French amateur mathematician, most famous for Fermat's Last Theorem.
Born the 20th of August 1601 in Beaumont-de-Lomagne, France.
In his adult life he worked as counsellor and Supreme Judge in Toulouse. He dedicated his free time to study of mathematics, although it appears he had no formal education in mathematics. Instead he studied Diophantus' Arithmetica, concerning number theory, on his own.
As a hobby mathematician, Fermat did not leave much written down to the afterworld. Most of his notes he made for himself in solving riddles and making discoveries inspired by the Arithmetica, and thus many of his conjectures, although very likely perfectly understood by Fermat himself, had to be proven by other mathematicians later.
One of the problems he encountered was concerning Pythagoras' theorem and Pythagorean triples, such as
x^2 + y^2 = z^2
These triples had an infinite number of whole-number solutions, but merely by changing the exponent from 2 to 3 Fermat discovered that the triple of the form
x^3 + y^3 = z^3
did not appear to have any solutions at all. He extended this to the form
x^n + y^n = z^n : no solutions for n > 2
This is what's called Fermat's Last Theorem, since it was the last of his propositions to be proven.
In the margin of his copy of Arithmetica he noted:
Cubem autem in duos cubos, aut quadratoquadratum in duos quadratoquatratos, et generaliter nullam in infinitum ultra quadratum potestatem in duos eiusdem nominis fas est dividere. Cuius rei demonstrationem mirabilem sane detexi hanc marginis exiguitas non caperet.
It is impossible for a cube to be written as a sum of two cubes or a fourth power to be written as the sum of two fourth powers or, in general, for any number which is a greater power than the second to be written as a sum of two powers. I have a truly marvellous demonstration of this proposition which this margin is too narrow to contain.
(Translation from the book Fermat's Last Theorem by Simon Singh).
Naturally, mathematicians and others tried to find a proof of this proposition, with very little success for over 350 years. Now this has been proved indirectly by Andrew Wiles through the proof of the Taniyama-Shimura conjecture.
See Fermat's Last Theorem, Andrew Wiles, Taniyama-Shimura | 
