METHODOLOGICAL FOUNDATIONS OF CRISES IN MATHEMATICS AND THEIR CONNECTION WITH THE EMERGENCE OF PARADOXES

Pak E. E.

The article is devoted to the problems of substantiating the foundations of mathematics and their resolution. This issue is considered from the point of view of the close connection between the crises of mathematics and the paradoxes that arise at a certain historical stage. The first two crises were successfully overcome by improving the mathematical apparatus: by introducing restrictions or additions. At this stage, the third crisis has worsened due to the rapid development of computing technology and artificial intelligence, in particular.

Keywords:mathematics, crises, paradoxes, foundations of mathematics, artificial intelligence