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The Shape of a Life

Shing-Tung Yau and Steve Nadis
Yale University Press
Publication Date: 
Number of Pages: 
[Reviewed by
Bill Satzer
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This autobiography of Shing-Tung Yau traces his life from earliest memories of the small village in China, where he was born, to his current position as one of the best-known mathematicians in the world. Yau’s family was very poor, but his parents valued learning and did their utmost to support his education. He attended Chung Chi College and completed work for a degree that was never awarded. Yau’s mathematical ability brought him to the attention of a young mathematician with a Ph.D. from Berkeley who contrived to get Yau admitted to the graduate program there. After that he was off and running.

Yau was particularly attracted to geometry and began work on unsolved problems almost immediately. His advisor was Shiing-Shen Chern with whom he had an uncomfortably complicated relationship. Yau’s official thesis was based on work he had done independently of Chern. Yau believes this created a conflict because Chern never felt like Yau’s real advisor. (At one point Chern had suggested that Yau’s thesis problem should to prove the Riemann hypothesis.)

Yau became a practitioner and an advocate of the field now often called “geometric analysis,” which combines geometry, topology and partial differential equations. One of his first major results was resolution of the Calabi conjecture on the existence of what came to be called Calabi-Yau manifolds. This eventually led him into wider contact with physicists and questions about string theory. Another of Yau’s major accomplishments was his solution of the positive mass conjecture in three dimensions.

Several things about Yau stand out in his book. One is how hard he works. He believes that his success is due to consistent and continuous hard work and not to any genius on his part. Notable too is the enormous number of acquaintances he has in the mathematics and physics communities. One is also struck by the number of universities and institutes where Yau has held positions and how extensively he has traveled. Beyond this, he has also done a great deal to support mathematics in China by establishing and finding funding for mathematical centers.

Yau’s book suggests that his overriding ambition is to pursue what is best for mathematics and mathematics education. This, together with a certain naiveté about institution politics and an overly aggressive pursuit of his goals, have led him into several controversies that he might have avoided.

Although there is a lot of discussion of mathematics in the book, it is at a very general level and accessible to all kinds of readers. There are descriptions and images of Calabi manifolds and other exotic structures, but a casual reader would never develop more than the vaguest notion of what they are from the text. Somehow this works, though there are likely to be readers who are frustrated by the lack of detail.

This is a well-written and readable story of a very accomplished man’s life. The extensive discussion of the controversies that Yau has inspired may put off some readers, at least partly because of the defensiveness he displays. But he has received some very harsh public criticism (the New Yorker article by Sylvia Nasar and David Gruber, for example), and this book has given him another opportunity to respond to it.

Bill Satzer ( was a senior intellectual property scientist at 3M Company. His training is in dynamical systems and particularly celestial mechanics; his current interests are broadly in applied mathematics and the teaching of mathematics.