Does reason evolve? (Does the reasoning in mathematics evolve?)

Abstract

Hersh (1997) in a book aptly named What Is Mathematics Really? stresses the great distance he detects between the reality of professional mathematical practice-contemporary and historical-and the reasoning in formal languages that philosophers (since Frege) have largely characterized mathematical proof in terms of. Hersh criticizes the reasoning-in-formal-languages view of mathematical practice and mathematical proof as “isolated,” “timeless,” “ahistorical,” and indeed, even “inhuman.” Hersh (1997, xi) contrasts this derivation-centered view of mathematics (and mathematical proof) with an alternative view that takes mathematics to be a human activity and a social phenomenon, one which historically evolves and is intelligible only in a social context. His alternative view pointedly roots mathematical practice in the actual proofs that mathematicians create-actual proofs that Hersh claims philosophers of mathematics often ignore.