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