EPISTEMOLOGICAL NORMS AND SOCIAL PRACTICES OF MATHEMATICAL PROOF

The widespread use of computers not only in obtaining or verifying mathematical results, but also as a means of organizing the mathematical community, will allow solving the problem of examining mathematical results and will also significantly change the epistemic characteristics of mathematical knowledge as knowledge generated and verified individually. The emerging mathematical Internet platforms pretend to act as independent structural elements of the "map of mathematical knowledge". They can often act as collective agents of mathematical activity. The creation of libraries of computational mathematics is the creation of unparalleled database structures that organize collective mathematical knowledge in an optimal way (historians of science emphasize the extraordinary importance of the invention of a library catalog for the development of science; it is difficult to imagine the scale of the stimulus for the development of computational mathematics as a result of the creation of such a new organization of mathematical knowledge). The most controversial aspect of computer knowledge, associated with the verification of boundless computer proofs, is also going through an essential stage associated with the development of the theory of univalent foundations. This theory claims to act not only as new foundations of mathematics, but also, due to its formalizability, as the basis of computer mathematics. The transformation of mathematical practice, caused by the introduction of computers both in the organization of the mathematical community and directly in the mathematical practice of obtaining and verifying results, indicates that the very social practice of examining and consolidating mathematical results is undergoing revolutionary changes in its scale. In the sociology of science and technology, a new direction of research is being formed - the social machine - associated with the study of the transformation of social practices on the basis of the emergence of human-computer cooperation in them. In the author's opinion, the development of computer mathematics turns the practice of modern mathematics into a most interesting field of research in this direction due to both the speed of the changes taking place and their scale. The first studies of this kind convincingly demonstrate the depth of the transformation of the accepted social standards of examination and the consolidation of mathematical results in connection with the increasing introduction of the computer into mathematical practice. In the author's opinion, the most intensive changes in the mathematical practice of production and verification of knowledge will be associated with the further development of the program of univalent foundations, which claims to be the foundations of both computational and most of mathematics in general.