The Poincare Conjecture: In Search of the Shape of the UniverseHenri 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. Poincaré's conjecture is one of the seven "millennium problems" that bring a onemilliondollar 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 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. 
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LibraryThing Review
User Review  dcunning11235  LibraryThingThis was a decent book, but a bit of a hard read. Firstly, the book introduces many concepts by name, with some short descriptions, and then goes on to discuss them in some qualitative detail; how one ... Read full review
LibraryThing Review
User Review  dcunning11235  LibraryThingThis was a decent book, but a bit of a hard read. Firstly, the book introduces many concepts by name, with some short descriptions, and then goes on to discuss them in some qualitative detail; how one ... Read full review
Contents
Madrid August 2006  195 
Glossary of Terms  241 
Glossary of Names  247 
Timeline  253 
259  
Art Credits  273 
Other editions  View all
The Poincare Conjecture: In Search of the Shape of the Universe Donal O'Shea Limited preview  2009 
The Poincare Conjecture: In Search of the Shape of the Universe Donal O'Shea Limited preview  2007 
The Poincaré Conjecture: In Search of the Shape of the Universe Donal O'Shea Limited preview  2008 
Common terms and phrases
180 degrees algebraic American Mathematical Society angle sum atlas axioms Berlin Bolyai boundary calculus called century circle Clay Institute connected sum correspondence curve defined Dehn Dehn's Dehn's lemma dimension direction disk distance Earth edge Elements Euclid Euclidean space Farkas Fields Medal fifth postulate figure finite French functions fundamental group Gauss geodesics geometrization conjecture German Göttingen Greek Grigory Perelman Hamilton Henri Poincaré Hilbert homeomorphic imagine Institute invariants János Klein knot lecture Lobachevsky loop mathe mathematical object mathematicians matical metric nearby points nonEuclidean geometry notion octagon paper Paris Perelman plane Poincaré conjecture Princeton problem professor proof proved Ptolemy Pythagoras Pythagorean real numbers region result Ricci flow Riemann Russian shape shrunk simply connected solid balls spherical straight lines student surface theorem theory threedimensional manifold threemanifolds threespace threesphere Thurston tions topologist topology translation triangle twodimensional manifold twodimensional sphere twoholed torus universe Veblen wrote