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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 pdf file icon, 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.

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

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