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
(Fermat’s Little Theorem) |
Leonhard Euler
(Pierre de Fermat) |
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 + …. |
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 |
All Primes Equal the Sum of Two Squares |
? |
? |
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 Coninuum 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
George Polya |
?
? |
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 |
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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 |
