The Poincare Conjecture

In Search of the Shape of the Universe

By: Donal O'Shea

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Hardcover | 6 March 2007

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Henri Poincare was one of the greatest mathematicians of the late nineteenth and early twentieth century. He revolutionized the field of topology, which studies properties of geometric configurations that are unchanged by stretching or twisting. The Poincare conjecture lies at the heart of modern geometry and topology, and even pertains to the possible shape of the universe. The conjecture states that there is only one shape possible for a finite universe in which every loop can be contracted to a single point.
Poincare's conjecture is one of the seven "millennium problems" that bring a one-million-dollar award for a solution. Grigory Perelman, a Russian mathematician, has offered a proof that is likely to win the Fields Medal, the mathematical equivalent of a Nobel prize, in August 2006. He also will almost certainly share a Clay Institute millennium award.
In telling the vibrant story of "The Poincare Conjecture," Donal O'Shea makes accessible to general readers for the first time the meaning of the conjecture, and brings alive the field of mathematics and the achievements of generations of mathematicians whose work have led to Perelman's proof of this famous conjecture.

Industry Reviews

"Donal O'Shea has written a truly marvelous book. Not only does he explain the long-unsolved, beautiful Poincare conjecture, he also makes clear how the Russian mathematician Grigory Perelman finally solved it. Around this drama O'Shea weaves a tapestry of elementary topology and astonishing concepts, such as the Ricci flow, that have contributed to Perelman's brilliant achievement. One can't read "The Poincare Conjecture "without an overwhelming awe at the infinite depths and richness of a mathematical realm not made by us."--Martin Gardner, author of "The Annotated Alice" and "Aha! Insight""The history of the Poincare conjecture is the story of one of the most important areas of modern mathematics. Donal O'Shea tells that story in a delightful and informative way--the concepts, the issues, and the people who made everything happen. I recommend it highly."--Keith Devlin, Stanford University, author of "The Millennium Problems""In "The Poincare Conjecture", Mr. O'Shea tells the fascinating story of this mathematical mystery and its solution by the eccentric Mr. Perelman . . . Mr. O'Shea does a good job of explaining the mathematics involved in solving the conjecture . . . [He] avoids cliche (we're spared the usual reference to coffee cups turning into doughnuts as an explanation of how surfaces might stretch without closing holes), and he tries to keep things lively."--"Amir D. Aczel, The Wall Street Journal"

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