Math was his hobby when he returned home from a long day at work. He was also a lawyer in terms of profession at the parliament of toulouse. While fermat made very important contributions to the development of the di. Interestingly, these are all prime numbers and are known as fermat primes, but all the higher fermat numbers which have been painstakingly identified over the years are not prime numbers. One of his greatest problems, aptly named his last theorem, stood unsolved until a proof was. By 1631, fermat was a lawyer and a government o cial in toulouse, as well as given the title of commissioner of requests. If p is prime and a is an integer, then apa is a multiple of p fermat s principle.
If p is a prime number and a is any other natural number not divisible by p, then the number is divisible by p. A letter to mersenne, dated christmas day 1640, suggests that he found a proof that such a number could be prime only if a is even and n is a power of 2 exercise 4. He made great contributions to analytic geometry, probability theory and optics. He is best known for fermat s last theorem, which he described in a note at the margin of a copy of diophantus arithmetica. There are deep and subtle connections between number theory and other branches of mathematics. In number theory, fermat studied pells equation, perfect numbers, amicable numbers and what would later become fermat numbers. He did path breaking research in into number theory and discovered several new patterns in numbers which had. Also he played a pivotal role in the development of analytic geometry, optics and probability. He made notable contributions to analytic geometry, probability, and optics. Fermat along with blaise pascal is also considered to be one of the founders of probability theory. The path taken by light is the path taking the least time. As a corollary, we obtain another proof of the infinitude of the prime numbers. Fermat made contributions in many areas of mathematics, such as probability theory, analytic geometry, optics, and infinitesimal calculus. Stating that it is impossible to split a cube into two cubes, or a fourth power into two fourth powers, or any higher power into two like powers, but not leaving behind the.
Fermat made important contributions to probability and number theory, and anticipated some results of differential calculus. Mathematician shinichi mochizuki of kyoto universitys research. But, if the game is interrupted at the point where fermat, say, is winning 8 points to 7, how is the 100 franc pot to divided. Pierre had a brother and two sisters and was almost certainly brought up in the town of. Andrew wiles fermat last theorem pdf to excel barneys. His monumental work is considered to be fermat s last theorem and fermat s principle for light propagation.
He did path breaking research in into number theory and discovered several new patterns in numbers which had puzzled mathematicians for centuries. He was the inventor of modern number theory, and this was where a lot of his work was concentrated. In particular, he is recognized for his discovery of an original method of finding the greatest and the. The first of the two players say, fermat and pascal to achieve ten points or wins is to receive a pot of 100 francs. In number theory, fermat studied pells equation, perfect numbers, amicable. Applications of number theory to fermats last theorem. This lesson will explore some of these contributions and accomplishments.
His work was such that he is sometimes regarded as the father of, both, differential calculus and number theory. He ventured into the areas of mathematics which included preevolved calculus and trigonometry. Famous mathematicians the greatest mathematicians of all. Fermats last theorem earns andrew wiles the abel prize. This result is commonly known as fermat s last theorem. He also developed the twosquare theorem, and the polygonal number theorem. But much more important for the future of mathematics is the substantial progress wiles made toward the shimurataniyama conjecture. His contribution to the study of the operator theory is equally important. Although he published little, fermat posed the questions and identified the issues that have shaped number theory ever since. Fermat and his method of infinite descent mathematics. It is important to note that during the late 16th century, considerable improvement occurred in the matter of algebraic notation, the lack of which hindered elementary manipulation of formulae.
It uses a number of basic number theory concepts to prove three cases of fermat s last theorem. Many people see him as the father of modern calculus his method of finding the biggest and smallest ordinates of curved lines also makes him a contributor to differential calculus, which was not known at that time his studies in the theory. He is ascribed with contributing to the areas of analytic geometry, probability, number theory, and optics. From viete, fermat inherited the idea of symbolic algebra as a formal. Stimulated and inspired by the arithmetica of the hellenistic mathematician diophantus, he went on to discover several new patterns in numbers which had defeated mathematicians for centuries. In many areas of mathematics, fermat was a player, although he was unusual in two ways. His day job was royal councillor at the parliament of toulouse. Around 1637 fermat was reading the book arithmetica by the greek mathematician diophantus the father of algebra diophantus was. French 17th century mathematician with important contributions to number theory and optics. The shimurataniyama conjecture is part of a more general philosophy. In particular, he is recognised for his discovery of an original method of finding. However, some people state fermats little theorem as, if p is a prime number and a is any other natural number, then the number is divisible by p. Fermat received his degree in civil law at the university of orleans before 1631 and served as a lawyer and then a councillor at toulouse. The problem of points at its simplest can be illustrated by a simple game of winner take all involving the tossing of a coin.
He invented fermat s factorization method as well as the proof technique of infinite descent. He was a french mathematician who is given credit for early developments that led to infinitesimal calculus. In 1648, fermat was promoted to a kings councilorship in the parliament of toulouse. There is some dispute about the date of pierre s birth as given above, since it is possible that he had an elder brother who had also been given the name pierre but who died young.
125 334 1117 532 69 1125 26 1493 385 178 756 129 808 1132 846 1323 522 507 1253 1661 1472 733 744 864 1628 856 199 463 200 1007 1375 1051 1395 396 57