Pierre De Fermat
1601-1665
French Mathematician
One of the most intriguing figures in the history of mathematics, Pierre de Fermat was the classic talented amateur. A lawyer and government official, he spent much of his time too busy with other affairs to devote any attention to his mathematical studies. But in the time that he did have, he conceived the principles of analytic geometry, independent of cofounder and acquaintance René Descartes (1596-1650); established number theory and, with friend Blaise Pascal (1623-1662), the theory of probability; laid down the fundamentals of differential calculus; and left behind a problem that bedeviled mathematicians for 325 years.
Fermat, who added the aristocratic "de" to his name in his early 1630s, was the son of Dominique Fermat, a successful leather merchant, and Claire de Long, who came from a highly respected family of lawyers. In 1631, Pierre Fermat married his fourth cousin, Louise de Long, with whom he had five children. By then he had studied at a number of institutions, including the universities of Toulouse, Bourdeaux, and Orleans. Having earned his degree in civil law from the latter, he began his law practice, and with the purchase of several key posts started a climb to the upper echelons of French jurisprudence. By 1648 he had received an appointment as king's councilor.
With no mathematical training, Fermat in the 1630s he became involved with the Paris mathematical circle of Marin Mersenne (1588-1648), Gilles Personne de Roberval (1602-1675), and Etienne Pascal (1588-1651), father of Blaise. He quickly earned a reputation as a brash upstart who in his first communicationwith the group claimed to have found fault with a statement of Galileo (1564-1642) regarding the path of a freely falling cannonball. As time went on, Roberval and Mersenne became increasingly irritated with Fermat, who had a habit of presenting them with incredibly difficult problems. In time they began to suspect that he did not know the solution to such problems himself, and started requesting that he provide full explanations regarding how such solutions were derived.
Fermat also ran afoul of Descartes, an almost inevitable result of the fact that both men discovered analytic geometry. Descartes actually made the discovery earlier, but Fermat, in his 1637 Introduction to Plane and Solid Loci, was first to present his findings to the Paris group. The latter continued to regard Fermat as an outsider, and his brash ways did little to win friends during the ensuing dispute with Descartes.
With his restoration of writings by the Greek mathematician Apollonius of Perga (262-190 B.C.), as well as his Method for Determining Maxima and Minima and Tangents to Curve Lines (1636), Fermat laid the groundwork for differential calculus. Yet from 1643 to 1654, he remained so occupied with professional and political concerns—and, thanks to an outbreak of the plague in 1651 that very nearly killed him, personal ones—that he had little communication with other mathematicians. During this time, however, he did manage to develop Fermat's Theorem for determining whether or not a number is prime: if n is any whole number and p any prime, then np –n is divisible by p.
A 1654 letter from Pascal, in which the latter requested Fermat's help with a problem involving consecutive throws of a die, led to a series of communications in which the two men set down the elements of probability theory. Pascal took less interest in another growing area of interest for Fermat, number theory. Fermat was, however, able to correspond with Dutch physicist and astronomer Christiaan Huygens (1629-1695) about that subject until Huygens, too, concluded that number theory—now an important branch of mathematics—was useless.
Fermat had been weakened by the plague, and his latter years saw him in increasingly poorer health. He died on January 12, 1665, and was buried in the Chapel of St. Dominique in Castres. During the last decade of his life, he conducted experiments with optics, and made a discovery known as Fermat's Principle, which states that light travels by the path of least duration. It was perhaps also during this time that, while reading a Latin translation of Arithmetic by Diophantus of Alexandria (3rd century A.D.), Fermat jotted down a theorem in the margin: for the equation xn + yn = zn, where n is greater than 2, there are no positive integer solutions for x,y, and z.
Though the theorem was apparently true, its proof remained elusive to mathematicians, who would grapple with the problem for more than three centuries. Only in 1994 did English mathematician Andrew Wiles (1953-), who had devoted much of his career to the quest, present a correct proof of what had long since become known as Fermat's Last Theorem. Given the complexity of Wiles's proof, some mathematicians have questioned whether Fermat himself was able to prove the theorem. As for Fermat himself, his only answer was a note in the space beside his theorem: "I have discovered a truly remarkable proof which this margin is too small to contain."
This is the complete article, containing 818 words
(approx. 3 pages at 300 words per page).
