The automation of proof: a historical and sociological exploration

Abstract

This article 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

Intelligent systems:

“…However, a history of theorem proving demonstrates a strong orientation toward just construction of the tautology chains like in a well-known AI case of resolution-refutation. A history of automation of proof is described in [193]. The orientation toward construction of the chains of tautology can be applied even under uncertainty [194], and in the cases of multistrategy situations, for example, using knowledge-bases [195].…”

High-Integrity System Specification and Design

“…Mathematical proof has essentially been a social process historically and accelerating this process using tool support in a software engineering context is difficult to achieve [178]. What a proof system does do, however, is to let us prove rigorously that the system we have implemented satisfies the requirements determined at the outset.…”

Discrete and Continuous: A Fundamental Dichotomy in Mathematics

“…Symbolic manipulation packages such as Mathematica, Matlab and Maple manipulate finite formulas and solve differential equations, draw graphs and can pass mathematics exams more reliably than most mathematics students. The search for theorem-proving and especially theorem-discovering software has been much less successful, but there are some worthwhile advances [3,23]. The end result is that finite machines with finite resources can output a product that reads to humans like mathematics, in greater quantity and quality than any individual human.…”