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