Pierre de Fermat

# Pierre de Fermat

Pierre de Fermat

Born: 17th August, 1601, Beaumont-de-Lomagne, France
Died: 12th January, 1665, Castres, France
Spouse: Louise Long Fermat
Books: Writings on Geometrical Loci
Parents: Dominique Fermat, FranÃ§oise Cazeneuve Fermat

The French mathematician, Pierre de Fermat is known as the founder of the modern theory of numbers. Fermat developed a system of analytic geometry which both preceded and surpassed that of Descartes. He developed methods of differential and integral calculus which Newton acknowledged as an inspiration. Fermat was also the first European to find the integration formula for the general polynomial. He used his calculus to find centers of gravity etc.

Fermat was the first person known to have evaluated the integral of general power functions. With his method, he was able to reduce this evaluation to the sum of geometric series. The resulting formula was helpful to Newton, and then Leibniz, when they independently developed the fundamental theorem of calculus.

In number theory, Fermat studied Pell's equationperfect numbersamicable numbers and what would later become Fermat numbers. He invented a factorization method—Fermat's factorization method—and popularized the proof by infinite descent, which he used to prove Fermat's right triangle theorem which includes as a corollary Fermat's Last Theorem for the case n = 4.

Although Fermat claimed to have proven all his arithmetic theorems, few records of his proofs have survived. Many mathematicians, including Gauss, doubted several of his claims, especially given the difficulty of some of the problems and the limited mathematical methods available to Fermat. His famous Last Theorem was first discovered by his son in the margin in his father's copy of an edition of Diophantus, and included the statement that the margin was too small to include the proof.

Although he carefully studied and drew inspiration from Diophantus, Fermat began a different tradition. Diophantus was content to find a single solution to his equations, even if it were an undesired fractional one. Fermat was interested only in integer solutions to his Diophantine equations, and he looked for all possible general solutions. He often proved that certain equations had no solution, which usually baffled his contemporaries.