Computing and the cultures of proving

Abstract

This article discusses the relationship between mathematical proof and the digital computer from the viewpoint of the ‘sociology of proof’: that is, an understanding of what kinds of procedures and arguments count for whom, under what circumstances, as proofs. After describing briefly the first instance of litigation focusing on the nature of mathematical proof, the article describes a variety of ‘cultures of proving’ that are distinguished by whether the proofs they conduct and prefer are (i) mechanized or non-mechanized and (ii) formal proofs or ‘rigorous arguments’. Although these ‘cultures’ mostly coexist peacefully, the occasional attacks from within one on another are of interest in respect to what they reveal about presuppositions and preferences. A variety of factors underpinning the diverse cultures of proving are discussed.