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

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