That's what they really meant! Instead of the greatest scientist and founder of number theory as well as combinatorics (along with Leibniz), analytical geometry (along with Descartes), probability theory (along with B. Pascal), wave optics theory (along with Huygens), differential calculus (along with Leibniz and Newton), whose heritage was used by the greatest scientists in the course of centuries, suddenly a “lover” of puzzles appear, who only enjoyed the fact that no one could solve them. And since arithmetic is puzzles then this most fundamental of all sciences is relegated to the level of crosswords. Such a “logic” is clearly sewn with white threads and to be convinced of this, it is enough just to point out some well-known facts.
History has not retained any evidence that during the period life and activity of P. Fermat, someone has solved at least one of his tasks.11 This fact became the basis for opponents else in those times to compose all kinds of tales about him. In the surviving letters, he reported that he had already sent proofs to his respondents three times. But none of these proofs reached us because Fermat's letters recipients in eyes of posterity of course, did not want to look like they could not cope with simple tasks. Another indisputable fact is that the Fermat's personal copy of the book “Arithmetic” by Diophantus edited in 1621 with his handwritten comments in the margins, none of the eyewitnesses have ever seen!!! Well, now just a most curious picture turns out. Fermat’s critics seriously believe a witty Gascon joke that the Honorable Senator (apparently because of his lack of paper!) writes accurate and verified text of thirty-six Latin words in the book's margins, but are absolutely don't believe that he (the greatest scientist!) indeed had “truly amazing proof” of his own theorem.12
It is even difficult to imagine how these critics would have been amazed to find out that in fact Fermat had never dealt with the search for this proof since at that time he could not know what exactly is to be proven. But namely in the last sentence of the FLT wording, which had so much outraged them, there is a keyword directly indicated how he have solved this problem. It so happened that for centuries the science world vainly tormented itself in search of the FLT proof, but Fermat himself was never looked for it and simply had declared that he had it discovered!13
It is possible also to remind to opponents ingeminating about Fermat’s deliberate refusal to publish his works that for example, Descartes had received permission to publishing from Most Reverend cardinal Richelieu himself. It was impossible for Fermat and there is even a written (!!!) testimony about it (see text on P. Fermat’s tombstone: “Vir ostentationis expers … – He was deprived the possibility of publication …”. See Appendix VI Pic. 93 – 94). Nevertheless, even being in such conditions, he had prepared the publication of Diophantus’ “Arithmetic” with the addition of his 48 comments, one of which got a name the “Fermat’s Last Theorem”.
The publication was supposed to appear in honor of the historically significant event – the foundation of the French Academy of Sciences, in which preparation Fermat himself participated through the correspondence with his long-time colleague from the Toulouse parliament Pierre de Carcavy who became the royal librarian. The royal decree of the creation of the French Academy of Sciences was prepared by Carcavy and the all-powerful Finance Minister Jean-Baptiste Colbert submitting it to the signing by Louis XIV. However, the Academy of Sciences was established only in 1666 i.e. a year after the Fermat's death.
Mathematicians are very famous for how they are strict pedants, formalists and quibblers, but as soon as it comes to the FLT, all these qualities immediately disappear somewhere. Fermat's opponents ignoring well-known facts, called him either a hermit (this is a senator from Toulouse!) or a prince of amateurs (this is one of the founders of the French Academy of Sciences!), and this despite his contribution to science comparable to its importance only with a couple or triple of the most prominent scientists in the history of science!
They also did not fail sarcastically to point out that no one would have known about Fermat if the greatest mathematician of all times and peoples Leonhard Euler had not become interested in his tasks. But just this magic name has played a cruel joke with them. Their boundless belief in Euler's innovatory researches was too blind to notice that it was namely thanks to him science received such a powerful blow, from which it cannot recover up to now!
Mathematicians not only have believed Euler, but also warmly supported him that algebra is the main mathematical science, while arithmetic is only one of its elementary sections.14 Euler's idea was really excellent because his algebra, which gained new possibilities through the use of "complex numbers" was to be a most powerful scientific breakthrough that would allow not only to expand the range of numbers from the number axis to the number plane, but also to reduce the most of all calculations to solving algebraic equations. 15
The need for "complex numbers" mathematicians explained very simply. To solve absolutely any algebraic equations, you need (not so much!) to make the equation x2 + 1 = 0 become solvable. 16 In Russian this is called: "Don’t sew the tail to a mare"! This equation is not at all harmless since it has nothing to do with practical tasks, but undermines the fundamentals of science very substantially. Nevertheless, the devilish temptation to create something very spectacular on empty place turned out to be stronger than common sense and Euler decided to demonstrate the new mathematical possibilities in practice.
Pic. 16. Leonhard Euler
The FLT, which Euler could not to prove, would be perfect for demonstrating the possibilities of a new wonder-algebra. However, the result turned out to be more than modest. Instead of a general proof of FLT, only one particular case for the 3rd power was proven [8, 30]. More ambitious was seemed the proof of other Fermat’s theorem about the only solution in integers of the equation y3 = x2 + 2 [36] because it was a very difficult task and like FLT, none of the mathematicians could solve it. Despite the fact that the very possibility of solvability of any algebraic equation has not yet been proven, these Euler's demonstrations were perceived by hurrah. It only remained to find a solution to the problem called the “Basic Theorem of Algebra”. In 1799 the real titan of science Carl Gauss coped brilliantly with this task presenting proof even in 4 different ways!
The scientific community greeted all these "achievements" with a storm of applause while the unholy was also so glad that it is impossible to imagine.
Pic. 17. Karl Friedrich Gauss
Yeah, this was need to be seen how the whole civilized scientific world has driven itself into a dead end! It is obvious that for science, which does not rely on arithmetic, there are no reasonable restrictions and the consequences will be sad – from the dominance of algebra, arithmetic will become so difficult that witlings will call it a science for the elitist mathematicians where they can demonstrate the sharpness of their mind! But the scientists themselves unsuspecting and full of the best intentions, continued to advance science forward to new heights, but so diligently that they either inadvertently or due to a misunderstanding… simply have lost the Fermat's Golden Theorem (FGT)! But this was one of the most impressive discoveries of Pierre Fermat in arithmetic, of which he was very proud.
