The question of changing standards of proof over time is touched upon in many essays in Tymoczko's New Directions in the Philosophy of Mathematics, revised edition, Princeton, 1998. Some are philosophical and some are historical, the latter category including my own "Is Mathematical Truth Time-Dependent" which focuses on the changing standards of proof in analysis between the 18th and 19th centuries. Abel's comments on the lack of rigor in 18th-century arguments as compared to the standards of Cauchy's Cours d'analyse are a case in point. This is a thought-provoking anthology.
Judith V. Grabiner Flora Sanborn Pitzer Professor of Mathematics Pitzer College (909) 607-3160