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The second miniature is no less curious, because it describes in detail two proofs of the same particular case of FLT for n=4, first by Leonard Euler and then by Pierre Fermat in the reconstruction of I. Bashmakova. Both proof as twin brothers are built on the Pythagoreans identity and in both the descent method is used. They differ only in the intricacies the logic of output to the same end result. These intricacies, although different, are quite complex, what indicates the highest skill of their authors. But the end of this miniature is simply amazing. And indeed, this proof can be obtained from the same Pythagoreans identity literally in a one line (!!!), and this very line is just in the FLT recording we restored in the margins of the book shown in Pic. 5.
In addition to the Euler proof of the special case of FLT presented here, it is also added the full text of all Euler's proofs related to Fermat's grandiose discovery of the truly magnificent properties of primes 4n+1 type. This work required the utmost exertion of all Euler's creative and physical powers within seven years, but the most important proof that these numbers always consist of the sum of two unique squares, is presented by him in such a way that it is unlikely that anyone except himself understands its essence. From Euler's letter to Goldbach with this proof, at first no one understood anything at all, and after the corrected version received by Goldbach in another letter, all the experts tacitly accepted his proof, although it is far from obvious and besides, numbers of this type should be the sum of two unique squares, but about it there is not a single word at all.
Finally, the third miniature is a journey into the past. There will be a lot of surprising and even shocking things, but here we will pay attention to only one a moment. This is the Fermat’s proof of his most grandiose discovery in the field of prime numbers, which is unknown until now and here it is presented by a special way and in amazingly beautiful form. The story about this through the mouth of Fermat's son Clement Samuel with a cherry on the cake in the form of a spectacular equation will make just as colorful an impression as the beauty of nature.
The method of vestment in the verbal form of the content of this book, chosen by us, although it requires an immense strain of all forces from the author, still yields a result, in which a small volume of the book carries the knowledge of thousands of scientific monographs! Perhaps such a precedent will be the first and the last, and in this sense, it is not a competitor to traditional scientific monographs. However, in essence it is just following the simple advice of a classic on choosing a style of exposition, where for words it would be cramped and for thoughts spacious.
The usual technical language does not achieve such an effect and this requires a higher level of literature accessible only to the elect, for example, such as Alexandre Dumas the Father. In one of his books Dumas even argued that writers understand history better than historians. Wherein, he has fib so famously and godlessly that historians could only smirk. However, in fact Dumas turned out be right because the lion’s share of the history set forth in the thick books did not really have place, but was simply invented and this fact also found a place in this book.
One of the features of our literary creativity is the mandatory presence in it of riddles, which are a
In real life false knowledge often takes the place of real ones. Behind this lies a lot of danger and u
In this book many different names are called, which created history by the will of Providence or case, and just because they turn special attention to themselves they deserve every respect, no matter in what circumstances and how they showed themselves because otherwise, there would simply not be events, from which the plot of our narrative was formed.
From what we have already talked about science here, it will look completely unattractive. Moreover, it will be presented as the source of all troubles, and sadly this is the harsh truth. But if the question about the place of science in society is not raised and, in any way, not clarified, then a catastrophe allegedly coming from scientists, will become inevitable and the very existence of our wonderful world will lose all meaning. This is not at all some formidable warning or apocalyptic prophecy, but merely an ascertaining that science is the only (!!!) field of human activity that predetermines all their other varieties!
Thus, in an intelligent society the highest priority of science must be ensured and supported by all available means, otherwise, it will receive only a global confrontation of ignoramuses balancing on the precarious verge of mutual destruction. And what we have now? Only that the management of society goes not in accordance with the objective laws of the world, but through blatant incompetence, irresponsibility, bribery, adventurism etc. Where is here the science? It is not even near visible anywhere. If even the applied science, which has been robbed by money-lenders to the last thread, somehow can still cling to its existence then for a fundamental science a long time ago there are no any prospects at all.
But perhaps scientists need to offer something themselves so that the fruits of their labor will be appreciated? Ha-ha-ha! There is a well-known case when Gregory Perelman had published without any conditions in free access the proof of the Poincare conjecture, which more than a hundred years apart from him could not be obtained by scientists. However, instead of (already offered to him!) a premium of US$ 1 million he got nothing. The press reported that allegedly he had himself refused under a fictitious pretext, but for some reason all thought that he was just an eccentric. However, in fact he did not even think about refusing, apparently naively believing that the prize he has fully deserved.
However, he did not take into account that in a society, in which the leading positions have not scientists, but usurers and bribe-takers, scientific discoveries that do not give immediate return with money, are even for free nobody need. In fact, they really offer prizes not for scientific discoveries, but for a well-known name that can be exploited in their own interests. Yet Perelman in this story brought the initiators of the award to a clean water after he offered to share prize with another scientist related to his scientific discovery and then it became obvious that in fact the refusal did not go at all from him, but from imaginary benefactors.
In terms of determining the value of scientific discoveries, there simply ca