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(born Aug. 17, 1601, Beaumont-de-Lomagne, France—died Jan. 12, 1665, Castres) French mathematician. Of Basque origin, Fermat studied law at Toulouse and developed interests in foreign languages, Classical literature, ancient science, and mathematics. A jurist by profession, he produced major mathematical breakthroughs independently and collaboratively. A contemporary of René Descartes, he discovered independently the basic principles of analytic geometry, but, because Fermat's work was published posthumously, the field became known as Cartesian geometry. He found equations for tangent lines to curves through processes equivalent to differentiation and was coauthor (with Blaise Pascal) of probability theory. His work in number theory, especially divisibility, led to some of its most important theorems. He seldom demonstrated his results, which led to a centuries-long quest to prove a famous conjecture that Fermat claimed was easily shown ( Fermat's last theorem).
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