Mathematics of the future

Abstract

Mathematics has entered a crisis of complexity. The main reason is the use of immutable concepts according to the law of identity of Aristotle's logic. The evidence has become super-long, unverifiable. Overcoming the crisis is possible in the transition from immutable concepts to "mobile" ones, in the generalization of the law of identity. In modern mathematics, there are prerequisites for such a transition – in qualitative theory, probability theory, algorithm theory, and foundations. The future of mathematics lies in the development of categories as transformative concepts.