The quest for better attitudes

This article is adapted from my Brouwer lecture of February 2001 [1]. It has been shortened by about one quarter and updated. Given the occasion (in 2001) I had thought it inappropriate to give a talk in my usual style, which is rich in equations and mathematical derivation. Instead, I attempted to give a talk rich in perspective and personal anecdotes (and maybe a few equations). Since the original lecture, my appreciation of the subject matter has grown and some addenda and corrigenda have become necessary.