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