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(Beaumont, France, 1601 - Castres, id., 1665) French mathematician. Continues the work of Diophantus in the field of integers and co-founder of the mathematical study of probability, along with Pascal, and geometry analytic, along with Descartes, Pierre de Fermat had correspondence with the great scientists of his time and already enjoyed in life of high esteem and great reputation, even though his natural modesty and your way of working , in excess dilettante, harmed the disclosure of contributions.

Pierre de Fermat

Fermat annotations in the margin

a work of Apollonius##

## Biography

The existence of this illustrious mathematician was certainly simple and prosaic, and little is known of his early years. Son of Dominique Fermat, bourgeois and second consul of Beaumont, studied law in Toulouse and perhaps Bordeaux to able to aspire to the exercise of the judiciary; come, indeed, Counselor of the Parliament of the city of Toulouse, was progressing there in its slow work and calmly, distinguished by his probity, his touch and his courteous manners.

Pierre de Fermat

Interested in mathematics, consecrated to them their leisure time, and towards 1637 was among the main European growers of this science. He befriended the mathematician Carcavi, who him related to the father Marin Mersenne, friend of all the French learned of the time. Father Mersenne put him in contact with Roberval and the great Rene Descartes (1637).

Dealing with difficult and restless genius of Descartes wasn't easy for anybody, nor did it to Pierre de Fermat, despite its discretion: both argued about scientific issues (violation of the light and the method of maximums and minimums). The mediation of Roberval and all the prudence of Fermat were necessary to maintain at least coolly correct personal relationships between the two scholars. Lively, on the other hand, was the friendship between Fermat and other great mathematician of the time, Blaise Pascal; both also met thanks to Carcavi.

Modest mood, Pierre de Fermat only came to printing works its monograph

*Dissertatio geometrica de linearum curvarum comparatione,*and made public some of his greatest discoveries only through brief letters and verbal communications. It was enough to make him known as one of the great mathematicians of the time, but their professional duties and their particular form of work reduced largely the impact of his work, extremely prolific. He for example had a habit of scoring, in the margins of the books I read, their ideas and their discoveries, unfortunately without their shows, for lack of space. Overcoming many difficulties, his writings were published posthumously by his son Samuel in 1679, in a volume entitled*Varia operates D. Petri de Fermat mathematics: Senatoris Tolosani*.## Mathematical investigations

The first contributions of Pierre de Fermat dating from 1629, when he tackled the task of rebuilding some lost demonstrations of the Greek mathematician Apollonius of Perga relating to loci; for this purpose it would develop, contemporary and regardless of René Descartes, an algebraic method to treat questions of geometry through a system of coordinates, of paramount importance for the creation of analytic geometry. Using the symbols of François Viète, was widely the equation of the straight line, and the Hyperbola, parabola and the circumference.

Fermat is also located between the mathematicians who gave the first impulse to the infinitesimal calculus, and was the first to study the issues of maximum and minimum (from 1636) with the method that we today call the "derivative", taking advantage of a great intuition which is presented for the first time in the work of the French prelate Nicholas of Oresme. He designed an algorithm of differentiation which could determine the maximum and minimum values of a polynomial curve and draw the corresponding tangent, achievements, all of which opened the way to the further development of the infinitesimal calculus by Newton and Leibniz.

In the field of geometrical optics, after correctly assume that when light moves in a more dense medium its speed decreases, it showed the path of a light Ray between two points is always one less time trouble go; This principle, called

*Fermat principle*, the laws of reflection and refraction are deducted. In 1654, and as a result of a long correspondence with Blaise Pascal developed the principles of the theory of probability.Fermat annotations in the margin

a work of Apollonius

Another field where he made original contributions was the theory of numbers, which became interested after consulting an edition of Diophantus

*arithmetic*; in the margin of a page of this edition was where scored which would be called*Fermat's last theorem*, which would take more than three centuries to be demonstrated. It can be said that the methodical study of the properties of integers really begins with Fermat, reason by which has been considered the true creator of the theory of numbers, to which old as Pythagoras, Euclid and Diophantus mathematicians had given just start. His work in this field led to important results related to the properties of prime numbers, many of which were expressed in the form of simple propositions and theorems. Unfortunately, all that reached us is contained almost exclusively in the narrow margins of a copy of Diophantus and some fragments of his correspondence. Fermat also developed an ingenious method of demonstration called "of the infinite descent".

## *Fermat's last theorem*

Despite so many and such valuable contributions, the name of the famous French mathematician is frequently associated with one of the most fascinating mysteries of the history of mathematics. When preparing the edition of the complete works of his father, Samuel de Fermat found a singular notation on one of the pages of the

*arithmetic*of Diophantus. In it, Fermat claimed that the equation x

^{n}+^{n}= z^{n}has no solution whole positive if the value of the exponent*n*is greater than 2. In other words: the sum of two squares can amount to a third square, as in equal 3 + 4^{2}^{2}= 5^{2/2}, but it is impossible to find a similar between numbers equal positive integers raised to the cube, to the fourth power, to the fifth power, etc. On the same note, Fermat said to have found a wonderful fact, but overly long show to be recorded in the margin of a book. During the three centuries that followed the publication followed one another relentlessly attempts to prove this theorem of Fermat, so difficult to prove that at certain times it became known as Fermat hypothesis. The names of Leonhard Euler, Sophie Germain, Peter Gustav Lejeune Dirichlet, Gabriel Lamé, Augustin-Louis Cauchy or Ernst Eduard Kummer give an idea of the number of great mathematicians who could not resist the temptation to try their luck.

In 1908, the impatience to find solution to a mystery that was already 250 years led to Paul Wolfskehl (a German industrialist who saved suicide thanks to the interest aroused in him by an article by Kummer about Fermat's theorem) to leave in his will a prize of one hundred thousand frames to who knew to find him a demonstration before a hundred years. It is said that only during the following four years at his death were published more than a thousand false evidence.

Efforts to demonstrate the theorem menbers in interesting contributions to the evolution of abstract algebra, such as the of the Kummer and his theory of ideal numbers. The last chapter of the story began to write in 1955, date in which Yutaka Taniyama addressed the study of the relationship between modular forms and elliptic equations. Taniyama failed to find solace in mathematics that they provided to Wolfskehl, and committed suicide in 1957. However, on the basis of his works and those of his fellow Goro Shimura, settled the conjecture that, after the work of Weil, would be called the Taniyama-Shimura-Weil conjecture.

André Weil, all a personality on the current theory of numbers, unveiled the conjecture to the mathematical community, European and American. In 1984 Gerhard Frey established the existence of a link between this conjecture and Fermat's last theorem, so that the first show should have as an immediate consequence the certainty of the second, which becomes so in expression of a fact relating to the fundamental properties of space.

Nine years later, the show was finally completed by Andrew Wiles, British mathematician and a professor at the US University of Princeton, who, after filing some aspects, published it in their permanently in May 1995 in the journal

*Annals of Mathematics*. In June 1997, in solemn ceremony, members of the Königliche Gesellschaft der Wissenschaften in Göttingen handed created ninety years earlier by Paul Wolfskehl Prize to Andrew Wiles. The mystery that will never be solved is if really Pierre de Fermat had found a demonstration of his theorem, and, if so, whether it was valid, and if so, that could be, since mathematical concepts completely unknown at the time of Fermat were used for the demonstration of Wiles.