Customer Reviews

Stephen Smale: The Mathematician Who Broke the Dimension Barrier

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This book not only provides a useful description of some of the theory at a level technical enough to be satisfying, but also gives a fascinating view into the life and thinking of a Field's Medal winner (1966). Who would have guessed that the future Field's Medal Winner received a C in Calculus II and Physics and that he had a B- average Jr. year at the University of Michigan? And perhaps particularly heartening to those who have been through the graduate school experience, that he was less favored than Munkries and received an ultimatum from the chairman to improve (and that in graduate school, according to Raul Bott, Smale sat in the back and it wasn't clear he was always paying attention). But, of course, Smale more than redeems himself resulting in a storied career and a reputation that surpasses the boundaries of his specialties. This is a marvelous book.

Batterson's book is the only book length biography of Stephen Smale, a Field medalist (1966), who made major contributions to topology and dynamical systems. In the first half of the book, Smale is depicted as a brilliant mathematician who had a relatively humble beginning and was a relatively late bloomer as well. A theme that runs through the book and one that predominates the middle part of the book is Smale's social activism. The last one-third of the book deals with a variety of topics - Smale interests in minerals and photography, his adventures trips (e.g. climbing mountains, sailing) and "other people" (family members, students and his involvement in a gender discrimination lawsuit filed a by a junior colleague). The book ends with a chapter with an assessment of Smale contributions and stature as a mathematician as well as his departure to take up an appointment in Hong Kong. Personally, I found the book to be fairly uneven - I particularly enjoyed reading the early chapters on Smale's coming of age as a creative mathematician. The middle part dealing his social activism was for me less enjoyable - partly due the extensive effort made to explain the socio-political events in the 1960s. These narratives distract the readers away from Smale mathematical work during this period but are essential as they provide the social-political environment within which Smale's activism was prominent. The last few chapters seemed to be a few chapters thrown together to cover topics that were left out earlier. The fact that I had such a mixed view of the book is probably not due to the author's writing ability but more to Smale's unusual character - very few mathematicians are known for their brilliance as well as for their active commitment to social issues.