Pierre de Fermat (1601-1665) Historical sketch
Much publicity fell upon the mathematician Andrew Wiles in 1994 when it was revealed that he had proved what is known as Fermat's Last Theorem*. Actually, its status was not that of a theorem but of a conjecture, made some 300 or so years earlier, that the equation
an + bn = cn
has no solution when a, b, c, and n are positive integers with n > 2. (For n = 2, this is the Pythagorean theorem.) Fermat wrote his conjecture in the margin of a book, as follows: "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 he had no proof and that this was just another of numerous bold conjectures made by Fermat, 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 have yet to be decided, for example the conjecture that 22N + 1 is prime for every positive integer N. All this may suggest that Fermat was a bit of a mathematical kook, but he certainly was not---he was a lawyer by profession but a brilliant and productive amateur 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, resulting in significant results about maxima and minima of geometric curves, identifying such by places where tangent lines are horizontal, just as you did in calculus. 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; however, his erudition in the subject spread to concern not only calculus, but probability theory, analytic geometry, optics, and the calculus of variations. As if all this weren't enough, he was fluent in Latin, Greek, and several modern languages; and he studied classic literature.
Fermat died of an unknown illness on January 12, 1665.
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*Wiles had decided when he first heard of the problem that he had to solve it. He was at that time ten years old.