Proofs, computers, and the a priori: Is there anything to fix?

Abstract

This paper aims to answer several epistemological questions raised by the use of computers in mathematical practice; for this purpose, it uses the template for a conceptual engineering project proposed in Isaac, Koch, and Nedft 2022. Some interesting theoretical questions raised by this change in the methodology of mathematics are whether proofs continue to be accessible to human mathematicians, whether computers are reliable and therefore should be trusted by mathematicians, and whether proof is still an a priori methodology even though the use of computers is essential for some of them. The paper begins by introducing the project, which is to assess the “functionality” of the notion of proof and apriority in relation to the novelty that the use of computers in proof has brought to mathematical practice. The paper suggests that there has been a development of the methodology that conveys an “improvement of the functionality” and enforces reasons to adopt a certain notion of apriority.