I Want to Be a Mathematician

I Want to be a Mathematician: An Automathography
by Paul R. Halmos



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At last we have a thorough account (one that stands the test of re-reading, and the only such, in fact) of the period that runs approximately from the forties to the present-day, a period that may go down in history as one of the golden ages of mathematics. However, the theme that emerges from this collection of amusing anecdotes is not the welcome lesson we would expect as the bequest of a golden age. Halmos's tales of incompetent department heads, of Neanderthal deans, of obnoxious graduate students unwittingly reveal, in the glaring light of gossip, the constant bungling, the lack of common sense, the absence of savoir faire that is endemic in mathematics departments everywhere. Take, for example, the turning point of the author's career, the incident of his leaving the University of Chicago. Even granting Halmos's contention that his papers may have lacked depth (at least, in someone's opinion) in comparison with those of certain colleagues of his (a debatable thesis, then and now), it still seems clear that the university made a mistake by dispensing with Halmos's services. Whatever his other merits, Halmos is now regarded as the best expositor of mathematics of his time. His textbooks have had an immense influence on the development of mathematics since the fifties, especially by their influence on mathematicians in their formative years. Halmos's glamor would have been a far sounder asset to the University of Chicago than the deep but dull results of an array of skillful artisans. What triumphed at the time is an idea that still holds sway in mathematics departments today, namely, the simplistic view of mathematics as a linear progression of problems solved and theorems proved, in which any other function that may contribute to the well-being of the field (most significantly, that of exposition) is to be valued roughly on a par with that of a janitor. It is as if in the filming of a movie all credits were to be granted to the scriptwriter, at the expense of other contributors (actors, directors, costume designers, musicians, etc.) whose roles are equally essential for the movie's success.

--Reviewed by Gian-Carlo Rota in The American Mathematical Monthly, 94 (August/September 1987), p. 700.