Computer Proofs and the Epistemological Status of Mathematical Theorems

Abstract

The article is an attempt at collecting and systematising views on the role and place of computers in mathematics, in particular the views on the consequences of using computers in proving mathematical theorems. The following issues are considered in the article: the problem connected with the concept of mathematical proof and its features; the attempts at answering the question whether computer proofs are genuine mathematical proofs; the problems with methods of checking the correctness of classical and computer-assisted proofs; and finally the problem of the reliability of proofs and a related problem of the validity of mathematical conjectures. The main issue under discussion is the problem of philosophical consequences of regarding computer-assisted proofs as rightful in mathematics and especially its possible influence on the opinion that mathematical knowledge is a priori.