Lawyer and a French mathematician who lived between 1601 and 1665. Credited with establishing the theory of recent issues, and calculating probabilities independently of Pascal, as well as the discovery of analytic geometry independently of Descartes, and you may get the results of the advanced areas of the foundations of analytical geometry and calculus, but can not be published, and declared that it proved the matter unresolved famously known as Fermat's last theorem.
Fermat developed a system of analytic geometry which both preceded and surpassed that of Déscartes; he developed methods of differential and integral calculus which Newton acknowledged as an inspiration. Solving df(x)/dx = 0 to find extrema of f(x) is perhaps the most useful idea in applied mathematics; this technique originated with Fermat. 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's contemporaneous rival René Déscartes is more famous than Fermat, and Déscartes' writings were more influential. Whatever one thinks of Déscartes as a philosopher, however, it seems clear that Fermat was the better mathematician. Fermat and Déscartes did work in physics and independently discovered the (trigonometric) law of refraction, but Fermat gave the correct explanation, and used it remarkably to anticipate the Principle of Least Action later enunciated by Maupertius (though Maupertius himself, like Déscartes, had an incorrect explanation of refraction). Fermat and Déscartes independently discovered analytic geometry, but it was Fermat who extended it to more than two dimensions, and followed up by developing elementary calculus.
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