CALCULUS Understanding Its Concepts and Methods

Pierre de Fermat (1601--1665) --- Historical sketch

Much publicity fell upon the mathematician Andrew Wiles in 1994 when he proved Fermat's Last Theorem, a conjecture, made some 300 years earlier, that the equation has no solution with , , , and positive integers and . (For , there are many solutions, called Pythagorean triples because of the Pythagorean theorem.) Fermat's Last Theorem was the last of Fermat's claims to be proved. Here is what Fermat had written in the margin of a book: "It is impossible for a cube to be the sum of two cubes, a fourth power to be the sum of two fourth powers, or in general for any number that is a power greater than the second to be the sum of two like powers. I have discovered a truly marvelous demonstration of this proposition that this margin is too narrow to contain."

Many historians believe Fermat had no proof and that this was just another of his numerous bold conjectures, many of which were later proved true. For example, another Fermat conjecture, made in 1638, asserts that every positive integer is a sum of at most three triangular numbers, four square numbers, five pentagonal numbers, etc. He claimed proof of this conjecture, but while no proof of his was ever found, it was later proved by Joseph Louis Lagrange. Some of his conjectures turned out to be false, for example the conjecture that is prime for every positive integer . All this may suggest that Fermat was a bit of a mathematical kook, but he certainly was not---he was a lawyer by profession and a brilliant and productive mathematician who figured prominently in the development of calculus. (Lagrange is said to have called Fermat the inventor of calculus.)

Pierre de Fermat was born of wealthy parents in Beaumont-de-Lomagne, near Toulouse in southern France, and attended the University of Toulouse. In his late 20s, he moved to nearby Bordeaux and began the serious pursuit of mathematics, producing significant results about maxima and minima of geometric curves, identifying them as places where the tangent line is horizontal. Fermat then studied law at the University of Orleans in north-central France, south of Paris, becoming a lawyer and moving back to Toulouse, where he lived for the rest of his life. In 1653, Fermat contracted the plague but recovered, and despite his woes, was deeply engrossed in mathematics.

Most of his mathematical interests centered on number theory, but he also became involved with calculus, probability theory, analytic geometry, optics, and the calculus of variations. He was fluent in Latin, Greek, and several modern languages, and he studied classical literature.

Fermat died of an unknown illness on January 12, 1665.

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Copyright © 2006 Darel Hardy, Fred Richman, Carol Walker, Robert Wisner. All rights reserved. Except upon the express prior permission in writing, from the authors, no part of this work may be reproduced, transcribed, stored electronically, or transmitted in any form by any method.