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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.

From the Publisher

“O'Shea tells the fascinating story of this mathematical mystery and its solution by the eccentric Mr. Perelman.”—Wall Street Journal

Publishers Weekly

The reclusive Russian mathematician Grigory Perelman became a minor media celebrity last summer when he refused the prestigious Fields medal, awarded every four years to a mathematician under the age of 40. Perelman had succeeded in solving the Poincaré conjecture, named for 19th-century French mathematician Henri Poincaré, and which contemporary cosmologists believe has implications for our understanding of the shape of the universe. O'Shea, a professor of mathematics at Mount Holyoke College, begins his account of the long and contentious search for a solution to the puzzle by looking at how we came to understand the shape of the Earth, beginning with the Greeks, in particular Pythagoras and Plato. Writing for generalist science buffs, O'Shea gives a brief course in geometry and in topology and the topological structures called manifolds that are the basis of Poincaré's puzzle. Inexplicably, however, O'Shea doesn't give readers a formal statement of the conjecture itself until well into the book. O'Shea describes mind-bending structures in topology as clearly as most of us can describe a cube, but readers will need to do a little Wikipedia-ing first to find out just what it is they're reading about. Illus. (Mar.)

Ian D. Gordon - Library Journal

In 1904, Henri Poincaré (1854–1912) challenged the world to solve one of the 20th century's most famous mathematical problems, collectively named the Poincaré Conjecture and involving configuring multidimensional space using algebraic topology. Poincaré asked a basic question of what it means for mathematical space to be curved. O'Shea (mathematics, Mount Holyoke Coll.) traces the footsteps of mathematicians like Euclid, Gauss, Riemann, and their contemporaries to prove one of mathematics' greatest puzzles, which eventually culminated with Grigori Perelman's eclectic, brilliant solution in 2003. O'Shea inspires readers to note the beauty, application, and humanity involved with this mathematical journey. Writing for readers with limited mathematical background, O'Shea successfully weaves mathematical proofs with curious insights to tell a great story, along with reams of valuable endnotes and figures. For all mathematicians and academic and larger public libraries.

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The Poincare Conjecture

Walker & Company

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