1. The Greatest Phenomenon of Science
Usually, the science's image is represented as an ordered system of knowledge about everything that can be observed in the world around us. However, this image is illusory and in fact there is not any orderliness in science since it is formed not by the development of knowledge from the simple to the complex, but only by the historical process of the emergence of new theories. The classic example is the Descartes – Fermat analytic geometry, where compared with Euclidean geometry, science sees only an analytic-friendly representation of numerical functions in a coordinate system, but does not evaluate the qualitative transition from naturalized elements (point, line, surface, etc.) to numbers.1
It would seem that this is so insignificant that it cannot have any consequences, but ironically, it was after the expansion of the numerical axis to the numerical plane, when science was hopelessly compromised, because it suddenly became clear that such a representation of numbers does not obey to the Basic theorem of arithmetic that the decomposing of an integer into prime factors is always unique. But then a corresponding conclusion should be made that no any numerical plane exists and everything connected with it should be written off to the archive of history.
But it’s really impossible! If there is no orderliness in science, then there is no reason to link new knowledge to earlier ones. Therefore, it is not at all news to the world of scientists that for the numerical plane the Basic theorem of arithmetic is not acted. This was known a century and a half ago and it never even occurred to anyone to abandon this idea. During this time, so much has been done that it’s so easily to take it all and throw away is in no way possible because many “experts” with their “scientific” research can lose their jobs and all monographs, reference books and textbooks on this theme will at once turn into tons of waste paper.2
Yes, not one of the scientists can be surprised by the fact that the Basic theorem of arithmetic is not acted, because they have already accustomed not only to such things. But they will be very surprised, when they know that nobody can prove BTA so far! All the “proofs” of this theorem in textbooks and on the Internet are either clearly erroneous or not convincing. But then it turns out that on the one hand, science deprives itself legitimacy since it does not recognize the Basic theorem, on which it itself holds, but on the other hand, it throughout all its history simply was not aware of the fact that it has no proof of this theorem.3
And what now to do? Can this blatant fact be perceived otherwise as the degradation of science in its very foundations? To some people such a conclusion may seem too categorical, but unfortunately for current science, this is even very mildly said. What a marvel, some theorem doesn’t act? And what about when the law of conservation of energy doesn’t act? Current astrophysics simply does not present itself without the “big bang theory”, according to which all the galaxies in the Universe are flowing away like fuzz. And such a crazy phantasmagoria is quite seriously presented today as one of the greatest "scientific" achievements, and fig leaves like "hidden energy" and "dark matter" easily cover the problems with the notorious conservation laws.
