Pierre de Fermat(1601-1665) is known for among other things, two theorems: Fermat's little Theorem and Fermat's Last Theorem. The latter was a conjecture for the longest time, and was proved only recently by Andrew Wiles --not to be confused with Andre Weil). The proof has finally been published in a refereed journal:
A. Wiles, Annals of Mathematics 142 (195), pp 443-551
Also see:
- Alf von der Poorten, "Notes on Fermat's Last Theorem", 1996, Wiley A.
- Book - Fermat's Last Theorem by Simon Singh.
The little (though remarkable) theorem says: a^p = a (mod p), where p is prime, a less than p. Here are a couple of nice derivations of the little theorem by Gowers.
Fermat's Last Theorem: For n>2, the equation x^n+y^n=z^n has no solutions in natural numbers.
Wiles' proof builds on work of several people, and fundamentally uses Elliptic Curves and Modular Forms.