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


















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