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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. Kasteleyn's Theorem
  2. The Third Isomorphism Theorem
  3. Bertrand's Ballot Theorem
  4. The Hanani–Tutte TheoremFibonacci imagePoster
  5. The Power of a Point Theorem
  6. Bézout's IdentityFibonacci imagePoster
  7. A Theorem about Gaussian Moats
  8. Euler's Product Formula for Sine    QED
  9. Euler's Product Formula for ζ(s)     QED
  10. The Alternating Series Test
  11. The LYM Inequality   QED
  12. A Theorem of Anderson, Cameron and Preece on Groups of Units
  13. The Pólya–Redfield Enumeration Theorem
  14. The Large Prime Gaps Theorem (Notes icon a Theorem under construction!)
  15. The Jones Knot Polynomial Theorem
  16. Kuratowski's 14-Set Theorem
  17. Euler's Even Zeta Formula
  18. Sylvester's Catalecticant
  19. Kemeny's Constant
  20. A Theorem on Modular Fibonacci Periodicity
  21. A Generalised Hlawka Inequality
  22. The Circle Area TheoremFibonacci imagePosterFibonacci imageGreek Poster
  23. The Riemann Explicit Formula
  24. Sophie Germain's Identity    QED
  25. Ore's Theorem in Graph Theory QEDFibonacci imageFrench version
  26. Poncelet's PorismFibonacci imageFrench version
  27. Fisher's Inequality    QED
  28. Cauchy's Theorem in Group Theory   QED
  29. Wolstenholme's Theorem
  30. The Spherical Law of Cosines
  31. Green's Theorem
  32. Tutte's Golden IdentityFibonacci imagePoster
  33. Faulhaber's Formula
  34. The Inclusion-Exclusion Principle
  35. The Pappus–Guldin Theorems
  36. Integration by Parts
  37. The Riemann Rearrangement Theorem
  38. Taylor's Theorem
  39. Irrationality of Circumference of Unit Circle
  40. Wedderburn's Little Theorem
  41. A Theorem on Maximal Sum-free Sets in Groups
  42. The 6-Circles Theorem
  43. Vizing's Theorem
  44. Willans' Formula   QED
  45. The Basel Problem   QED
  46. The Erdős Discrepancy Problem (Notes icon a Theorem under construction!)
  47. Toricelli's Trumpet QED
  48. The Eratosthenes-Legendre Sieve QED
  49. Euler's Formula QED
  50. The Classification of the Semiregular Tilings
  51. Singmaster's Binomial Multiplicity Bound (Notes icon a Theorem under construction!)  QED
  52. Euler's Continued Fraction Correspondence
  53. The Friedlander–Iwaniec Theorem
  54. Jensen's Inequality
  55. Minkowski's Convex Body Theorem QED
  56. Fermat's Two-Squares Theorem QED
  57. The Art Gallery Theorem QED
  58. The Robin–Lagarias Theorem
  59. The Cantor–Bernstein–Schröder Theorem QED
  60. The Erdős–Ko–Rado Theorem QED
  61. Wilson's Theorem QED
  62. Frieze's Theorem on Expected Minimum Tree Length
  63. The Rotation Distance Bound
  64. L'Hospital's Rule
  65. Jackson's Theorem on Compatible Euler ToursFibonacci imagemonochrome
  66. The Handshaking Lemma QED
  67. al-Kāshi's Law of Cosines
  68. Karp's Theorem (Detail) QED
  69. The Insolvability of the Entscheidungsproblem QED
  70. Kőnig's Bipartite Matching Theorem
  71. von Neumann's Minimax Theorem
  72. Theorema Egregium
  73. The Girard-Newton Identities
  74. Archimedes' Equiareal Map Theorem
  75. The Greibach Normal Form Theorem
  76. The Descartes Circle Theorem
  77. Sendov's Conjecture (Notes icon a Theorem under construction!)
  78. The Heine–Borel Theorem QED
  79. The Existence Theorem for Bachelor Latin Squares
  80. The Bungers–Lehmer Theorem on Cyclotomic Coefficients
  81. The Cameron–Fon-Der-Flaass IBIS Theorem
  82. The Ramanujan Partition Congruences
  83. The Andrews–Garvan–Dyson Crank
  84. The BEST TheoremFibonacci imagePoster
  85. Machin's Formula
  86. Sokal's Theorem on Chromatic Roots
  87. The Max-Flow Min-Cut Theorem
  88. The Lindemann–Weierstrass Theorem
  89. Haken's Unknot Theorem
  90. Lin McMullin's Theorem
  91. The Diaconis–Holmes–Montgomery Coin Tossing Theorem
  92. The Friendship Theorem
  93. Heath's Finitely Discontinuous Function Theorem
  94. Quadratic Nonresidue is Zero-Knowledge Provable QED
  95. The Classification of Archimedean 4-Polytopes
  96. The McIver–Neumann 1/2-n Bound
  97. The Albert–Brauer–Hasse–Noether Main Theorem
  98. The Transversal Matroid Theorem
  99. The Lecture Hall Partition Theorem
  100. A Tripartite Turán Theorem
  101. The Remainder Theorem QED
  102. Euler's Partition Identity QED
  103. De Moivre's Theorem
  104. The Small Prime Gaps Theorem
  105. Woodall's Hopping Lemma
  106. Euclid's Triangular Prism QED
  107. A Theorem of Schur on Real-Rootedness
  108. The Sophomore's Dream
  109. The Panarboreal Formula
  110. The Contraction Mapping Theorem QED
  111. Lieb's Square Ice Theorem
  112. The Robinson–Schensted–Knuth Correspondence QED
  113. Sylvester's Law of Inertia
  114. The Piff–Welsh Theorem
  115. A Theorem on Rectangular Tensegrities
  116. Strassen's Matrix Theorem (Notes icon a Theorem under construction!) QED
  117. Vaughan Pratt's Theorem
  118. Wallis's Product
  119. Theorems of Euler and Rényi on 'e'
  120. Praeger's Theorem on Bounded Movement
  121. The Change of Variables Theorem
  122. The Total Probability Theorem
  123. Theaetetus' Theorem on the Platonic Solids
  124. The Existence Theorem for Orthogonal Diagonal Latin Squares
  125. A Theorem on Apollonian Circle Packings
  126. The Ollerenshaw–Brée Formula
  127. The Euclid–Euler Theorem
  128. The Lucas–Lehmer Test
  129. The Asymptotic (Half) Liar Formula
  130. The Skolem–Noether Theorem
  131. The Lagrange Interpolation Formula QED
  132. The Wedderburn–Artin Theorem
  133. The Borsuk–Ulam Theorem
  134. Lambert's Formula
  135. The Lovász Local Lemma
  136. Kneser's Conjecture
  137. Catalan's Conjecture (Mihăilescu's Theorem)
  138. A Theorem of Erdős and Wilson on Edge Colouring
  139. The Polynomial Coprimality Theorem
  140. The Hardy–Ramanujan Asymptotic Partition Formula
  141. The Lagrange Property for Moufang Loops
  142. van der Waerden's Conjecture
  143. Bregman's Theorem
  144. De Morgan's Laws QED
  145. The Robbins Problem
  146. The Beardwood–Halton–Hammersley Theorem
  147. The Analyst's Travelling Salesman Theorem
  148. The Tverberg Partition Theorem
  149. Babbitt's Theorem
  150. The Pumping Lemma
  151. The Goins–Maddox–Rusin Theorem on Heron Triangles
  152. The Parking Function Formula QED
  153. Viète's Formula
  154. Kepler's Conjecture (Notes icon a Theorem under construction!)
  155. The Design of the Century
  156. The Happy Ending Problem QED
  157. Cartwright's Theorem
  158. Nevanlinna's Five-Value Theorem
  159. The Rule of Sarrus QED
  160. The Convolution Theorem
  161. Cayley's Formula
  162. The Generalised Hexachord Theorem
  163. The Quadratic Formula QED
  164. Khinchin's Theorem on Continued Fractions
  165. Cardano's Cubic Formula
  166. The Abel–Hurwitz Binomial Theorem
  167. The Cauchy–Kovalevskaya Theorem
  168. Lamé's Theorem QED
  169. Noether's Symmetry Theorem
  170. Cayley's Theorem
  171. The Five Circle Theorem
  172. The Delsarte–Goethals–Seidel Theorem
  173. Gruenberg's Theorem on Nilpotent Groups
  174. The Lutz–Nagell Theorem
  175. 1-Factorisation of Regular Graphs (Notes icon a Theorem under construction!)  Fibonacci imagemonochrome
  176. The Fifteen Theorem
  177. The Three-Distance Theorem
  178. Pick's Theorem
  179. Brahmagupta's Formula
  180. Gödel's Second Incompleteness Theorem
  181. Gödel's First Incompleteness Theorem
  182. Goodstein's Theorem
  183. MacWilliams' Identity
  184. Sharkovsky's Theorem
  185. The 1-2-3 Conjecture (Notes icon a Theorem under construction!)
  186. Arrow's Impossibility Theorem
  187. The Stable Marriage Theorem
  188. Reidemeister's Theorem
  189. An Erdős–Ko–Rado Theorem on Intersecting Permutations
  190. The Sims Conjecture
  191. Neumann's Separation Lemma
  192. Thales' Theorem
  193. The Marriage Theorem and The Frobenius–Kőnig Theorem
  194. Moufang's Theorem
  195. The Strong Perfect Graph Theorem
  196. Germain's TheoremFibonacci imagePosterFibonacci imageGreek Poster
  197. Galois' Theorem on Finite Fields
  198. The Birkhoff–von Neumann Theorem
  199. Morley's Miracle
  200. Miquel's Triangle Theorem
  201. The Bose Equivalence Theorem in Design Theory (600KB — a smaller version is here)
  202. Bailey's Theorem on Latin SquaresFibonacci imagemonochrome
  203. The Robertson–Seymour Graph Minors Theorem
  204. A Theorem of Melody Chan on Group Actions
  205. The Euler–Hierholzer "Bridges of Königsberg" Theorem
  206. Netto's Conjecture (Dixon's Theorem)Fibonacci imagemonochrome
  207. Beineke's Theorem on Line Graphs
  208. The Binomial Theorem
  209. Cameron's Theorem on Distance-Transitive Graphs
  210. Binet's Formula
  211. Pappus' Theorem
  212. The DPRM Theorem
  213. Zeckendorf's Theorem
  214. Lagrange's Theorem
  215. Stirling's Approximation
  216. Pascal's Rule QED
  217. Lucas' Theorem
  218. Girard's Theorem QED
  219. Euler's Identity QED
  220. The Second Isomorphism Theorem
  221. The First Isomorphism Theorem
  222. The Prime Number Theorem
  223. The Green–Tao Theorem on Primes in Arithmetic Progression
  224. Benford's Law
  225. The Law of Large Numbers
  226. Gauss's Law of Quadratic Reciprocity
  227. Ramsey's Theorem
  228. The Pythagorean Theorem    QED
  229. Euler's Polyhedral Formula QED
  230. Wagner's Theorem
  231. Kuratowski's Theorem
  232. Cantor's Theorem QED
  233. Cantor's Uncountability Theorem QED
  234. Brun's Theorem
  235. The Merton College Theorem
  236. Dilworth's Theorem
  237. Brouwer's Fixed Point Theorem
  238. The Well-Ordering Theorem
  239. Sperner's Lemma QED
  240. The Orbit Counting Lemma
  241. Cook's Theorem on NP-completeness
  242. Fermat's Little Theorem QED
  243. The Matrix Tree Theorem
  244. Lagrange's Four-Squares TheoremFibonacci imagePosterFibonacci imageGreek Poster
  245. Bayes' Theorem
  246. Fermat's Last Theorem
  247. The Central Limit Theorem
  248. The Fundamental Theorem of Arithmetic
  249. The Fundamental Theorem of Algebra
  250. The Chinese Remainder Theorem QED
  251. Euclid's Infinity of Primes QED
  252. The Bruck–Ryser–Chowla Theorem on Finite Projective Planes
  253. The Fundamental Theorem of the Calculus
  254. 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, 2005–2018, except where otherwise acknowledged. See FAQ for more.
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