Pierre de Fermat

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Pierre de Fermat (August 17, 1601 – January 12, 1665) was a French lawyer at the Parlement of Toulouse, southern France, and a mathematician who is given credit for the development of modern calculus. In particular, he is the precursor of differential calculus with his method of finding the greatest and the smallest ordinates of curved lines, analogous to that of the then unknown differential calculus. Perhaps even more important, his brilliant researches in the theory of numbers entitle him to the rank of the founder of the modern theory. He also made notable contributions to analytic geometry and probability.

With his insightful theorems Fermat created the modern theory of numbers. The depth of his work can be gauged by the fact that many of his results were not proved for over a century after his death, and one of them, the Last Theorem, took more than 3 centuries to prove.

Although he carefully studied and drew inspiration from Diophantus, Fermat inaugurated a different tradition. Diophantus was content to find a single solution to his equations, even if it was a fraction. Fermat was only interested in integer solutions to his diophantine equations and he looked for all solutions of the equation. He also proved that certain equations had no solution, an activity which baffled his contemporaries.

He studied Pell's equation and Fermat, perfect, and amicable numbers. It was while researching perfect numbers that he created Fermat's theorem.

He created the principle of infinite descent and Fermat's factorization method.

He created the two-square theorem, and the polygonal number theorem, which states that each number is a sum of 3 triangular numbers, 4 square numbers, 5 pentagonal numbers, ...

He was the first to evaluate the integral of general power functions. Using an ingenious trick, he was able to reduce this evaluation to summing geometric series. The formula that resulted was a key hint to Newton and Leibniz when they independently developed the fundamental theorems of calculus.

Although Fermat claimed to be able to prove all his arithmetical results, few of his proofs (if he had them) have survived. And considering that some of the results are so difficult (especially considering the mathematical tools at his disposal) many, including Gauss, believe that Fermat was unable to do so.

Together with René Descartes, Fermat was one of the two leading mathematicians of the first half of the 17th century. Independently of Descartes, he discovered the fundamental principle of analytic geometry. Through his correspondence with Blaise Pascal, he was a founder of the theory of probability.

Holographic will handwritten by Pierre de Fermat on March 4, 1660 - kept at the Departmental Archives of Haute-Garonne, in Toulouse

Fermat was born at Beaumont-de-Lomagne, 58 kilometers (36 miles) north-west of Toulouse, France. He died at Castres, 79 kilometers (49 miles) east of Toulouse. The oldest and most prestigious high-school in Toulouse is called Pierre de Fermat. This high-school has preparatory classes for engineering and business schools (grandes écoles), and is ranked in the top 10 of France's best preparatory classes. The late 15th century mansion where Fermat was born in Beaumont-de-Lomagne is now a museum.

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[edit] Bibliography

Singh, Simon (2002). Fermats Last Theorem. Fourth Estate Ltd. ISBN 1-84115-791-0.
Mahoney, Michael Sean (1994). The mathematical career of Pierre de Fermat, 1601 - 1665. Princeton Univ. Press. ISBN 0-691-03666-7.