Pierre de fermat contributions to number theory book

Around 1637 fermat was reading the book arithmetica by the greek mathematician diophantus the father of algebra diophantus was. 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. Alongside blaise pascal, he established the foundations of probability theory, which is the mathematics of gambling, risk and change. Fermat died on january 1 2, 1665 in castres, france. Math was his hobby when he returned home from a long day at work. Etienne despagnet, who had inherited a library of important books including some. 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. 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. He made notable contributions to analytic geometry, probability, and optics. Made contributions to algebra in compendious book on calculation by completing and balancing equation. 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.

He was also fluent in french, italian, spanish, latin, and greek. 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. He was the inventor of modern number theory, and this was where a lot of his work was concentrated. Contributed to math in discoveries in probability theory, optics, and number theory. While still young, he, along with blaise pascal, made some discoveries in regard. French 17th century mathematician with important contributions to number theory and optics. 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. 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. His most famous statement was attached to this theorem, which states. Also, when newton was asked where he got the idea of calculus from, he credited monsieur fermat s method of drawing tangents. With some help from euler and weil, mahony shows very convincingly and fits together how. Fermat made important contributions to probability and number theory, and anticipated some results of differential calculus. An approach through history from hammurapi to legendre.

In number theory, fermat studied pells equation, perfect numbers, amicable numbers and what would later become fermat. In his day, apollonius was a popular name, so you shouldnt confuse the apollonius of perga. Although euclid handed down a precedent for number theory in books viiix of the. 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. If p is a prime number and a is any other natural number not divisible by p, then the number is divisible by p. 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. If p is prime and a is an integer, then apa is a multiple of p fermat s principle. Fermat is best remembered for this work in number theory, in particular for fermats last theorem. Together with rene descartes, fermat was one of the two leading mathematicians of the first half of the 17th century. The first of the two players say, fermat and pascal to achieve ten points or wins is to receive a pot of 100 francs. For this account, the author intertwines the biographical information available about fermat including his parliamentary, judiciary and legal duties with his mathematical work. However it was during this time that fermat worked on number theory. He did path breaking research in into number theory and discovered several new patterns in numbers which had.

Although he published little, fermat posed the questions and identified the issues that have shaped number theory ever since. Fermat made contributions in many areas of mathematics, such as probability theory, analytic geometry, optics, and infinitesimal calculus. His contribution to the study of the operator theory is equally important. 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. 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. Famous mathematicians the greatest mathematicians of all. He was also a lawyer in terms of profession at the parliament of toulouse. Fermat along with blaise pascal is also considered to be one of the founders of probability theory. 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. This book inspired a great number of new ideas from fermat. Arithmetica was published for the first time in very approximately the year 250 ad. 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. Apollonius of perga was known as the great geometer.

First edition, a fine copy, of fermat s annotated edition of diophantus arithmetica. The path taken by light is the path taking the least time. Fermat and the greatest problem in the history of mathematics. Made significant contributions to mathematics in his mathematical notation, complex analysis, and number theory. 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 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. Despite these impressive accomplishments, however, it is as a mathematician that he is best remembered. Pierre had a brother and two sisters and was almost certainly brought up in the town of. One of his greatest problems, aptly named his last theorem, stood unsolved until a proof was. In particular, he is recognised for his discovery of an original method of finding. 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 solved many fundamental calculus problems, and made important contributions to number theory and optics. 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. He had a copy of arithmetica a book by the great greek mathematician diophantus. Since most of fermat s work in number theory remained unpublished in his lifetime. He is ascribed with contributing to the areas of analytic geometry, probability, number theory, and optics. This lesson will explore some of these contributions and accomplishments. He was a competent classical scholar and philologist, was fluent in five languages, and composed poetry.