Pierre de Fermat (1601-1665) is often called the
"Prince of Amateurs." He was the son of a prosperous
leather merchant, and became a lawyer and magistrate.
Fermat enjoyed the pleasure of discovery more than any
reputation it might gain him and published only one
important manuscript during his lifetime using the
concealing initials M.P.E.A.S. When Roberval offered to
edit and publish some of his works, Fermat replied
"whatever of my works is judged worthy of publication,
I do not want my name to appear there."
However, he carried on voluminous correspondence with
mathematicians, often stating his results piecemeal or
as challenges. Fermat was one of the founders of analytic
geometry, establish probability theory with Pascal,
and helped lay the foundation for calculus. Yet,
his true love was number theory.
In 1640, while studying perfect numbers, Fermat wrote to Mersenne that if p is prime, then 2p divides 2p-2. Shortly thereafter he expanded this into what is now called Fermat's Little Theorem. As usual, Fermat stated "I would send you a proof, if I did not fear its being too long." Perhaps his most famous statement of this form was attached to (the so-called) Fermat's Last Theorem: about which he had written in the margin of his copy of Diophantus' Arithmetica "For this, I have found a truly wonderful proof, but the margin is too small to contain it." Few believe Fermat had such a proof, and Wiles found the first accepted proof in 1995, some 350 years later.
Fermat developed a method of solving equations of the form x2-ay2 = 1, now incorrectly called a Pell equation. He incorrectly stated that all numbers were prime. (These are now known as the Fermat numbers.) Fermat developed a method of factoring based on expressing a number as a difference of squares and was known for his love of the method of "infinite descent" to solve problems.
See Also: FermatsLastTheorem