Pierre de fermat contributions to number theory book

However it was during this time that fermat worked on number theory. In particular, he is recognised for his discovery of an original method of finding. With some help from euler and weil, mahony shows very convincingly and fits together how theorems and proofs on number theory emerged over time for the man who was. His most famous statement was attached to this theorem, which states. 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. Fermat also made contributions in the field of optics and provided a law on light travel fermat s most important work was done in the development of modern number theory which was one of his favorite areas in math. 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. Made significant contributions to mathematics in his mathematical notation, complex analysis, and number theory. The first of the two players say, fermat and pascal to achieve ten points or wins is to receive a pot of 100 francs. Fortunately, fermat himself comes to our assistance here, since he did give one fairly detailed number theory proof in his lifetime, and it used a method that he regarded as his greatest contribution to the subject. Pierre had a brother and two sisters and was almost certainly brought up in the town of. His contribution to the study of the operator theory is equally important. In particular, he is recognized for his discovery of an original method of finding the greatest and the smallest ordinates of curved lines, which is analogous to that of differential calculus, then unknown, and his research into number theory. He made notable contributions to analytic geometry, probability, and optics.

Fermat made important contributions to probability and number theory, and anticipated some results of differential calculus. The problem of points at its simplest can be illustrated by a simple game of winner take all involving the tossing of a coin. Little is known of his life but his works have had a very great influence on the development of mathematics, in particular his famous book conics introduced terms which are familiar to us today such as parabola, ellipse, and hyperbola. He was the inventor of modern number theory, and this was where a lot of his work was concentrated. He had a copy of arithmetica a book by the great greek mathematician diophantus. He is best known for his fermat s principle for light propagation and his fermat s last theorem in number theory, which he described in a note at the margin of a copy of diophantus arithmetica. He was also a lawyer in terms of profession at the parliament of toulouse. We have seen his contributions to calculus, the law of refraction, and most importantly to number theory. Made contributions to algebra in compendious book on calculation by completing and balancing equation.

Fermat along with blaise pascal is also considered to be one of the founders of probability theory. Famous mathematicians the greatest mathematicians of all. 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. Together with rene descartes, fermat was one of the two leading mathematicians of the first half of the 17th century. Fermat made contributions in many areas of mathematics, such as probability theory, analytic geometry, optics, and infinitesimal calculus. Also, when newton was asked where he got the idea of calculus from, he credited monsieur fermat s method of drawing tangents. This lesson will explore some of these contributions and accomplishments. Fermat and the greatest problem in the history of mathematics. Contributed to math in discoveries in probability theory, optics, and number theory. Despite these impressive accomplishments, however, it is as a mathematician that he is best remembered.

Math was his hobby when he returned home from a long day at work. Apollonius of perga was known as the great geometer. For fermat s contributions on number theory however, only a few historical documents are available as fermat was very secretive about his findings and reluctant to publish anything. Around 1637 fermat was reading the book arithmetica by the greek mathematician diophantus the father of algebra diophantus was. First edition, a fine copy, of fermat s annotated edition of diophantus arithmetica. 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. This is the first printing of fermat s contributions to the theory of numbers, of which he is the undisputed founder, including his famous statement of fermat s last theorem.

With some help from euler and weil, mahony shows very convincingly and fits together how. Fermat died on january 1 2, 1665 in castres, france. One of his greatest problems, aptly named his last theorem, stood unsolved until a proof was. The path taken by light is the path taking the least time. He did path breaking research in into number theory and discovered several new patterns in numbers which had. 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. While still young, he, along with blaise pascal, made some discoveries in regard.

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 is best remembered for this work in number theory, in particular for fermats last theorem. He was a competent classical scholar and philologist, was fluent in five languages, and composed poetry. If p is prime and a is an integer, then apa is a multiple of p fermat s principle. Although he published little, fermat posed the questions and identified the issues that have shaped number theory ever since. He was also fluent in french, italian, spanish, latin, and greek. An approach through history from hammurapi to legendre. Since most of fermat s work in number theory remained unpublished in his lifetime. For this account, the author intertwines the biographical information available about fermat including his parliamentary, judiciary and legal duties with his mathematical work.

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 number theory, fermat studied pells equation, perfect numbers, amicable numbers and what would later become fermat. Although euclid handed down a precedent for number theory in books viiix of the. This book inspired a great number of new ideas from fermat. Etienne despagnet, who had inherited a library of important books including some. Arithmetica was published for the first time in very approximately the year 250 ad. In his day, apollonius was a popular name, so you shouldnt confuse the apollonius of perga. Alongside blaise pascal, he established the foundations of probability theory, which is the mathematics of gambling, risk and change.