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