The Automation of Proof: A Historical and Sociological Exploration

Abstract

This paper reviews the history of the use of computers to automate mathematical proofs. It identifies three broad strands of work: automatic theorem proving where the aim is to simulate human processes of deduction; automatic theorem proving where any resemblance to how humans deduce is considered to be irrelevant; and interactive theorem proving, where the proof is directly guided by a human being. The first strand has been underpinned by commitment to the goal of artificial intelligence; the practitioners of the second strand have been drawn mainly from mathematical logic; and the third strand has been rooted primarily in the verification of computer programs and hardware designs.