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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.

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 translation  icon 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   NotesFibonacci imageFrench version
  5. Tunnell's Theorem    Notes
  6. The Shoelace Formula    Notes
  7. The Polygonal Number Theorem    QED   Notes
  8. Euclid's Pythagorean Formula   NotesFibonacci imageFrench 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   NotesFibonacci imagePoster
  19. The Power of a Point Theorem     QED   Notes
  20. Bézout's Identity     QED   NotesFibonacci imagePoster
  21. A Theorem about Gaussian Moats    Notes
  22. Euler's Product Formula for Sine    QEDNotes
  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 (Notes icon 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   NotesFibonacci imagePosterFibonacci imageGreek Poster
  37. The Riemann Explicit Formula   Notes
  38. Sophie Germain's Identity    QED   Notes
  39. Ore's Theorem in Graph Theory QED   NotesFibonacci imageFrench version
  40. Poncelet's Porism   NotesFibonacci imageFrench version
  41. Fisher's Inequality    QED   Notes
  42. Cauchy's Theorem in Group Theory   QED   NotesFibonacci imageFrench version
  43. Wolstenholme's Theorem   Notes
  44. The Spherical Law of Cosines   Notes
  45. Green's Theorem   Notes
  46. Tutte's Golden Identity    NotesFibonacci imagePoster
  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 (Notes icon a Theorem under construction!)   Notes
  61. Toricelli's Trumpet QED   NotesFibonacci imageFrench 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 (Notes icon 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   NotesFibonacci imagemonochrome
  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 (Notes icon 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    NotesFibonacci imagePoster
  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 (Notes icon 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)   NotesFibonacci imageSpanish 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 (Notes icon 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 (Notes icon a Theorem under construction!)    NotesFibonacci imagemonochrome
  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 (Notes icon 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    NotesFibonacci imagePosterFibonacci imageGreek Poster
  211. Galois' Theorem on Finite Fields   Notes
  212. The Birkhoff–von Neumann Theorem   Notes
  213. Morley's Miracle    NotesFibonacci imageFrench 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    NotesFibonacci imagemonochrome
  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   NotesFibonacci imageFrench version
  247. Cantor's Uncountability Theorem QED   NotesFibonacci imageFrench version
  248. Brun's Theorem   Notes
  249. The Merton College Theorem   Notes
  250. Dilworth's Theorem   Notes
  251. Brouwer's Fixed Point Theorem   NotesFibonacci imageFrench version
  252. The Well-Ordering Theorem   Notes
  253. Sperner's Lemma QED   Notes
  254. The Cauchy–Frobenius Lemma   NotesFibonacci imageFrench 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   NotesFibonacci imagePosterFibonacci imageGreek 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    NotesFibonacci imagePosterFibonacci imageGreek PosterFibonacci imageFrench version

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