Компьютер как новая реальность математики. I. Personal account

Abstract

In the last decades there was much ado about computer proofs, computer aided proofs, computer verified proofs, etc. It is obvious that the advent and proliferation of computers have drastically changed applications of mathematics. What one discusses much less, however, is how computers changed mathematics itself, and mathematicians’ stance in regard of mathematical reality, both as far as the possibilities to immediately observe it, and the apprehension of what we can hope to prove. I am recounting my personal experience of using computers as a mathematical tool, and the experience of such similar use in the works of my colleagues that I could observe at close range. This experience has radically changed my perception of many aspects of mathematics, how it functions, and especially, how it should be taught. This first introductory part consists mostly of reminiscences and some philosophical observations. Further parts describe several specific important advances in algebra and number theory, that would had been impossible without computers.