The phenomenology of mathematical proof

Gian-Carlo Rota

pp. 134-150

in: Gian-Carlo Rota, Fabrizio Palombi, Indiscrete thoughts, Berlin, Springer, 1997

Abstract

Everybody knows what a mathematical proof is. A proof of a mathematical theorem is a sequence of steps which leads to the desired conclusion. The rules to be followed in this sequence of steps were made explicit when logic was formalized early in this century and they have not changed since. These rules can be used to disprove a putative proof by spotting logical errors; they cannot, however, be used to find the missing proof of a mathematical conjecture.