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