Book Description

Not so long ago, about 30 years ago, not only the world community of mathematicians, but other scientific communities and even non-scientific communities with close attention — some with partiality, some without partiality — but followed with interest, and even delved into scientific details of the proof of the Russian mathematician Grigory Perelman of the hypothesis that was formulated in 1904 by the outstanding French mathematician Henri Poincaré. I was also interested in the same evidence. True, the reason for my interest was not so much Perelman’s proofs in their mathematical details, but rather the formulation of the hypothesis itself, which seemed to me an extremely interesting formulation of the problem of such manifolds, the topological and metric properties of which, in their unity with each other, are the cause of the geometric shape of the space of the universe. If someone asks, why start the same scientific business if there is already a mathematical proof of the same hypothesis. Firstly, if anything determines the geometric shape of any space, including the space of the universe, then perhaps its physical content. If so, then from the standpoint of the spatial unity of the geometric form of the space of the universe and the physical content of the same geometric form, Poincaré’s mathematical hypothesis is certainly a theoretically incomplete hypothesis. All the same justifies the need for the science of physical and geometric science in their unity with themselves and among themselves to prove those manifolds, physical and geometric manifolds, the natural properties of which in their unity with each other are responsible for the spatial unity of the universe with itself. Secondly, since truth is not an absolute truth, it reveals itself each time as a relative truth, which does not prohibit, but permits another proof of the same mathematical hypothesis, which in a given place is no longer mathematical, but geometrically physical and physically geometric.