Reshaping the metaphor of proof

Abstract

The simplistic view of Mathematics as a logical system of formal truths deduced from a limited set of axioms by a limited set of inference rules immediately shatters when confronted with the history of Mathematics, or current mathematical practice. To become useful, mathematical Philosophy should contemplate what Mathematics actually was, over centuries, and what it is now, rather than speculate what it should be according to the philosophical orthodoxy. The first dogma that must be completely revised is the idea of proof as a text, rather than what it is for mathematicians themselves: a process, a plethora of interwoven arguments, a multi-dimensional structure. This article is part of the theme issue ‘The notion of ‘simple proof’ - Hilbert's 24th problem’.