The Process of proof can be considered as some kind of thought experiment. In the history of philosophy, Schopenhauer was one of the first considered in detail the fact that the presentation of evidence the process of proof in a strict form does not match the actual contents of the named process. From his reasoning we can accept the idea that a strictly formal calculations do not exhaust the content of the evidence. However, it is impossible to agree with him that these calculations are not necessary. A set of formal calculations in the language of "science fiction" can be called "formal proof". In contrast, "informal proof," or "informal argument", aims to convince that this judgment is true. So the "informal argument" can be really held only when there is already a "formal proof". The human mind is multidimensional, and processes of constructing proofs and their perception are connected not only with linguistic and logical-mathematical abilities, but with all the other abilities. Serious problems in understanding the nature of the proofs and the significance of the judgments that they support, are related with the using of the computers.