ABSTRACT
When I studied modern algebra as an undergraduate, the instructor, Professor Ellis Kolchin, contemptuously defined a physicist as “someone who thinks that a vector is an ordered triple.” Roughly at the same time, Murray Gell-Mann was arguing that, really, physicists do not need to know mathematics, since the drive for abstraction and rigor characteristic of modern mathematics is only to avoid recondite counterexamples that never appear in nature.1 While these two statements probably could not be made today —we live in the era of string theory, whose practitioners no longer know whether they are doing physics or mathematics-they do reflect an attitude by physicists to both mathematical abstraction and mathematical rigor.
