2000;
306 pp;
Softcover

MSC: Primary 01;
Secondary 34; 55; 58; 65

**Print ISBN: 978-0-8218-2696-6
Product Code: MBDB.S**

List Price: $44.00

AMS Member Price: $35.20

MAA member Price: $39.60

#### Supplemental Materials

# Stephen Smale: The Mathematician Who Broke the Dimension Barrier

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*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.

#### Readership

General mathematical audience; historians; nonmathematicians interested in biographies.

#### Reviews & Endorsements

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