LITMIR.BIZ

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If Fermat's working notes were found, it would turn out that his methods for solving tasks are much simpler than those that are now known, i.e. the current science has not yet reached the level that took place in his lost works. But how could it happen that these recordings disappeared? There may be two possible versions. The first version is being Fermat’s cache, which no one knew about him. If this was so, there is almost no chance it has persisted. The house in Toulouse, where the Fermat lived with his family, was not preserved, otherwise there would have been a museum. Then there remain the places of work, this is the Toulouse Capitol (rebuilt in 1750) and the building in the city of Castres (not preserved) where Fermat led the meeting of judges. Only ghostly chances are that at least some walls have been preserved from those times. Another version is that Fermat’s papers were in his family’s possession, but for some reason were not preserved (see Appendix IV, year 1660, 1663 and 1680).

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For mathematicians and programmers, the notion of function argument is quite common and has long been generally accepted. In particular, f (x, y, z) denotes a function with variable arguments x, y, z. The definition of the essence of a number through the notion of function arguments makes it very simple, understandable and effective since everything what is known about the number, comes from here and all what this definition does not correspond, should be questioned. This is not just the necessary caution, but also an effective way to test the strength of all kinds of structures, which quietly replace the essence of the number with dubious innovations that make science gormlessly and unsuitable for learning.

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An exact definition the notion of data does not exist unless it includes a description from the explanatory dictionary. From here follows the uncertainty of its derivative notions such as data format, data processing, data operations etc. Such vague terminology generates a formulaic thinking, indicating that the mind does not develop, but becomes dull and by reaching in this mishmash of empty words critical point, it simply ceases to think. In this work, a definition the notion of “data” is given in Pt. 5.3.2. But for this it is necessary to give the most general definition the notion of information, which in its difficulty will be else greater than the definition the notion of number since the number itself is an information. The advances in this matter are so significant that after they will follow a real technological breakthrough with such potential of efficiency, which will be incomparably higher than which was due to the advent of computers.

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Computations are not only actions with numbers, but also the application of methods to achieve the final result. Even a machine can cope with actions if the mind equips it with appropriate methods. But if the mind itself becomes like a machine i.e. not aware the methods of calculation, then it is able to create only monsters that will destroy also him selves. Namely to that all is going now because of the complete lack of a solution to the problem of ensuring data security. But the whole problem is that informatics as a science simply does not exist.

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Specialists who comment on the ancients in their opinion the Euclid's "Elements" and the Diophantus' "Arithmetic", as if spellbound, see but cannot acknowledge the obvious. Neither Euclid nor Diophantus can be the creators the content of these books, this is beyond the power of even modern science. Moreover, these books appeared only in the late Middle Ages when the necessary writing was already developed. The authors of these books were just translators of truly ancient sources belonging to another civilization. Nowadays, people with such abilities are called medium.

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If from the very beginning we have not decided on the concept of a number and have an idea of it only through prototypes (the number of fingers, or days of the week etc.), then sooner or later we will find that we don’t know anything about numbers and follow the calculations an immense set of empirical methods and rules. However, if initially we have an exact definition the notion of number, then for any calculations, we can use only this definition and the relatively small list of rules following from it. If we ourselves creating the required numbers, we can do this through the function arguments, which are represented in the generally accepted number system. But when it is necessary to calculate unknown numbers corresponding to a given function and task conditions, then special methods will often be required, which without understanding the essence of numbers will be very difficult.

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The content of Peano’s axioms is as follows: (A1) 1 is a natural number; (A2) For any natural number n there is a natural number denoted by n' and called the number following n; (A3) If m'=n' for any positive integers m, n then m = n; (A4) The number 1 does not follow any natural number i.e. n' is never equal to 1; (A5) If the number 1 has some property P and for any number n with the property P the next number n' also has the property P then any natural number has the property P.

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In the Euclid's "Elements" there is something similar to this axiom: "1. An unit is that by virtue of each of the things that exist is called one. 2. A number is a multitude composed of units” (Book VII, Definitions).

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So, count is the nominate starting numbers in a finished (counted) form so that on their basis it becomes possible using a similar method to name any other numbers. All this of course, is not at all difficult, but why is it not taught at school and simply forced to memorize everything without explanation? The answer is very simple – because science simply does not know what a number is, but in any way cannot acknowledge this.

40

The axioms of actions were not separately singled out and are a direct consequence of determining the essence a notion of number. They contribute both to learning and establish a certain responsibility for the validity of any scientific research in the field of numbers. In this sense, the last 6th axiom looks even too categorical. But without this kind of restriction any gibberish can be dragged into the knowledge system and then called it a “breakthrough in science”.

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The reconstructed proof of Fermat excludes the mistake made by Euclid. However, beginning from Gauss, other well-known proofs the Basic theorem of arithmetic repeat this same mistake. An exception is the proof received by the German mathematician Ernst Zermelo, see Appendix I.

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Facsimile of the edition with the Cauchy's GTF proof was published by Google under the title MEMIRES DE LA CLASSE DES SCIENCES MATHTÉMATIQUES ET PHYSIQUES DE L’INSTITUT DE France. ANNEES 1813, 1814, 1815: https://books.google.de/books?id=k2pFAAAAcAAJ&pg=PA177#v=onepage&q&f=false What we need is on page 177 under the title DEMONSTRATION DU THÉORÉME GÉNÉRAL DE FERMAT, SUR LES NOMBRES

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