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I Want to Be a Mathematician...An Automathography

Paul R. Halmos
Mathematical Association of America
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The Basic Library List Committee recommends this book for acquisition by undergraduate mathematics libraries.

[Reviewed by
Fernando Q. Gouvêa
, on

Paul Halmos's "automathography" is a classic of the genre. First published in 1985, it contains Halmos's memories of his (then) 50-year career as a mathematician, from the 1930s to the 1980s. This is an essentially unchanged reprint of the original Springer edition. The changes are cosmetic: the cover is prettier, it's a paperback, and a few of the photographs have been replaced or retouched.

Halmos's basic approach is made clear in the "overture":

Sure, I had parents (two) and wives (two, one at a time, the present one for forty years), and cats… I like Haydn, long walks, Nero Wolfe, and dark beer, and for a few years I tried TM. All that is true, but it's none of your business — that's not what this book is about.

Instead, the book is about his life as a mathematician among mathematicians. It shows us a little about how Halmos thinks about mathematics, about what interested and motivated him, and about how he interacted with others. It includes a lot of what might, somewhat uncharitably, be described as "gossip": stories and anecdotes about mathematics, mathematics departments, and mathematicians.

In my experience, mathematicians love this sort of thing. Those of my colleagues who have read this book have enjoyed it. My students have liked it much less, partly because they aren't that interested in the world of mathematics, partly because they feel "turned off" by what they describe as Halmos's "arrogance." I think what bothers them is Halmos's bluntness about what counts and what does not count as significant in mathematics. That Halmos's harshness is mostly directed at his own work doesn't change my students' assessment. If all this famous guy can say, after trying for fifty years, is "I want to be a mathematician," they argue, then we students have no chance at all.

Well, there's some truth to that impression. Very few of us can aspire to being as good as Paul Halmos. And the mathematics community does tend to have very high standards for "what counts," sometimes overly high standards. Outsiders find this strange. Robert Preston, writing in the New Yorker in 1992, said that "a certain impression I had of mathematicians was… that they spent immoderate amounts of time declaring each other's work trivial. " There isn't too much of this kind of thing in I Want to Be a Mathematician, but there certainly is some.

But Halmos's book was never really intended for outsiders. For us members of his community, who aspire to be mathematicians ourselves, it gives us a glimpse of what one particularly successful mathematical life was like, shows us a little about what our community was like in the past, and yes, shares some juicy gossip.

Fernando Q. Gouvêa teaches at Colby College in Waterville, ME. He often asks his students to read books about mathematics and mathematicians.


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