An Inconvenient Proof: A Testimony to Math’s Deductive Spirit

Abstract

The embrace of deductive reasoning during the Classical Era redefined epistemology, promoting our notion of mathematical truth from that of empirical science to a quasi-sacrosanct standard characterized by elegance, permanence, and logical consistency. Recently, the advent of high-speed computers has enabled software programs to perform lengthy, enumerative proofs-by exhaustion, while expert systems that emulate human decision making have demonstrated the capacity to form novel inferences. While artificial intelligence has immense potential to accelerate knowledge acquisition, casual embrace of automated theorem proving may jeopardize mathematics’ intellectual foundations.