In July, 1999, Paul and Jack Abad presented their list of “The Hundred Greatest Theorems.” I was intrigued and though it might be interesting to re-post.
Their ranking is based on the following criteria: “the place the theorem holds in the literature, the quality of the proof, and the unexpectedness of the result.”
The list is of course as arbitrary as the movie and book list, but the theorems here are all certainly worthy results.
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)
… (view the rest of the list)
March 27th, 2007 at 11:41 am
According to Godel, this list doesn’t have everything.