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