Henri Poincar 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 Poincar 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.

Poincar '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 Poincar 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.

多纳尔·欧谢是马塞诸塞州曼荷莲学院的伊丽莎白·T·凯南讲席教授。在过去的25年里,他的著作和论文被世界范围的学者们阅读,并被翻译成多种欧洲文字,以及俄文、中文和日文。欧谢是高维空间奇点拓扑学和几何学方面的专家。