Free Research Paper About Pierre De Fermat

Abstract

Pierre de Fermat is a French mathematician, one of the founders of analytic geometry, calculus, probability theory and number theory. His most famous contribution in mathematics is Fermat's Great Theorem. In this paper a biography we will discuss his life history, mathematical discoveries and the benefits of these discoveries to humankind.

Body

Biography
Pierre de Fermat was born August 17, 1601 in the Gascon town of Beaumont-de-Lomagne (Beaumont-de-Lomagne, France). His father, Dominic Fermat, was a prosperous merchant, the second city consul; mother, Claire de Long - teacher of mathematics. In the family, in addition to Pierre, were another son and two daughters. The Fermat has a law degree - first in Toulouse and then in Bordeaux and Orleans. In 1631 he successfully completing training, Fermat bought the position of the royal counselor of the parliament (in other words, a member of the High Court) in Toulouse. In the same year he married a distant relative of his mother, Louise de Long. They had five children. Quick service growth has become a member of the House Fermat edicts in Castro (1648). It is this capacity, he is obliged to adding to his name tag of nobility - the particle “de”; since that time, he became Pierre de Fermat.
Around 1652 Fermat had to deny a message about his death during the plague; he really was infected but survived. In 1660 he had a meeting planned with Pascal, but because of the poor health of both scientists meeting never took place. Pierre de Fermat died January 12, 1665 in the town of Castres, while Eyre. Initially, he was buried there, in Castres, but soon (1675) transferred the remains to the family tomb Fermat, in the church of the Augustinian (Toulouse). The eldest son, Clement, Samuel, published posthumous collection of his works, from which contemporaries and learn about the wonderful discoveries of Pierre de Fermat. Contemporaries describe Fermat as an honest, accurate, balanced and affable man, brilliantly erudite in mathematics, and in the humanities, a connoisseur of many ancient and living languages ​​in which he wrote good poetry.

Scientific Activity

Work adviser in the parliament of the city of Toulouse did not interfere Fermat to study mathematics. Gradually, he gained fame as one of the first mathematicians of France, though not writing books (scientific journals has not yet been), limited only letters to colleagues. Among his correspondents were Descartes, Pascal B., G. Desargues, Roberval J. and others. The findings of Fermat came to us because of his extensive collection of correspondence (mainly through Mersenne), published posthumously by Fermat’s son.
Unlike Galileo, Descartes and Newton, Fermat was a pure mathematician - the first great mathematician of the new Europe. Regardless of Descartes, he created analytic geometry. Previously, Newton was able to use differential methods for tangent, finding maxima and calculate areas. However, Fermat, unlike Newton, not brought these methods into the system, but Newton later admitted that it was the work of Fermat led him to the creation of analysis. However, the main merit of Pierre de Fermat is the creation of the theory of numbers.
Mathematics of ancient Greece since Pythagoras collected and proven a variety of statements relating to the natural numbers (for example, methods of construction of all Pythagorean triples, a method for constructing perfect numbers, and so on. N.). Diophantus of Alexandria (III century BC. E.) In his "Arithmetic" considered the many challenges of the solution in rational numbers of algebraic equations with several unknowns (now called Diophantine equations to be solved in integers). This book (not completely) became known in Europe in the XVI century, and in 1621 it was published in France and became a handbook of Fermat.
The Fermat was always interested in arithmetic problems, share challenges with his contemporaries. For example, in his letter, called "Second call mathematicians" (February 1657), he offered to find a general rule solving Pell's equation in integers. In the letter, he offered to find solutions for a = 149, 109, 433. The complete solution of Fermat's problem was found only in 1759 by Euler.
Fermat began with problems about magic squares and cubes, but gradually switched to the laws of natural numbers - arithmetic theorem. No doubt the influence of Diophantus on the Fermat, and it is symbolic that he writes his amazing discoveries in the fields of "Arithmetic".
Fermat discovered that if a is not divisible by a prime p, the number is always divisible by p. Later, Euler gave a proof and a generalization of this important result.
Found that the number is simple when k ≤ 4, Fermat decided that these numbers are simple for all k, but Euler later showed that for k = 5 has a divider 641. It is still unknown, of course or infinitely many Fermat’s primes.
Euler proved (1749) another hypothesis of Fermat (Fermat is rarely causes proof of his allegations) primes of the form 4k + 1 are represented as the sum of squares (5 = 4 + 1, 13 = 9 + 4), where the only way, and for numbers, containing in its prime factorization prime numbers of the form 4k + 3 odd degree, such a representation is not possible. Euler is proof of worth 7 years of work; Fermat himself proved this theorem indirectly, he invented the inductive "method of infinite descent." This method was published only in 1879; However, Euler method are restored to a few remarks in letters Fermat and successfully apply it repeatedly. Later, an improved version of the method was used by Poincare and André Weil.
The Fermat has developed a systematic way of finding all divisors of, formulated a theorem on the representation of an arbitrary number as a sum of not more than four squares (Lagrange's four-square theorem). The most famous of his statement - "Fermat's Last Theorem”.
Many arithmetic open Fermat ahead of time and were forgotten for 70 years until they are not interested in Euler published systematic theory of numbers. One reason for this - the interests of the majority of mathematicians switched to mathematical analysis.
Fermat practically modern rules found tangent to algebraic curves. These works prompted Newton to the creation of analysis. In textbooks on mathematical analysis can be found important Fermat's theorem, or a necessary attribute of an extremum at the points of extremum derivative is zero. Fermat formulated the general law of differentiation of fractional powers and extended formula of integration degree the case of fractional and negative indicators.
Along with Descartes, Fermat considered the founder of analytical geometry. In his "Introduction to the theory of planar and spatial locations", which became known in 1636, he spent the first classification of curves depending on the order of the equation, found that the first-order equation defines direct and second-order equation - conic section. Developing these ideas, Fermat went on Descartes' analytic geometry and applied to the space.
Regardless of Pascal's Fermat developed the foundations of probability theory. That correspondence with Fermat and Pascal (1654), in which they, in particular, came to the notion of expectation and theorems of addition and multiplication of probabilities, counts its history this wonderful science. The results of Fermat and Pascal were given in the book of Huygens' On calculations in gambling "(1657), the first manual on probability theory.
Fermat name has basic principle of geometrical optics, whereby the light in an inhomogeneous medium chooses the path that takes the least time (however, Fermat believed that the speed of light is infinite, and formulated the principle of a more vague). With this thesis begins the story of the basic law of physics - the principle of least action. Fermat moved to the three-dimensional case (internal contact areas) algorithm for the problem of Apollonius Vieta (tangency).
Pierre de Fermat is well known for the so-called great (or last) Fermat's Last Theorem. The theorem was formulated by him in 1637, on the margins of the book "Arithmetic" with a note that they found an ingenious proof of this theorem is too long to bring it in the fields.

The statement of the theorem is quite simple:

For any natural number n>2 the following equation:
an+bn=cn
does not have natural solutions a, b and c.
Most likely, his testimony was not true, as he later published a proof only for the case of n = 4. Proof of that was found in 1994 by Andrew Wiles, contains 129 pages and is published in the journal “Annals of Mathematics” in 1995. The simplicity of the formulation of this theorem has attracted many mathematicians amateur so-called “Fermatists”. Even after all the solutions Wiles Academy of Sciences are letters with "proof" Fermat's last theorem.

Conclusion

Despite the fact that he left behind a farm only fragmentary records and handwritten versions of works, most brilliant research scientist still fall into the hands of his descendants. Farm contribution to mathematical science cannot be overestimated. He was not only the author of his own discoveries, but also the inspiration for subsequent generations of mathematicians. In honor of the great scientist named one of the most prestigious and oldest high schools in France - Lycée Pierre de Fermat in Toulouse.

References

Weil, André (1984). Number Theory: An approach through history From Hammurapi to Legendre. Birkhäuser. ISBN 0-8176-3141-0.
Eves, Howard. An Introduction to the History of Mathematics, Saunders College Publishing, Fort Worth, Texas, 1990.
"Pierre de Fermat". The Mactutor History of Mathematics. Retrieved 29 May 2013.