Pierre de Fermat

Pierre de Fermat

Pierre de Fermat [pjɛːʀ dəfɛʀˈma] (* at the end of of 1607 or at the beginning of of 1608 in Beaumont de Lomagne; † 12. January 1665 in Castres) was a French mathematician and lawyer.

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as date of birth applied until recently the 17. August 1601, careful searches (see below.) however it resulted in thatFermat at the end of of 1607 or at the beginning of of 1608 was born.

Fermat studied jurisprudence at the universities in Toulouse, Bordeaux and Orléans. 1631 he became a judge and civil servant of the government in Toulouse, where he lived up to his death. Due to thesePosition it was ennobled.

1652 it was carried to the highest criminal court. 1643 to 1654, when in Europe civil war and plague raged, broke off Fermat its contacts to Paris and dedicated themselves strengthen the number theory. 1653 got sickhe at the plague and was likewise explained erroneously for dead.

Fermat studied from 1623 to 1626 civil law at the University of Orléans and locked this study in July 1626 with baccalaureus juris civilis. In the autumn of the same yearly leftit as a lawyer to parlement itself de Bordeaux down, where it remained to at the end of of 1630. It studied neither in Bordeaux nor in Toulouse. Then he bought the office more conseiller you parlement de Toulouse and became to 14. May1631 in this office swear in.

In the time of 1643 to 1653 Fermat dedicated itself does not strengthen to the number theory (the time of its large pay-theoretical discoveries there already lay behind it). Rather it became by the manifold obligations from its officeas more conseiller so much taken up that no time for its mathematical research remained practical for it. Farmer rebellions in the Languedoc because of brutal tax collections, whose illegal and inhuman practices were uncovered by Fermat, and which in Southern France particularly violent military conflictswith the Fronde, which pulled also Fermats birth city Beaumont de Lomagne in, for the largest part of Southern France politically responsible person parliament of Toulouse and also Fermat in breath held. Thus Fermat belonged for example to the negotiation commission of the royalist parliament ofToulouse, which led lengthy negotiations with the general conditions of the Languedoc, which had struck themselves on the side of the Fronde, to the re-establishment of the right peace. Also Fermat prevented the destruction of its hometown Beaumont by courageous personal employment by royal troops.

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Contributions to mathematics

Fermat was one of the most important „amateurs “in the history of mathematics, certainly at a time, when itself still hardly a researcher exclusively with mathematics busy. Thus Fermats influence on its correspondence with many was limitedimportant scholars of its time (like z. B. Carcavi, Beaugrand, Descartes and Mersenne) and on the expenditure of its deduction made by its son, including which of it commentated arithmetic of the Diophant (see below). It has important contributions to Number theory, probability calculation, variation and differential calculus performed. It communicated its results often only in the form of „brainteasers “- of problems without indication of the solution -.

After Fermat are among other things designated:

  • As Fermat numbers numbers of the form become <math> F_n = 2^ {2^n} +1< /math> designated. Fermatassumed 1637 that all Fermat numbers are prime numbers. This was disproved however 1732 by Euler.
  • The Fermat two-square set reads: An odd prime number< math> p< /math> is exactly the sum of two squares if it a number of the form <math> 4 n + 1< /math>is, and this representation is clear (up to the order).
    <math> p = a^2 + b^2 \ iff p = 4 n + 1< /math>
    The first proof of this sentence decreases/goes back on Euler. The two smallest prime numbers with this characteristic are <math> 5(=1^2 + 2^2)< /math> and <math> 13 (=2^2+3^2)< /math>.
  • Small fermatscher sentence: To each prime number p applies:
    <math> a^p \ equiv A \ (\ mathrm {mod} \ p) </math> for all <math> A \ in \ mathbb {Z}< /math>.
    On this sentence the Fermat prime number test is based. Also in this case findsitself the first received proof with Euler.
  • Fermats last sentence , Fermat assumption or large one fermatscher sentence : This most famous statement decreasing/going back on Fermat means that the diophantische equation
    <math> \ x^n + y^n = z^n </math>
    with <math> x, y, z \ in\ mathbb {N} </math> for no natural number <math> n> 2 </math> is fulfilled. There are thus no analogues to the Pythagorean Tripel for the third or higher powers. Its celebrity attained this sentence by the fact that Fermat in a marginal note of its copy that Arithmetica of the Diophant maintained for it one „marvelous “proof to have found for which however „on the edge enough place “was not. The case <math> n=4 </math> by Fermat with other place one proved, further cases later by other mathematicians. Inits public remained the statement until recently one of the most famous unresolved problems of mathematics. Only 1993 (1995 with a contribution of smelling pool of broadcasting corporations publish Taylor) succeeded it to the British mathematician Andrew Wiles to prove the Fermat assumption.Therefore this is called also sentence of Fermat Wiles or sentence of Wiles Taylor.

to the rectification of Fermats date of birth

Pierrede Fermat did not become to 17. August 1601 and not at all in the year 1601 born. To 20. August 1601 in Beaumont de Lomagne baptized „Pierre Fermat “is early a deceased half brother of same name from the first marriage of its fatherDominique Fermat with Francoise Cazeneuve, which deceased in the year 1603. The mathematician Pierre Fermat was born in the last quarter of the yearly 1607 or in the first twelve days of January 1608. Its nut/mother is Claire de Long, those its father1604 married.

see also


  • Simon Singh: Fermats last sentence dtv publishing house, ISBN 3-423-33052-X
  • Klaus Barner: How old did Fermat become? In: The life Fermats, reports of the German mathematician combination, number 3, 9 (2001), Berlin,S. 209-228

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