Fermat was unable to notice what is now considered the Fundamental Theorem of Calculus, however, his work on this subject aided in the development of differential calculus Parker, page His main contribution was finding the tangents of a curve as well as its points of extrema.

Inspired by an edition in of the Arithmetic of Diophantusthe Greek mathematician of the 3rd century ad, Fermat had discovered new results in the so-called higher arithmetic, many of which concerned properties of prime numbers those positive integers that have no factors other than 1 and themselves.

Around this time, one of Descartes students was collecting his correspondence for publication and he turned to Fermat for help with the Fermat - Descartes correspondence.

These combinations are 16 in number, namely, aaaa, aaab, aaba, aabb; abaa, abab, abba, The life and work of pierre de fermat baaa, baab, baba, babb; bbaa, bbab, bbba, bbbb. A proof of this, first given by Euler, is well known. In Fermat had started a correspondence with Huygens.

But his influence was circumscribed by his reluctance to publish. He would then state that it could easily be converted to a synthesis. Voila sommairement le conte de mes recherches sur le sujet des nombres.

Through his work on the properties of curves, Fermat contributed to the development of calculus. He believed that his tangent-finding method was an extension of his method for locating extrema Rosenthal, page He applied his method of minima and maxima and made the assumption that light travels less rapidly in the medium.

Unsuccessful attempts to prove the theorem over a year period led to the discovery of commutative ring theory and a wealth of other mathematical discoveries. Principle of Light Transmission Fermat had a strong interest in maximum-minimum problems, which he applied in the field of optics.

He prepared an edition of Diophantus, and the notes and comments thereon contain numerous theorems of considerable elegance. The period from to was one when Fermat was out of touch with his scientific colleagues in Paris.

The theorems last mentioned were published only after his death; and probably they were not written till after he had read the works of Cavalieri and Wallis.

A brief note explained that he had discovered a remarkable proof of the complex theorem that was too long to fit in the margin, but the proof was never found. He introduced the famous laws of refraction and reflection. He was fluent in Latin, Greek, Italian and Spanish, and was praised for his written verse in several languages, and eagerly sought for advice on the emendation of Greek texts.

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. InFermat formally entered the legal profession, serving in the local Parliament at Toulouse.

This theorem remained unsolved until the late 20th century.

However Fermat had now deduced it from a fundamental property that he proposed, namely that light always follows the shortest possible path. He also contributed to the development of calculus through his work on the properties of curves.

The assumption has been made by some writers; it is true of real numbers, but it is not necessarily true of every complex number. He communicated with all the great mathematicians in Europe, posing and solving problems, disseminating ideas of various math subjects and inventing new mathematics such as probability theory.

When he married, his wife brought a dowry of 12, livres. Inhe and Pascal had exchanged letters on problems in probability concerning games of chance. Fermat also differed from Descartes in his views on optics. This value of x makes the given expression a maximum.

It is ironic that Fermat did not see what we now call the Fundamental Theorem of Calculus. Work on theory of numbers Fermat vainly sought to persuade Pascal to join him in research in number theory.

Pierre de Fermat contributed to the development of various theories in mathematics, including number theory, theory of probability, little theorem and laws of refraction, and many more.

What Fermat failed to explain in this letter is how the smaller number is constructed from the larger number. Everyone failed to see that Fermat had been hoping his specific problems would lead them to discover, as he had done, deeper theoretical results.

What Fermat failed to explain in this letter is how the smaller number is constructed from the larger. Meanwhile, Descartes had observed the same basic principle of analytic geometry, that equations in two variable quantities define plane curves.

He gave a dowry of 12, livres, which was not a problem for the young lawyer. In mathematical terms, this is written:PIERRE DE FERMAT Yogita Chellani Term Paper, History of Mathematics, Rutgers.

The French mathematician Pierre de Fermat() was possibly the most productive mathematician of his era, making many contributions, some of which were to calculus, number theory, and the law of refraction.

Pierre de Fermat, (born August 17,Beaumont-de-Lomagne, France—died January 12,Castres), French mathematician who is often called the founder of the modern theory of numbers. Together with René Descartes, Fermat was one of the two. The Mathematical Career of Pierre de Fermat, 2nd Edition.

In one of the first full-length investigations of Fermat's life and work, Michael Sean Mahoney provides rare insight into the mathematical genius of a hobbyist who never sought to publish his work, yet who ranked with his contemporaries Pascal and Descartes in shaping the /5(3).

Pierre de Fermat ( - ) From `A Short Account of the History of Mathematics' (4th edition, ) by W. W. Rouse Ball. While Descartes was laying the foundations of analytical geometry, the same subject was occupying the attention of another and not less distinguished Frenchman.

Pierre de Fermat was born on August 17, in Beaumont-de-Lomagne, France, and died on January 12, in Castres. He was the son of a prosperous leather merchant, and became a lawyer and magistrate (Singh, page 35).

The Background of Pierre de Fermat. Fermat was baptized on August 20, (this is accepted as his date of birth in both mathematical and historical communities) in the town of Beaumont-de-Lomagne, France, near Montauban.

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