The Poincare Conjecture: In Search of the Shape of the Universe

The Poincare Conjecture: In Search of the Shape of the Universe

by Donal OShea, Shea
     
 

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Henri Poincaré 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 Poincaré conjecture lies at the heart of modern geometry and topology, and even pertains to the possible shape

Overview

Henri Poincaré 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 Poincaré 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.

Poincarés 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 Poincaré Conjecture, Donal OShea 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 Perelmans proof of this famous conjecture.

Editorial Reviews

In everyday life, conjectures are cheap; in mathematics, they sometimes stimulate years of vigorous theorizing. In the case of Henri Poincaré (1854-1912), the supposition was simply stated. "Consider a compact 3-dimensional manifold V without boundary," he wrote. "Is it possible that the fundamental group of V could be trivial, even though V is not homeomorphic to the 3-dimensional sphere?" At the time of his death, this pregnant thought was still in gestation. It would take almost a century for a mathematician to offer a persuasive proof of this major conundrum. Written for nonprofessional readers, The Poincaré Conjecture explains why the issue has loomed so large in scientific circles and also provides stimulating capsule biographies of the thinkers who prepared the way for its solution.

Product Details

ISBN-13:
9780802718945
Publisher:
Bloomsbury USA
Publication date:
05/26/2009
Sold by:
Barnes & Noble
Format:
NOOK Book
Pages:
304
Sales rank:
873,211
File size:
9 MB

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The Poincare Conjecture

In Search of the Shape of the Universe
By O'Shea, Donal

Walker & Company

Copyright © 2007 O'Shea, Donal
All right reserved.

ISBN: 080271532X

"Mathematical knowledge builds on the work of those who have gone before us. Any one of us with an elementary school education can solve arithmetic and algebraic problems that would have defeated the most learned Babylonian scribes. Any one of us with a few courses of calculus and linear algebra can solve problems that Pythagoras, Archimedes, or even Newton could not have touched. A mathematics graduate student today can handle topological calculations that Riemann and Poincaré could not have begun. We are not smarter than they. Rather, we are their beneficiaries."

Continues...

Excerpted from The Poincare Conjecture by O'Shea, Donal Copyright © 2007 by O'Shea, Donal. Excerpted by permission.
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Meet the Author

Donal OShea is professor of mathematics and dean of faculty at Mount Holyoke College. He has written scholarly books and monographs, and his research articles have appeared in numerous journals and collections. He lives in South Hadley, Massachusetts.
Donal OShea is professor of mathematics and dean of faculty at Mount Holyoke College. He has written scholarly books and monographs, and his research articles have appeared in numerous journals and collections. He lives in South Hadley, Massachusetts.

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