Fermat's Theorem, its riddle and endless search for a solution occupy a unique position in mathematics in many ways. Despite the fact that a simple and elegant solution was never found, this problem served as an impetus for a number of discoveries in the theory of sets and prime numbers. The search for an answer turned into an exciting process of competition between the world's leading mathematical schools, and also revealed a huge number of self-taught people with original approaches to certain mathematical problems.
Pierre Fermat himself was a prime example of just such a self-taught person. He left behind a number of interesting hypotheses and proofs, not only in mathematics, but also, for example, in physics. However, he became famous largely due to a small entry in the margins of the then popular "Arithmetic" of the ancient Greek researcher Diophantus. This entry stated that, after much thought, he had found a simple and "truly miraculous" proof of his theorem. This theorem, which went down in history as "Fermat's Last Theorem", stated that the expression x^n + y^n=z^n cannot be solved if the value of n is greater thantwo.
Pierre Fermat himself, despite the explanation left in the margins, did not leave any general solution after himself, while many who undertook to prove this theorem turned out to be powerless before it. Many tried to build on the proof of this postulate found by Fermat himself for the special case when n is equal to 4, but for other options it turned out to be unsuitable.
Leonhard Euler, at the cost of great efforts, managed to prove Fermat's theorem for n=3, after which he was forced to abandon the search, considering it unpromising. Over time, when new methods for finding infinite sets were introduced into scientific circulation, this theorem gained its proofs for the range of numbers from 3 to 200, but it was still not possible to solve it in general terms.
Fermat's theorem received a new impetus at the beginning of the 20th 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 some time turned into a real competition, in which not only venerable scientists participated, but also ordinary citizens: Fermat's theorem, the formulation of which did not imply any double interpretation, gradually became no less famous than the Pythagorean theorem, from which, by the way,, she once came out.
With the advent of first adding machines, and then powerful electronic computers, it was possible to find proofs of this theorem for an infinitely large value of n, but in general it was still not possible to find a proof. However, andno one could disprove this theorem either. Over time, interest in finding the answer to this riddle began to subside. This was largely due to the fact that further evidence was already at a theoretical level that was beyond the power of the average man in the street.
A peculiar end to the most interesting scientific attraction called "Fermat's theorem" was the research of E. Wiles, which today is accepted as the final proof of this hypothesis. If there are still those who doubt the correctness of the proof itself, then everyone agrees with the correctness of the theorem itself.
Despite the fact that no "elegant" proof of Fermat's theorem has been received, its searches have made a significant contribution to many areas of mathematics, significantly expanding the cognitive horizons of mankind.
