157. The Hardy–Ramanujan Asymptotic Partition Formula   Notes
158. The Lagrange Property for Moufang Loops   Notes
159. van der Waerden's Conjecture   Notes
160. Bregman's Theorem   Notes
161. De Morgan's Laws   QED   Notes
162. The Robbins Problem   Notes
163. The Beardwood–Halton–Hammersley Theorem   Notes
164. The Analyst's Travelling Salesman Theorem   Notes
165. The Tverberg Partition Theorem   Notes
166. Babbitt's Theorem   Notes
167. The Pumping Lemma   Notes
168. The Goins–Maddox–Rusin Theorem on Heron Triangles   Notes
169. The Parking Function Formula   QED   Notes
170. Viète's Formula   Notes
171. Kepler's Conjecture ( a Theorem under construction!)   Notes
172. The Design of the Century   Notes
173. The Happy Ending Problem   QED   Notes
174. Cartwright's Theorem   Notes
175. Nevanlinna's Five-Value Theorem   Notes
176. The Rule of Sarrus   QED   Notes
177. The Convolution Theorem   Notes
178. Cayley's Formula    Notes
179. The Generalised Hexachord Theorem   Notes
180. The Quadratic Formula   QED   Notes
181. Khinchin's Theorem on Continued Fractions   Notes
182. Cardano's Cubic Formula   Notes
183. The Abel–Hurwitz Binomial Theorem   Notes
184. The Cauchy–Kovalevskaya Theorem   Notes
185. Lamé's Theorem   QED   Notes
186. Noether's Symmetry Theorem   Notes
187. Cayley's Theorem   Notes
188. The Five Circle Theorem    Notes
189. The Delsarte–Goethals–Seidel Theorem    Notes
190. Gruenberg's Theorem on Nilpotent Groups   Notes
191. The Lutz–Nagell Theorem   Notes
192. 1-Factorisation of Regular Graphs ( a Theorem under construction!)    Notes   monochrome
193. The Fifteen Theorem   Notes
194. The Three-Distance Theorem   Notes
195. Pick's Theorem   Notes
196. Brahmagupta's Formula   Notes
197. Gödel's Second Incompleteness Theorem   Notes
198. Gödel's First Incompleteness Theorem    Notes
199. Goodstein's Theorem   Notes
200. MacWilliams' Identity   Notes
201. Sharkovsky's Theorem   Notes
202. The 1-2-3 Conjecture ( a Theorem under construction!)    Notes
203. Arrow's Impossibility Theorem   Notes
204. The Stable Marriage Theorem   Notes
205. Reidemeister's Theorem   Notes
206. An Erdős–Ko–Rado Theorem on Intersecting Permutations   Notes
207. The Sims Conjecture   Notes
208. Neumann's Separation Lemma   Notes
209. Thales' Theorem   Notes
210. The Marriage Theorem and The Frobenius–Kőnig Theorem   Notes
211. Moufang's Theorem   Notes
212. The Strong Perfect Graph Theorem   Notes
213. Germain's Theorem    Notes  Poster  Greek Poster
214. Galois' Theorem on Finite Fields   Notes
215. The Birkhoff–von Neumann Theorem   Notes
216. Morley's Miracle    Notes  French version
217. Miquel's Triangle Theorem    Notes
218. The Bose Equivalence Theorem in Design Theory (600KB — a smaller version is here)    Notes
219. Bailey's Theorem on Latin Squares    Notes   monochrome
220. The Robertson–Seymour Graph Minors Theorem   Notes
221. A Theorem of Melody Chan on Group Actions   Notes
222. The Euler–Hierholzer "Bridges of Königsberg" Theorem   Notes
223. Netto's Conjecture (Dixon's Theorem)    Notes
224. Beineke's Theorem on Line Graphs   Notes
225. The Binomial Theorem   Notes
226. Cameron's Theorem on Distance-Transitive Graphs   Notes
227. Binet's Formula   Notes
228. Pappus' Theorem    Notes
229. The DPRM Theorem   Notes
230. Zeckendorf's Theorem    Notes
231. Lagrange's Theorem    Notes
232. Stirling's Approximation    Notes
233. Pascal's Rule   QED   Notes
234. Lucas' Theorem   Notes
235. Girard's Theorem   QED   Notes
236. Euler's Identity   QED   Notes
237. The Second Isomorphism Theorem   Notes
238. The First Isomorphism Theorem   Notes
239. The Prime Number Theorem   Notes
240. The Green–Tao Theorem on Primes in Arithmetic Progression   Notes
241. Benford's Law   Notes
242. The Law of Large Numbers   Notes
243. Gauss's Law of Quadratic Reciprocity   Notes
244. Ramsey's Theorem   Notes
245. The Pythagorean Theorem    QED    Notes
246. Euler's Polyhedral Formula   QED    Notes
247. Wagner's Theorem   Notes
248. Kuratowski's Theorem   Notes
249. Cantor's Theorem   QED   Notes  French version
250. Cantor's Uncountability Theorem   QED   Notes  French version
251. Brun's Theorem   Notes
252. The Merton College Theorem   Notes
253. Dilworth's Theorem   Notes
254. Brouwer's Fixed Point Theorem   Notes  French version
255. The Well-Ordering Theorem   Notes
256. Sperner's Lemma   QED   Notes
257. The Cauchy–Frobenius Lemma   Notes   French version
258. Cook's Theorem on NP-completeness   Notes
259. Fermat's Little Theorem   QED   Notes
260. The Matrix Tree Theorem   Notes
261. Lagrange's Four-Squares Theorem   Notes   Poster   Greek Poster
262. Bayes' Theorem   Notes
263. Fermat's Last Theorem   Notes
264. The Central Limit Theorem   Notes
265. The Fundamental Theorem of Arithmetic   Notes
266. The Fundamental Theorem of Algebra   Notes
267. The Chinese Remainder Theorem   QED   Notes
268. Euclid's Infinity of Primes   QED   Notes
269. The Bruck–Ryser–Chowla Theorem on Finite Projective Planes   Notes
270. The Fundamental Theorem of the Calculus   Notes
271. The Four-Colour Theorem    Notes  Poster  Greek Poster  French version