Pierre de Fermat (redirected from P. Fermat)

Fermat, Pierre de 

Born Aug. 17, 1601, in Beaumont-de-Lomagne; died Jan. 12, 1665, in Castres. French mathematician.

A lawyer by profession, Fermat became a councillor of the parliament of Toulouse in 1631. He produced a number of remarkable works; most of them were published posthumously in 1679 in his Varia opera mathematica (Various Mathematical Works), which was edited by his son. The results that Fermat obtained became known to scholars during his lifetime through correspondence and personal contact.

Fermat is one of the founders of the theory of numbers. Two famous theorems in this field bear his name: Fermat’s last theorem, also known as Fermat’s great theorem, and Fermat’s lesser theorem, which is usually called simply Fermat’s theorem. In geometry he developed the method of coordinates in a more systematic form than did R. Descartes; Fermat found the equations of the straight line and of second-degree curves and outlined a proof for the assertion that all second-degree curves are conies.

In the area of the method of infinitesimals, Fermat systematically studied the process of differentiation; he gave a general rule for the differentiation of powers and applied the rule to the differentiation of fractional powers. A method devised by him for finding extrema was of great importance in the development of modern methods of differential calculus. Before Fermat the rule for the integration of a power had been known for some special cases. He provided a general proof of the rule’s correctness and extended the rule to the cases of fractional and negative powers. Both of the fundamental processes of the method of infinitesimals thus received systematic development by Fermat. Like his contemporaries, however, he failed to notice the relation between the operations of differentiation and integration. This relation was established somewhat later in systematic form by G. von Leibniz and I. Newton.

Through his works Fermat had a great influence on the subsequent development of mathematics. In physics he set forth the fundamental law of geometrical optics now known as Fermat’s principle.

WORKS

Oeuvres, vols. 1–4. Paris, 1891–1912.

REFERENCES

Bourbaki, N. Ocherki po istorii matematiki [book 8]: Elementy matematiki. Moscow, 1963. (Contains bibliography.) (Translated from French.)
Istoriia matematiki s drevneishikh vremen do nachala XIX stoletiia, vol. 2. Moscow, 1970.