Pierre de Fermat
Born: 17th August, 1601, Beaumont-de-Lomagne, France
Died: 12th January, 1665, Castres, France
Education: University of Orléans (1623–1626)
Spouse: Louise Long Fermat
Books: Writings on Geometrical Loci
Parents: Dominique Fermat, Françoise 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
equation, perfect numbers, amicable 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.