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Adventures of a Mathematician

S. M. Ulam
University of California Press
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The Basic Library List Committee strongly recommends this book for acquisition by undergraduate mathematics libraries.

[Reviewed by
Benjamin Linowitz
, on

Adventures of a Mathematician is what Paul Halmos would call an automathography:

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.

Adventures of a Mathematician is the story of Stanislaw Ulam’s life as a mathematician. We learn a bit about his parents, sure, but we learn much more about the coffeeshop culture of the Lwow mathematicians, and the character about which Ulam writes most affectionately is Hungarian mathematician John von Neumann. (The book was originally intended to be a biography of von Neumann.) Ulam led an extraordinary life, and it is fascinating to read about Polish mathematical culture, the difficulty that jewish scientists fleeing Eastern Europe in the 1930s and 40s had in securing academic jobs in the US, and what life was like as a mathematician working at the Manhattan Project in Los Alamos.

As a mathematician I have to say that I loved this book. It was fascinating to read the story of how a pure mathematican that once “sunk so low that his latest paper actually contained numbers with decimal points” came to play a crucial role in the Manhattan Project and the exploration of space. A large part of the appeal of Adventures of a Mathematician to mathematicians, I am sure, is that its pages are full with stories about celebrated mathematicians and physicists (Banach, Birkhoff, Erdős, Fermi, …) whose names one normally only encounters in textbooks and research papers. Having said this, the book was written for a general audience and I find it sad that rather than showing these scientists’ humanity so much time is spent linearly ordering their work and stature in terms of importance. This may be an accurate depiction of mathematical culture, but it’s a superficial one that makes me wonder whether my students would find this book as enjoyable as I did.

Ulam was in many ways a mathematician’s mathematician. In the pages of his book he explains that mathematics is above all else a creative enterprise, describes the way we speak to one another (e.g., “such and such is trivial”), tells math jokes (“Any two points in Los Angeles were at least an hour’s drive apart; a disctete topological space.”) and even grouses about his teaching load at the University of Wisconsin. As a mathematician Ulam had incredibly broad research interests, which is part of the reason that he spends some of the final pages of his book lamenting the manner in which mathematics in the 1970s had fragmented into a disjoint union of subfields that rarely interact with one another. I cannot imagine how horrified Ulam would be to learn about the mathematical landscape some 45 years later.

Ultimately, this is a book about mathematicians and their culture. It offers snapshots of some of the most important events in early to mid-twentieth century mathematics, written by an insider that speaks our language and knows the sort of gossip we want to hear about. If a student were to approach me and ask where they could go to learn about what mathematical life was like back then, this book would be the first place I would send them.

Benjamin Linowitz ( is an Assistant Professor of Mathematics at Oberlin College. His research concerns the theory of arithmetic groups, a fascinating area lying at the intersection of algebraic number theory and differential geometry. He is also interested in the history of mathematics. His website can be found at

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