Poincare's Prize: The Hundred-Year Quest to Solve One of Math's Greatest Puzzles

Science News,  August 4, 2007  

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POINCARE'S PRIZE: The Hundred-Year Quest to Solve One of Math's Greatest Puzzles GEORGE G. SZPIRO

In 1904, French mathematician Henri Poincare proposed the following problem: Imagine an ant crawling on a large surface. How would it know whether that surface were flat, spherical, or bagel shaped? The obvious answer is that it would have to lift off into space to observe the object. But is it possible to prove that a surface is spherical without actually seeing it? Poincare struggled unsuccessfully to solve his conjecture. During the century that followed, it became the holy grail of mathematics. Its solution would, mathematicians declared, enable us to understand the shape of the universe. Szpiro chronicles the history of Poincare's conjecture, the key events of the mathematician's life, and the many failed attempts to solve this topological problem. His story then takes a new turn. In 2003, an ascetic Russian mathematician named Gregory Perelman solved the century-old problem and unceremoniously posted on the Internet three papers summarizing his findings. Szpiro profiles Perelman's landmark proof and his mystifying desire to avoid the accompanying celebrity and honors. Dutton, 2007, 309 p., hardcover, $24.95.

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