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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.

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. Bertrand's Ballot Theorem
  2. The Hanani–Tutte TheoremFibonacci imagePoster
  3. The Power of a Point Theorem
  4. Bézout's IdentityFibonacci imagePoster
  5. A Theorem about Gaussian Moats
  6. Euler's Product Formula for Sine    QED
  7. Euler's Product Formula for ζ(s)     QED
  8. The Alternating Series Test
  9. The LYM Inequality   QED
  10. A Theorem of Anderson, Cameron and Preece on Groups of Units
  11. The Pólya–Redfield Enumeration Theorem
  12. The Large Prime Gaps Theorem (Notes icon a Theorem under construction!)
  13. The Jones Knot Polynomial Theorem
  14. Kuratowski's 14-Set Theorem
  15. Euler's Even Zeta Formula
  16. Sylvester's Catalecticant
  17. Kemeny's Constant
  18. A Theorem on Modular Fibonacci Periodicity
  19. A Generalised Hlawka Inequality
  20. The Circle Area TheoremFibonacci imagePosterFibonacci imageGreek Poster
  21. The Riemann Explicit Formula
  22. Sophie Germain's Identity    QED
  23. Ore's Theorem in Graph Theory QEDFibonacci imageFrench version
  24. Poncelet's PorismFibonacci imageFrench version
  25. Fisher's Inequality    QED
  26. Cauchy's Theorem in Group Theory   QED
  27. Wolstenholme's Theorem
  28. The Spherical Law of Cosines
  29. Green's Theorem
  30. Tutte's Golden IdentityFibonacci imagePoster
  31. Faulhaber's Formula
  32. The Inclusion-Exclusion Principle
  33. The Pappus–Guldin Theorems
  34. Integration by Parts
  35. The Riemann Rearrangement Theorem
  36. Taylor's Theorem
  37. Irrationality of Circumference of Unit Circle
  38. Wedderburn's Little Theorem
  39. A Theorem on Maximal Sum-free Sets in Groups
  40. The 6-Circles Theorem
  41. Vizing's Theorem
  42. Willans' Formula   QED
  43. The Basel Problem   QED
  44. The Erdős Discrepancy Problem (Notes icon a Theorem under construction!)
  45. Toricelli's Trumpet QED
  46. The Eratosthenes-Legendre Sieve QED
  47. Euler's Formula QED
  48. The Classification of the Semiregular Tilings
  49. Singmaster's Binomial Multiplicity Bound (Notes icon a Theorem under construction!)  QED
  50. Euler's Continued Fraction Correspondence
  51. The Friedlander–Iwaniec Theorem
  52. Jensen's Inequality
  53. Minkowski's Convex Body Theorem QED
  54. Fermat's Two-Squares Theorem QED
  55. The Art Gallery Theorem QED
  56. The Robin–Lagarias Theorem
  57. The Cantor–Bernstein–Schröder Theorem QED
  58. The Erdős–Ko–Rado Theorem QED
  59. Wilson's Theorem QED
  60. Frieze's Theorem on Expected Minimum Tree Length
  61. The Rotation Distance Bound
  62. L'Hospital's Rule
  63. Jackson's Theorem on Compatible Euler ToursFibonacci imagemonochrome
  64. The Handshaking Lemma QED
  65. al-Kāshi's Law of Cosines
  66. Karp's Theorem (Detail) QED
  67. The Insolvability of the Entscheidungsproblem QED
  68. Kőnig's Bipartite Matching Theorem
  69. von Neumann's Minimax Theorem
  70. Theorema Egregium
  71. The Girard-Newton Identities
  72. Archimedes' Equiareal Map Theorem
  73. The Greibach Normal Form Theorem
  74. The Descartes Circle Theorem
  75. Sendov's Conjecture (Notes icon a Theorem under construction!)
  76. The Heine–Borel Theorem QED
  77. The Existence Theorem for Bachelor Latin Squares
  78. The Bungers–Lehmer Theorem on Cyclotomic Coefficients
  79. The Cameron–Fon-Der-Flaass IBIS Theorem
  80. The Ramanujan Partition Congruences
  81. The Andrews–Garvan–Dyson Crank
  82. The BEST TheoremFibonacci imagePoster
  83. Machin's Formula
  84. Sokal's Theorem on Chromatic Roots
  85. The Max-Flow Min-Cut Theorem
  86. The Lindemann–Weierstrass Theorem
  87. Haken's Unknot Theorem
  88. Lin McMullin's Theorem
  89. The Diaconis–Holmes–Montgomery Coin Tossing Theorem
  90. The Friendship Theorem
  91. Heath's Finitely Discontinuous Function Theorem
  92. Quadratic Nonresidue is Zero-Knowledge Provable QED
  93. The Classification of Archimedean 4-Polytopes
  94. The McIver–Neumann 1/2-n Bound
  95. The Albert–Brauer–Hasse–Noether Main Theorem
  96. The Transversal Matroid Theorem
  97. The Lecture Hall Partition Theorem
  98. A Tripartite Turán Theorem
  99. The Remainder Theorem QED
  100. Euler's Partition Identity QED
  101. De Moivre's Theorem
  102. The Small Prime Gaps Theorem
  103. Woodall's Hopping Lemma
  104. Euclid's Triangular Prism QED
  105. A Theorem of Schur on Real-Rootedness
  106. The Sophomore's Dream
  107. The Panarboreal Formula
  108. The Contraction Mapping Theorem QED
  109. Lieb's Square Ice Theorem
  110. The Robinson–Schensted–Knuth Correspondence QED
  111. Sylvester's Law of Inertia
  112. The Piff–Welsh Theorem
  113. A Theorem on Rectangular Tensegrities
  114. Strassen's Matrix Theorem (Notes icon a Theorem under construction!) QED
  115. Vaughan Pratt's Theorem
  116. Wallis's Product
  117. Theorems of Euler and Rényi on 'e'
  118. Praeger's Theorem on Bounded Movement
  119. The Change of Variables Theorem
  120. The Total Probability Theorem
  121. Theaetetus' Theorem on the Platonic Solids
  122. The Existence Theorem for Orthogonal Diagonal Latin Squares
  123. A Theorem on Apollonian Circle Packings
  124. The Ollerenshaw–Brée Formula
  125. The Euclid–Euler Theorem
  126. The Lucas–Lehmer Test
  127. The Asymptotic (Half) Liar Formula
  128. The Skolem–Noether Theorem
  129. The Lagrange Interpolation Formula QED
  130. The Wedderburn–Artin Theorem
  131. The Borsuk–Ulam Theorem
  132. Lambert's Formula
  133. The Lovász Local Lemma
  134. Kneser's Conjecture
  135. Catalan's Conjecture (Mihăilescu's Theorem)
  136. A Theorem of Erdős and Wilson on Edge Colouring
  137. The Polynomial Coprimality Theorem
  138. The Hardy–Ramanujan Asymptotic Partition Formula
  139. The Lagrange Property for Moufang Loops
  140. van der Waerden's Conjecture
  141. Bregman's Theorem
  142. De Morgan's Laws QED
  143. The Robbins Problem
  144. The Beardwood–Halton–Hammersley Theorem
  145. The Analyst's Travelling Salesman Theorem
  146. The Tverberg Partition Theorem
  147. Babbitt's Theorem
  148. The Pumping Lemma
  149. The Goins–Maddox–Rusin Theorem on Heron Triangles
  150. The Parking Function Formula QED
  151. Viète's Formula
  152. Kepler's Conjecture (Notes icon a Theorem under construction!)
  153. The Design of the Century
  154. The Happy Ending Problem QED
  155. Cartwright's Theorem
  156. Nevanlinna's Five-Value Theorem
  157. The Rule of Sarrus QED
  158. The Convolution Theorem
  159. Cayley's Formula
  160. The Generalised Hexachord Theorem
  161. The Quadratic Formula QED
  162. Khinchin's Theorem on Continued Fractions
  163. Cardano's Cubic Formula
  164. The Abel–Hurwitz Binomial Theorem
  165. The Cauchy–Kovalevskaya Theorem
  166. Lamé's Theorem QED
  167. Noether's Symmetry Theorem
  168. Cayley's Theorem
  169. The Five Circle Theorem
  170. The Delsarte–Goethals–Seidel Theorem
  171. Gruenberg's Theorem on Nilpotent Groups
  172. The Lutz–Nagell Theorem
  173. 1-Factorisation of Regular Graphs (Notes icon a Theorem under construction!)  Fibonacci imagemonochrome
  174. The Fifteen Theorem
  175. The Three-Distance Theorem
  176. Pick's Theorem
  177. Brahmagupta's Formula
  178. Gödel's Second Incompleteness Theorem
  179. Gödel's First Incompleteness Theorem
  180. Goodstein's Theorem
  181. MacWilliams' Identity
  182. Sharkovsky's Theorem
  183. The 1-2-3 Conjecture (Notes icon a Theorem under construction!)
  184. Arrow's Impossibility Theorem
  185. The Stable Marriage Theorem
  186. Reidemeister's Theorem
  187. An Erdős–Ko–Rado Theorem on Intersecting Permutations
  188. The Sims Conjecture
  189. Neumann's Separation Lemma
  190. Thales' Theorem
  191. The Marriage Theorem and The Frobenius–Kőnig Theorem
  192. Moufang's Theorem
  193. The Strong Perfect Graph Theorem
  194. Germain's TheoremFibonacci imagePosterFibonacci imageGreek Poster
  195. Galois' Theorem on Finite Fields
  196. The Birkhoff–von Neumann Theorem
  197. Morley's Miracle
  198. Miquel's Triangle Theorem
  199. The Bose Equivalence Theorem in Design Theory (600KB — a smaller version is here)
  200. Bailey's Theorem on Latin SquaresFibonacci imagemonochrome
  201. The Robertson–Seymour Graph Minors Theorem
  202. A Theorem of Melody Chan on Group Actions
  203. The Euler–Hierholzer "Bridges of Königsberg" Theorem
  204. Netto's Conjecture (Dixon's Theorem)Fibonacci imagemonochrome
  205. Beineke's Theorem on Line Graphs
  206. The Binomial Theorem
  207. Cameron's Theorem on Distance-Transitive Graphs
  208. Binet's Formula
  209. Pappus' Theorem
  210. The DPRM Theorem
  211. Zeckendorf's Theorem
  212. Lagrange's Theorem
  213. Stirling's Approximation
  214. Pascal's Rule QED
  215. Lucas' Theorem
  216. Girard's Theorem QED
  217. Euler's Identity QED
  218. The Second and Third Isomorphism Theorems
  219. The First Isomorphism Theorem
  220. The Prime Number Theorem
  221. The Green–Tao Theorem on Primes in Arithmetic Progression
  222. Benford's Law
  223. The Law of Large Numbers
  224. Gauss's Law of Quadratic Reciprocity
  225. Ramsey's Theorem
  226. The Pythagorean Theorem    QED
  227. Euler's Polyhedral Formula QED
  228. Wagner's Theorem
  229. Kuratowski's Theorem
  230. Cantor's Theorem QED
  231. Cantor's Uncountability Theorem QED
  232. Brun's Theorem
  233. The Merton College Theorem
  234. Dilworth's Theorem
  235. Brouwer's Fixed Point Theorem
  236. The Well-Ordering Theorem
  237. Sperner's Lemma QED
  238. The Orbit Counting Lemma
  239. Cook's Theorem on NP-completeness
  240. Fermat's Little Theorem
  241. The Matrix Tree Theorem
  242. Lagrange's Four-Squares TheoremFibonacci imagePosterFibonacci imageGreek Poster
  243. Bayes' Theorem
  244. Fermat's Last Theorem
  245. The Central Limit Theorem
  246. The Fundamental Theorem of Arithmetic
  247. The Fundamental Theorem of Algebra
  248. The Chinese Remainder Theorem QED
  249. Euclid's Infinity of Primes QED
  250. The Bruck–Ryser–Chowla Theorem on Finite Projective Planes
  251. The Fundamental Theorem of the Calculus
  252. The Four-Colour TheoremFibonacci 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, 2005–2017, except where otherwise acknowledged. See FAQ for more.
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