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Pierre de Fermat (French: [pjɛːʁ də fɛʁma]; between 31 October and 6 December 1607[1] – 12 January 1665) was a French lawyer[3] at the Parlement of Toulouse, France, and a mathematician who is given credit for early developments that led to infinitesimal calculus, including his technique of adequality. In particular, he is recognized for his discovery of an original method of finding the greatest and the smallest ordinates of curved lines, which is analogous to that of differential calculus, then unknown, and his research into number theory. He made notable contributions to analytic geometry, probability, and optics. He is best known for his Fermat's principle for light propagation and his Fermat's Last Theorem in number theory, which he described in a note at the margin of a copy of Diophantus' Arithmetica.

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Holographic will handwritten by Fermat on 4 March 1660—kept at the Departmental Archives of Haute-Garonne, in Toulouse

Assessment of his work

Together with René Descartes, Fermat was one of the two leading mathematicians of the first half of the 17th century. According to Peter L. Bernstein, in his b

Together with René Descartes, Fermat was one of the two leading mathematicians of the first half of the 17th century. According to Peter L. Bernstein, in his book Against the Gods, Fermat "was a mathematician of rare power. He was an independent inventor of analytic geometry, he contributed to the early development of calculus, he did research on the weight of the earth, and he worked on light refraction and optics. In the course of what turned out to be an extended correspondence with Blaise Pascal, he made a significant contribution to the theory of probability. But Fermat's crowning achievement was in the theory of numbers."[23]

Regarding Fermat's work in analysis, Isaac Newton wrote that his own early ideas about calculus came directly from "Fermat's way of drawing tangents."[24]

Of Fermat's number theoretic work, the 20th-century mathemat

Regarding Fermat's work in analysis, Isaac Newton wrote that his own early ideas about calculus came directly from "Fermat's way of drawing tangents."[24]

Of Fermat's number theoretic work, the 20th-century mathematician André Weil wrote that: "what we possess of his methods for dealing with curves of genus 1 is remarkably coherent; it is still the foundation for the modern theory of such curves. It naturally falls into two parts; the first one ... may conveniently be termed a method of ascent, in contrast with the descent which is rightly regarded as Fermat's own."[25] Regarding Fermat's use of ascent, Weil continued: "The novelty consisted in the vastly extended use which Fermat made of it, giving him at least a partial equivalent of what we would obtain by the systematic use of the group theoretical properties of the rational points on a standard cubic."[26] With his gift for number relations and his ability to find proofs for many of his theorems, Fermat essentially created the modern theory of numbers.