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

Theorem of the Day is maintained by Robin Whitty. Comments or suggestions are welcomed by me.
"Theorem of the Day" is registered as a UK Trademark, no. 00003123351. All text and images and associated .pdf files © Robin Whitty, 2005–2018, except where otherwise acknowledged. See FAQ for more.
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