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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. Some of the theorems have matching Java applets: these will open in the same window and will usually prompt for permission before running.

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