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