Autobiography of pierre de fermat

Pierre had a brother and two sisters and was almost certainly brought up in the town of his birth.

Autobiography of pierre de fermat: Pierre de Fermat was a

Although there is little evidence concerning his school education it must have been at the local Franciscan monastery. He attended the University of Toulouse before moving to Bordeaux in the second half of the s. In Bordeaux he began his first serious mathematical researches and in he gave a copy of his restoration of Apollonius 's Plane loci to one of the mathematicians there.

He received a degree in civil law and he purchased the offices of councillor at the parliament in Toulouse. So by Fermat was a lawyer and government official in Toulouse and because of the office he now held he became entitled to change his name from Pierre Fermat to Pierre de Fermat. For the remainder of his life he lived in Toulouse but as well as working there he also worked in his home town of Beaumont-de-Lomagne and a nearby town of Castres.

From his appointment on 14 May Fermat worked in the lower chamber of the parliament but on 16 January he was appointed to a higher chamber, then in he was promoted to the highest level at the criminal court. Still further promotions seem to indicate a fairly meteoric rise through the profession but promotion was done mostly on seniority and the plague struck the region in the early s meaning that many of the older men died.

Fermat himself was struck down by the plague and in his death was wrongly reported, then corrected:- I informed you earlier of the death of Fermat.

Autobiography of pierre de fermat: Pierre de Fermat was a French

He is alive, and we no longer fear for his health, even though we had counted him among the dead a short time ago. The following report, made to Colbert the leading figure in France at the time, has a ring of truth:- Fermat, a man of great erudition, has contact with men of learning everywhere. But he is rather preoccupied, he does not report cases well and is confused.

Of course Fermat was preoccupied with mathematics. He kept his mathematical friendship with Beaugrand after he moved to Toulouse but there he gained a new mathematical friend in Carcavi. Fermat met Carcavi in a professional capacity since both were councillors in Toulouse but they both shared a love of mathematics and Fermat told Carcavi about his mathematical discoveries.

In Carcavi went to Paris as royal librarian and made contact with Mersenne and his group. Mersenne 's interest was aroused by Carcavi 's descriptions of Fermat's discoveries on falling bodies, and he wrote to Fermat. Fermat replied on 26 April and, in addition to telling Mersenne about errors which he believed that Galileo had made in his description of free fall, he also told Mersenne about his work on spirals and his restoration of Apollonius 's Plane loci.

Fermat mathematician made significant contributions to number theory, probability theory, analytic geometry and the early development of infinitesimal calculus. He ventured into the areas of mathematics which included pre-evolved calculus and trigonometry. Fermat contributed to the development of calculus through his work on the properties of curves.

Fermat, along with Pascal, is known as the founder of Theory of Probabilities. His views on fundamental principles of the subject became the foundation of the probability theory. Fermat had a strong interest in maximum-minimum problems, which he applied in the field of optics. In some of these letters to his friends, he explored many of the fundamental ideas of calculus before Newton or Leibniz.

Fermat was a trained lawyer making mathematics more of a hobby than a profession. Nevertheless, he made important contributions to analytical geometryprobability, number theory and calculus. This naturally led to priority disputes with contemporaries such as Descartes and Wallis. Anders Hald writes that, "The basis of Fermat's mathematics was the classical Greek treatises combined with Vieta's new algebraic methods.

In Methodus ad disquirendam maximam et minimam et de tangentibus linearum curvarumFermat developed a method adequality for determining maxima, minima, and tangents to various curves that was equivalent to differential calculus. Fermat was the first person known to have evaluated the integral of general power functions. With his method, he was able to reduce this evaluation to the sum of geometric series.

In number theory, Fermat studied Pell's equationperfect numbersamicable numbers and what would later become Fermat numbers. It was while researching perfect numbers that he discovered Fermat's little theorem. Fermat developed the two-square theoremand the polygonal number theoremwhich states that each number is a sum of three triangular numbersfour square numbersfive pentagonal numbersand so on.

Autobiography of pierre de fermat: In one of the first

Although Fermat claimed to have proven all his arithmetic theorems, few records of his proofs have survived. Many mathematicians, including Gaussdoubted several of his claims, especially given the difficulty of some of the problems and the limited mathematical methods available to Fermat. His Last Theorem was first discovered by his son in the margin in his father's copy of an edition of Diophantusand included the statement that the margin was too small to include the proof.

It seems that he had not written to Marin Mersenne about it.

Autobiography of pierre de fermat: He was of Basque origin

It was first proven inby Sir Andrew Wilesusing techniques unavailable to Fermat. Through their correspondence inFermat and Blaise Pascal helped lay the foundation for the theory of probability. From this brief but productive collaboration on the problem of pointsthey are now regarded as joint founders of probability theory. In it, he was asked by a professional gambler why if he bet on rolling at least one six in four throws of a die he won in the long term, whereas betting on throwing at least one double-six in 24 throws of two dice resulted in his autobiography of pierre de fermat.

Fermat showed mathematically why this was the case. The first variational principle in physics was articulated by Euclid in his Catoptrica. It says that, for the path of light reflecting from a mirror, the angle of incidence equals the angle of reflection. Hero of Alexandria later showed that this path gave the shortest length and the least time.

The terms Fermat's principle and Fermat functional were named in recognition of this role. Pierre de Fermat died on January 12,at Castresin the present-day department of Tarn. According to Peter L. Bernsteinin his book Against the GodsFermat "was a mathematician of rare power. The dispute was chiefly due to the obscurity of Descartes, but the tact and courtesy of Fermat brought it to a friendly conclusion.

Fermat was a good scholar, and amused himself by conjecturally restoring the work of Apollonius on plane loci. Except a few isolated papers, Fermat published nothing in his lifetime, and gave no systematic exposition of his methods. Some of the most striking of his results were found after his death on loose sheets of paper or written in the margins of works which he had read and annotated, and are unaccompanied by any proof.

It is thus somewhat difficult to estimate the dates and originality of his work. He was constitutionally modest and retiring, and does not seem to have intended his papers to be published. It is probable that he revised his notes as occasion required, and that his published works represent the final form of his researches, and therefore cannot be dated much earlier than I shall consider separately i his investigations in the theory of numbers; ii his use in geometry of analysis and of infinitesimals; and iii his method for treating questions of probability.

He prepared an edition of Diophantus, and the notes and comments thereon contain numerous theorems of considerable elegance. Most of the proofs of Fermat are lost, and it is possible that some of them were not rigorous - an induction by analogy and the intuition of genius sufficing to lead him to correct results. The following examples will illustrate these investigations.

A proof of this, first given by Euler, is well known. A more general theorem is that mod nwhere a is prime to n and is the number of integers less than n and prime to it. Fermat's proof is as follows. Lagrange gave a solution of this. This question was issued as a challenge to the English mathematicians Wallis and Digby. This proposition has acquired extraordinary celebrity from the fact that no general demonstration of it has been given, but there is no reason to doubt that it is true.