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

Theorem of the Day is maintained by Robin Whitty. Comments or suggestions are welcomed by me.
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