Stephen Smale: The Mathematician Who Broke the Dimension Barrier

by Steve Batterson

In 1957 Stephen Smale startled the mathematical world by showing that, in a theoretical sense, it is possible to turn a sphere inside out. A few years later, from the beaches of Rio, he introduced the horseshoe map, demonstrating that simple functions could have chaotic dynamics. His next stunning mathematical accomplishment was to solve the higher-dimensional Poincaré conjecture, thus demonstrating that higher dimensions are simpler than the more familiar three. In 1966 in Moscow, he was awarded the Fields Medal, the most prestigious prize in mathematics. Smale's vision and influence extended beyond mathematics into two vastly different realms. In 1965 in Berkeley, he initiated a program with Jerry Rubin of civil disobedience directed at ending the Vietnam War. And as a mineral collector, he accumulated a museum-quality collection that ranks among the finest in the world. Despite these diverse accomplishments, Smale's name is virtually unknown outside mathematics and mineral collecting. One of the objectives of this book is to bring his life and work to the attention of a larger community. There are few good biographies of mathematicians. This makes sense when considering that to place their lives in perspective requires some appreciation of their theorems. Biographical writers are not usually trained in mathematics, and mathematicians do not usually write biographies. Though the author, Steve Batterson, is primarily a mathematician, he has long been intrigued by the notion of working on a biography of Smale. In this book, Batterson records and makes known the life and accomplishments of this great mathematician and significant figure in intellectual history.

306 pages, Hardcover

First published February 1, 2000

Reviews

[Michael Connolly · Rating 3 out of 5]

Steve Smale was the first mathematician to show that topology does not permanently get more and more complicated as the dimension increases, but rather only temprarily. Starting in dimension five, the topology actually starts getting simpler as the dimension increases. The dimensions of maximal complexity are three and four. In dimensions three and four, there is enough room for things to get complicated, but not enough room to uncomplicate them. In recent years, there has been an explosion of work in dimensions three and four. Smale was way ahead of his time.