100 Greatest Theorems are listed here. The millennium seemed to encourage many to compile a “Top 100” or “Top 100” list of many topics, including movies (by the American Film Institute) and books (by the Modern Library).

This article will give an overview of 100 Greatest Theorems.

Mathematicians were not deterrent, and at the Mathematics Conference in July 1999, Paul and Jack Abad presented their “The Hundred Greatest Theorem” list.

Their ranking is based on the following criteria: “The place in which the subject matter in the literature occupies, the quality of the evidence and the outcome is unexpected”

The list is, of course, voluntary as a movie and book list, but the subtypes here are definitely worthwhile results. I hope to include links to proof of all of them over time; Now, you have to satisfy yourself with the list and the biography of the overseers. (source)

## 100 Greatest Theorems

1 | The Irrationality of the Square Root of 2 | Pythagoras and his school | 500 B.C. |

2 | Fundamental Theorem of Algebra | Karl Frederich Gauss | 1799 |

3 | The Denumerability of the Rational Numbers | Georg Cantor | 1867 |

4 | Pythagorean Theorem | Pythagoras and his school | 500 B.C. |

5 | Prime Number Theorem | Jacques Hadamard and Charles-Jean de la Vallee Poussin (separately) | 1896 |

6 | Godel’s Incompleteness Theorem | Kurt Godel | 1931 |

7 | Law of Quadratic Reciprocity | Karl Frederich Gauss | 1801 |

8 | The Impossibility of Trisecting the Angle and Doubling the Cube | Pierre Wantzel | 1837 |

9 | The Area of a Circle | Archimedes | 225 B.C. |

10 | Euler’s Generalization of Fermat’s Little Theorem | Leonhard Euler | 1760
(1640) |

11 | The Infinitude of Primes | Euclid | 300 B.C. |

12 | The Independence of the Parallel Postulate | Karl Frederich Gauss, Janos Bolyai, Nikolai Lobachevsky, G.F. Bernhard Riemann collectively | 1870-1880 |

13 | Polyhedron Formula | Leonhard Euler | 1751 |

14 | Euler’s Summation of 1 + (1/2)^2 + (1/3)^2 + ‘ (the Basel Problem). | Leonhard Euler | 1734 |

15 | Fundamental Theorem of Integral Calculus | Gottfried Wilhelm von Leibniz | 1686 |

16 | Insolvability of General Higher Degree Equations | Niels Henrik Abel | 1824 |

17 | DeMoivre’s Theorem | Abraham DeMoivre | 1730 |

18 | Liouville’s Theorem and the Construction of Trancendental Numbers | Joseph Liouville | 1844 |

19 | Four Squares Theorem | Joseph-Louis Lagrange | 1770 |

20 | Primes that Equal to the Sum of Two Squares (Genus theorem) | ? | ? |

21 | Green’s Theorem | George Green | 1828 |

22 | The Non-Denumerability of the Continuum | Georg Cantor | 1874 |

23 | Formula for Pythagorean Triples | Euclid | 300 B.C. |

24 | The Undecidability of the Continuum Hypothesis | Paul Cohen | 1963 |

25 | Schroeder-Bernstein Theorem | ? | ? |

26 | Leibnitz’s Series for Pi | Gottfried Wilhelm von Leibniz | 1674 |

27 | Sum of the Angles of a Triangle | Euclid | 300 B.C. |

28 | Pascal’s Hexagon Theorem | Blaise Pascal | 1640 |

29 | Feuerbach’s Theorem | Karl Wilhelm Feuerbach | 1822 |

30 | The Ballot Problem | J.L.F. Bertrand | 1887 |

31 | Ramsey’s Theorem | F.P. Ramsey | 1930 |

32 | The Four Color Problem | Kenneth Appel and Wolfgang Haken | 1976 |

33 | Fermat’s Last Theorem | Andrew Wiles | 1993 |

34 | Divergence of the Harmonic Series | Nicole Oresme | 1350 |

35 | Taylor’s Theorem | Brook Taylor | 1715 |

36 | Brouwer Fixed Point Theorem | L.E.J. Brouwer | 1910 |

37 | The Solution of a Cubic | Scipione Del Ferro | 1500 |

38 | Arithmetic Mean/Geometric Mean (Proof by Backward Induction)
(Polya Proof) |
Augustin-Louis Cauchy | ?
? |

39 | Solutions to Pell’s Equation | Leonhard Euler | 1759 |

40 | Minkowski’s Fundamental Theorem | Hermann Minkowski | 1896 |

41 | Puiseux’s Theorem | Victor Puiseux (based on a discovery of Isaac Newton of 1671) | 1850 |

42 | Sum of the Reciprocals of the Triangular Numbers | Gottfried Wilhelm von Leibniz | 1672 |

43 | The Isoperimetric Theorem | Jacob Steiner | 1838 |

44 | The Binomial Theorem | Isaac Newton | 1665 |

45 | The Partition Theorem | Leonhard Euler | 1740 |

46 | The Solution of the General Quartic Equation | Lodovico Ferrari | 1545 |

47 | The Central Limit Theorem | ? | ? |

48 | Dirichlet’s Theorem | Peter Lejune Dirichlet | 1837 |

49 | The Cayley-Hamilton Thoerem | Arthur Cayley | 1858 |

50 | The Number of Platonic Solids | Theaetetus | 400 B.C. |

51 | Wilson’s Theorem | Joseph-Louis Lagrange | 1773 |

52 | The Number of Subsets of a Set | ? | ? |

53 | Pi is Trancendental | Ferdinand Lindemann | 1882 |

54 | Konigsberg Bridges Problem | Leonhard Euler | 1736 |

55 | Product of Segments of Chords | Euclid | 300 B.C. |

56 | The Hermite-Lindemann Transcendence Theorem | Ferdinand Lindemann | 1882 |

57 | Heron’s Formula | Heron of Alexandria | 75 |

58 | Formula for the Number of Combinations | ? | ? |

59 | The Laws of Large Numbers | <many> | <many> |

60 | Bezout�s Theorem | Etienne Bezout | ? |

61 | Theorem of Ceva | Giovanni Ceva | 1678 |

62 | Fair Games Theorem | ? | ? |

63 | Cantor’s Theorem | Georg Cantor | 1891 |

64 | L’Hopital’s Rule | John Bernoulli | 1696? |

65 | Isosceles Triangle Theorem | Euclid | 300 B.C. |

66 | Sum of a Geometric Series | Archimedes | 260 B.C.? |

67 | e is Transcendental | Charles Hermite | 1873 |

68 | Sum of an arithmetic series | Babylonians | 1700 B.C. |

69 | Greatest Common Divisor Algorithm | Euclid | 300 B.C. |

70 | The Perfect Number Theorem | Euclid | 300 B.C. |

71 | Order of a Subgroup | Joseph-Louis Lagrange | 1802 |

72 | Sylow’s Theorem | Ludwig Sylow | 1870 |

73 | Ascending or Descending Sequences | Paul Erdos and G. Szekeres | 1935 |

74 | The Principle of Mathematical Induction | Levi ben Gerson | 1321 |

75 | The Mean Value Theorem | Augustine-Louis Cauchy | 1823 |

76 | Fourier Series | Joseph Fourier | 1811 |

77 | Sum of kth powers | Jakob Bernouilli | 1713 |

78 | The Cauchy-Schwarz Inequality | Augustine-Louis Cauchy | 1814? |

79 | The Intermediate Value Theorem | Augustine-Louis Cauchy | 1821 |

80 | The Fundamental Theorem of Arithmetic | Euclid | 300 B.C. |

81 | Divergence of the Prime Reciprocal Series | Leonhard Euler | 1734? |

82 | Dissection of Cubes (J.E. Littlewood’s ‘elegant’ proof) | R.L. Brooks | 1940 |

83 | The Friendship Theorem | Paul Erdos, Alfred Renyi, Vera Sos | 1966 |

84 | Morley’s Theorem | Frank Morley | 1899 |

85 | Divisibility by 3 Rule | ? | ? |

86 | Lebesgue Measure and Integration | Henri Lebesgue | 1902 |

87 | Desargues’s Theorem | Gerard Desargues | 1650 |

88 | Derangements Formula | ? | ? |

89 | The Factor and Remainder Theorems | ? | ? |

90 | Stirling’s Formula | James Stirling | 1730 |

91 | The Triangle Inequality | ? | ? |

92 | Pick’s Theorem | George Pick | 1899 |

93 | The Birthday Problem | ? | ? |

94 | The Law of Cosines | Francois Viete | 1579 |

95 | Ptolemy’s Theorem | Ptolemy | 120? |

96 | Principle of Inclusion/Exclusion | ? | ? |

97 | Cramer’s Rule | Gabriel Cramer | 1750 |

98 | Bertrand’s Postulate | J.L.F. Bertrand | 1860? |

99 | Buffon Needle Problem | Comte de Buffon | 1733 |

100 | Descartes Rule of Signs | Rene Descartes | 1637 |

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