"O'Shea tells the fascinating story of this mathematical mystery and its solution by the eccentric Mr. Perelman."-Wall Street Journal
In 1904, Henri Poincaré, a giant among mathematicians who transformed the fledging area of topology into a powerful field essential to all mathematics and physics, posed the Poincaré conjecture, a tantalizing puzzle that speaks to the possible shape of the universe. For more than a century, the conjecture resisted attempts to prove or disprove it. As Donal O'Shea reveals in his elegant narrative, Poincaré's conjecture opens a door to the history of geometry, from the Pythagoreans of ancient Greece to the celebrated geniuses of the nineteenth-century German academy and, ultimately, to a fascinating array of personalities-Poincaré and Bernhard Riemann, William Thurston and Richard Hamilton, and the eccentric genius who appears to have solved it, Grigory Perelman. The solution seems certain to open up new corners of the mathematical universe.
|Publisher:||Walker & Company|
|Edition description:||First Edition|
|Product dimensions:||5.56(w) x 8.33(h) x 0.85(d)|
About the Author
Donal O'Shea is a professor of mathematics and the dean of faculty and vice president for academic affairs of Mount Holyoke College in Massachusetts. This is his first book for a general audience. He lives in South Hadley, Massachusetts.
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The Poincare ConjectureIn Search of the Shape of the Universe
By O'Shea, Donal
Walker & CompanyCopyright © 2007 O'Shea, Donal
All right reserved.
"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."
Excerpted from The Poincare Conjecture by O'Shea, Donal Copyright © 2007 by O'Shea, Donal. Excerpted by permission.
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Table of Contents
Cambridge, April 2003 1
The Shape of the Earth 6
Possible Worlds 21
The Shape of the Universe 32
Euclid's Geometry 46
The Non-Euclideans 57
Bernhard Riemann's Probationary Lecture 75
Riemann's Legacy 88
Klein and Poincare 106
Poincare's Topological Papers 122
The Great Savants 137
The Conjecture Takes Hold 151
Higher Dimensions 163
A Solution in the New Millennium 182
Madrid, August 2006 195
Glossary of Terms 241
Glossary of Names 247
Further Reading 271
Art Credits 273