The more you read the works of great mathematicians, the more you realize that their geometry is, after all, anthropometric, since it always has an infinitesimal fraction of the human dimension. This share of anthropometrical especially when you feel a familiarity with the work of mathematician Gregory Perelman. This proportion is the result of limited human intelligence as a product of the brain that creates models of the world around us. There will always be a gap of human meanings between the surrounding world and the models of the surrounding world created by the human intellect. This gap is absent only between the intellect and the inner world of a person. In this case, the person directly perceives the thoughts and images that open before his inner eye, and, it would seem, does not need to create models of elements of the surrounding world, that is, to create models about models.
And yet, a person manages to create models of elements of their inner world. This is what psychology does. A person wants to know the origins of where the inner world came from: thoughts, images, etc.? who and why "fits" all these elements of the inner world to a person? The most powerful attempts to answer these questions were made by the discoverer of the theory of the unconscious, Sigmund Freud. For the first time, he analyzed the mechanisms of occurrence of only some unconscious processes. The remaining giant part of these unconscious processes still does not have any theoretical psychological models. These attempts are made despite the fact that there is a smaller gap of meaning between the human intellect and the inner world than between the intellect and the outer world.
If you try to deeply perceive the inner world of a person as something externally viewed by our inner eye, it can gradually turn into a component of the external world. And again there will be a Gulf of meaning between us and what appears to us as something that we call the inner world. These deep-philosophical reflections, in the end, will lead us to understand the instability between the inner and outer world of man.
Moreover, we can, on the one hand, assert that there is no external world and that it is always reducible to the internal world, thanks to the phenomenology developed by Edmund Husserl.
Thus, everything that was discovered by the genius mathematician Grigory Perelman is only phenomenology, and if the space of the Universe could "speak", it would hardly answer humanity that it recognized itself in these Perelman pictures about itself. Most likely, these pictures of the Universe are drawn by Perelman himself, that is, the Man himself with his phenomena.
On the other hand, it can also be argued that our entire inner world and our inner eye, viewing this inner world, are so unconscious that they can be perceived as components of the external world, working according to a certain program. This program gives us the illusion of freedom of choice and that we are the masters of our soul and are even able to learn about ourselves and the world around us. Moreover, these psychic programs give us the illusion that our inner eye, or the observer of thoughts, is activated at our own discretion and desire.
Thus, the gap of meaning between the surrounding world and man will yawn as before, and the greatness of man, basking in the illusion of discovering the properties of the infinite Universe, will also amuse humanity, including the genius of Grigory Perelman.
Alas! Most mathematicians do not realize the origins of their mathematical intelligence, which they are carriers of, living in a stream of programs set by an unknown force. They either understand or do not understand that they are not authors in their depth, that they are visited by their receptacle, which is located in a small geometric space called the brain.
Associate Professor of the Institute of psychology and education of KFU, candidate of psychological Sciences Ramil Garifullin