Fermat's theorem and its role in the development of mathematics

Fermat's theorem, its mystery and the endless search for solutions occupy a unique position in mathematics in many respects. Despite the fact that a simple and elegant solution was not found, this task served as an impetus for a number of discoveries in the field of set theory and prime numbers. The search for an answer turned into an exciting process of competition between the leading mathematical schools of the world, and also revealed a huge number of self-taught students with original approaches to some or other mathematical problems.

Pierre Fermat himself was a vivid example of just such self-taught. He left behind him a whole series of interesting hypotheses and proofs, not only in mathematics, but also, for example, in physics. However, he became known largely due to a small entry on the fields of the then popular "Arithmetic" of the ancient Greek explorer Diophantus. This record said that after much thought he found a simple and "truly miraculous" proof of his theorem. This theorem, which went down in history as "Fermat's big theorem," asserted that the expression x ^ n + y ^ n = z ^ n can not be solved if the value of n is greater than two.

Pierre Fermat himself , in spite of the explanation left in the margin, did not leave a general solution after himself, but many who took up the proof of this theorem were rendered powerless by it. Many tried to build on the evidence of Fermat's own proof of this postulate for a particular case, when n is 4, but for other variants it proved to be unsuitable.

Leonard Euler at great effort was able to prove Fermat's theorem for n = 3, after which he was forced to abandon the search, finding them unpromising. Over time, when new methods for finding infinite sets were introduced into the scientific revolution, this theorem found its evidence for the range of numbers from 3 to 200, but it was still not possible to solve it in general form.

Fermat's theorem was given a new impetus at the beginning of the twentieth century, when a prize of one hundred thousand marks was announced to the one who would find its solution. The search for a solution for a while turned into a real competition, in which not only venerable scientists, but also ordinary citizens participated: the Fermat theorem, the formulation of which did not presuppose any double interpretation, gradually became no less famous than Pythagoras' theorem, from which, incidentally , She once came out.

With the advent of first arithmometers and then powerful electronic computers, it was possible to find the proofs of this theorem for an infinitely large value of n, but in general terms the proof was still not possible. However, no one could refute this theorem either. Over time, interest in finding the answer to this riddle began to subside. In many respects this was due to the fact that further evidence was already coming at a theoretical level that the ordinary citizen can not do.

A peculiar ending of the most interesting scientific attraction, called "Fermat's theorem", was the research of E. Wiles, who are currently accepted as the final proof of this hypothesis. If there were doubts about the correctness of the proof itself, then with the correctness of the theorem itself all agree.

Despite the fact that Fermat's theorem never received any "elegant" proof, her search made a significant contribution to many areas of mathematics, greatly enlarging the cognitive horizons of mankind.