The restored remarks follow in chronological order and may diverge in time over years. The margins' records of the book were made after they were prepared separately, but it was not intended that they be published in the same view. On the contrary, in the final formulation of the FLT everything that could be concealed from the history and components of this brilliant scientific discovery, was completely removed. Only the final result has been remained, which turned out to be beyond the powers of all subsequent science right up to the beginning of the XXI century!
If this reconstruction of the original FLT recording on the margins of the book appeared 30 years earlier, it would have caused a quite stir in the scientific world since the sixth entry develops (!!!) this theorem to the general case with the different of power's indexes! However, this stir did nevertheless take place 25 years ago, and again it was caused not by a professional, but by an amateur interested in FLT with his conjecture corresponding to the restored sixth entry. Of course, to believe in all this is not easily, but also to invent such a thing is also hardly possible. Now we have to explain in more detail these restored entries in the margins and this will be done in the next points of our work and the same senator who started this whole story, will help us in this.
2. The History of Delusions
An unprecedented succession of failures, wrecks of secret hopes and defeats in the protracted for centuries storming of an impregnable fortress under name the Fermat's Last Theorem, turned into a such nightmare for science that even its very existence have been questioned. Like the fierce plague epidemic, the FLT not only deprived the minds of numerous amateur fermatists, scientists and unrecognized geniuses, but also very much contributed to the fact that the whole science was plunged into the abyss of uncontrollable chaos.
Pic. 12. Andrew Wiles
Already three and a half centuries have passed since the first publication of the FLT and twenty-five years after it was announced that in 1995 this problem was allegedly solved by Professor Princeton University USA Andrew Wiles.6 However, once again it turned out this “epochal” event has nothing to do with the FLT!7 “The proof” of Wiles rests solely on the idea proposed by the German mathematician Gerhard Frey. This idea was rated as brilliant, but apparently only because that it was an elementary and even very common error!!!
Pic. 13. Gerhard Frey
Instead of proving the impossibility of the Fermat equation an+bn=cn in integers for n>2 here is proven only its incompatibility in the system with the equation y2=x(x−an)(x+bn). In a similar way any nonsense can be proven. If the same work would be presented by one of the students, any of the professors would quickly bring him to clean water pointing to the obvious substitution of the subject of proof. Nevertheless, this super sensational news with great fanfare was noted in the world's leading media. The most influential newspaper of the USA “The New York Times” has been reported this right on the front page … in whole 2 years before the appearance of the “proof” itself!!! Andrew Wiles as the author of the "proof" became a member of the French Academy of Sciences and the laureate of as many as 18 of the most prestigious awards!!! To cover this momentous event, the British broadcaster BBC released an enthusiastic film and also it was invited the writer Simon Singh who published a book in 1997 titled “The Fermat's Last Theorem. The story of a riddle that confounded the world's greatest minds for 358 years”.
Pic. 15. Simon Singh
Pic. 14. “The New York Times” of 06/24/1993 with an Article About Solving the FLT Problem
If Singh independently was preparing this book, then he would have so many questions that he would not have them managed for 20 years. Of course, he was helped in every way by the very heroes-professors having glorified in the BBC film, therefore the book became a success and it is really interesting to read it even to those who know about mathematics only by hearsay. The first thing that immediately catches your eye, is the fact that in the book it was made an arithmetic error (!) and not somewhere, but in its very name! Indeed, it is well known that “the greatest minds” could not know anything about the FLT before 1670 when its wording first appeared in a book published by Fermat’s son Clément Samuel “Arithmetic” by Diophantus with comments by K. Bachet and P. Fermat (see Appendix VI Pic. 96).8 But then it should be not 358 but 325 years and it turns out that Singh simply did not notice the error?
However, don't rush to conclusions! This is not the book's author error and not at all accidental. These same professors vividly told Singh that supposedly back in 1637 9 Fermat himself had noticed an error in his proof, but simply forgot to strike out recording of this theorem in the margins of the book. Who had invented this tale is unknown, but many scientists perceived it as a known fact and repeated time after time in their works. One can understand them because otherwise we could believe that Fermat turned out to be smarter than all of them! When Andrew Wiles said (https://www.pbs.org/wgbh/nova/article/andrew-wiles-fermat/):
“I don't believe Fermat had a proof” – this opinion was not new at all because many reputable scientists have repeated this many time. However, this is clearly against logic. It turns out that Fermat somehow managed to formulate an absolutely not obvious theorem without any reason whatsoever.10
Another contradiction in Singh’s book is a clear discrepancy between the documentary facts and the assessments of Fermat as a scientist by consultants. It is necessary to pay tribute to Singh in that he is in good faith (although not fully) outlined that part of the Fermat's works, which relates to his contribution to science and is confirmed documental. Especially it should be noted that arithmetic is called in his book "the most fundamental of all mathematical disciplines". Only one listing of Fermat's achievements in science is enough to be sure that there were only a few scientists of such a level in the entire history of science.
But if this is so, then why was it necessary to think out something that is not confirmed by any facts and only distorts the real picture? This is very similar to the desire to convince everyone that Fermat could not prove the FLT since this is allegedly confirmed by historians. But historians received information from those mathematicians who did not cope with the Fermat’s tasks and could in this way express their discontent. Hence, it's clear how appear all the arguments taken from nowhere that Fermat was an amateur scientist, arithmetic attracted him only with puzzles, which he “invented”, FLT also was by him “invented” looking at the Pythagorean equation, and his proofs he did not want to publish because fear of criticism of colleagues.
