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Stephen Smale: The Mathematician Who Broke the Dimension Barrier
Steve Batterson, Emory University, Atlanta, GA

2000; 306 pp; softcover
ISBN-10: 0-8218-2696-4
ISBN-13: 978-0-8218-2696-6
List Price: US$44
Member Price: US$35.20
Order Code: MBDB.S
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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.


General mathematical audience; historians; nonmathematicians interested in biographies.


"To write this biography involved tremendous work, but the result is brilliant ... accessible for nonmathematicians ... On the other hand, the author's skillful presentation of Smale's mathematical discoveries will surely attract the interest of professional mathematicians ... in many respects it is a masterpiece."

-- European Mathematical Society Newsletter

"This well-researched book provides a great deal of personal and historical information on Smale, and also attempts to portray his mathematics for a general reader."

-- Mathematical Reviews

"Batterson's book is readable by, and accessible to, high school students ... Smale's life is inspiring; Batterson's book is fascinating."

-- Mathematics Teacher

"Steve Batterson's book lays many legends to rest and verifies much chronology and many details ... This fascinating life story makes for compelling reading ... [Batterson] gets not just mathematical details but their relative importance right ... Waiting for history's verdict on Smale's numerical analysis, we might just as well curl up with Batterson's book ... this is a fascinating biography of a fascinating mathematician."

-- SIAM Review

"This is a comprehensive and frank biography of Stephen Smale, one of the best-known American mathematicians ... I found the book fascinating ... Smale deserved his Fields Medal for his work in topology and his early work (e.g., the horseshoe) in dynamical systems ... he should be seen as an excellent example of how to avoid stagnation in a field one has pioneered and instead to stay active by trying new subjects ... All in all, Steve Smale is a first-rate Fields Medalist who has led a rich and varied life."

-- Notices of the AMS

"Batterson has done an outstanding job of collecting factual information on Smale's youth and education ... This information should be read by the rank and file of all undergraduate and graduate students in mathematics ... Read this book. You are certain to react. Batterson's insight on Smale's personality is a wonderful suggestion for all in research."

-- MAA Online

Table of Contents

  • One room schoolhouse
  • Marxism and mathematics at Ann Arbor
  • Early mathematical audacity
  • On the beaches of Rio
  • Berkeley to Columbia and back to Berkeley
  • The Lone Ranger of the antiwar movement
  • The summer of 1966
  • Smale versus the National Science Foundation
  • The aesthetic side: Minerals and photography
  • Adventure and physical risks
  • Other people
  • Smale the mathematician
  • Mathematical appendix A: Smale's thesis
  • Mathematical appendix B: Everting the sphere
  • Mathematical appendix C: Chaos and the horseshoe
  • Mathematical appendix D: The higher dimensional Poincaré conjecture
  • Notes
  • Index
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