[Math Lair] Pierre de Fermat

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Pierre de Fermat (born Pierre Fermat) was a seventeenth-century French mathematician. Born sometime in the first decade of the century and dying in 1665, he was a contemporary of Descartes and Pascal.

Fermat was a lawyer by profession; to him, studying mathematics was a hobby. He was one of the most significant amateur mathematicians of the modern era. He had a strong interest in the literature of antiquity, including scientific and mathematical works, and attempted to "restore" lost works. His interest in ancient mathematical works spurred him to make many important mathematical discoveries.

Fermat had a bit of a habit of writing marginal notes in his books describing, often without proof, related mathematical discoveries. describing his discoveries. This is the case in the discovery that made Fermat the most famous, Fermat's Last Theorem (actually a bit of a misnomer, since it wasn't Fermat's last, and until recently it had not been proved and so was not a theorem). Fermat's Last Theorem states that, for any natural number n ≥ 3, there are no integers x, y, and z such that xn + yn = zn. Fermat wrote, "I have a truly marvelous proof of this proposition that this margin is too narrow to contain.", but does not appear to have provided such a proof and, based on the complexity of the proof (which was not found until 1994) it seems unlikely that Fermat actually had a correct proof.

Fermat also found many other important results in the field of number theory, essentially being the founder of modern number theory. He was quite interested in the subject, investigating perfect numbers (during which he discovered what is known as Fermat's little theorem), amicable numbers, figurate numbers (triangular numbers, square numbers, etc.), magic squares, prime numbers, and what would later be known as Fermat numbers. Some of his results he proved using the method of infinite descent.

Fermat also investigated analytic geometry; his work on the topic was circulating in manuscript form before Descartes' La géométrie was published, so Fermat could be considered a codiscoverer of analytic geometry. He also made great strides toward calculus, doing significant work on differentiations and integrations and helped to set the stage for the work of Leibniz later in the century.

Sources used (see bibliography page for titles corresponding to numbers): 38.