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