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