The Poincare Conjecture: In Search of the Shape of the Universe (Google eBook)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. 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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Review: The Poincare Conjecture: In Search of the Shape of the Universe
User Review  Katlego Makgoale  GoodreadsI enjoy books about mathematics. Not a daunting read, easily understood and very clear explainations. Takes some imagination and thinking to get ones mind around the concepts discussed but all in all ... Read full review
Review: The Poincare Conjecture: In Search of the Shape of the Universe
User Review  Snoakes  GoodreadsI assume that as you've read past the title, then you have embraced your inner nerd. Because you'll need to be quite nerdy to appreciate this book (I've given it four stars  says quite a lot about me ... Read full review
Contents
1  
6  
Possible Worlds  21 
The Shape of the Universe  32 
Euclids Geometry  46 
The NonEuclideans  57 
Bernhard Riemanns Probationary Lecture  75 
Riemanns Legacy  88 
The Conjecture Takes Hold  151 
Higher Dimensions  163 
A Solution in the New Millennium  182 
Madrid August 2006  195 
Notes  201 
Glossary of Terms  241 
Glossary of Names  247 
Timeline  253 
Klein and Poincare  106 
Poincares Topological Papers  122 
The Great Savants  137 
259  
Art Credits  273 
Common terms and phrases
180 degrees algebraic American Mathematical Society angle sum atlas axioms Berlin Betti numbers 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 geodesies geometrization conjecture German Gottingen Greek Hamilton Henri Poincare Hilbert homeomorphic ideas imagine Institute invariants Janos Klein knot lecture Lobachevsky loop mathe mathematical object mathematicians matical metric nonEuclidean geometry notion octagon paper Paris Perelman plane Poincare conjecture Poincare's Princeton problem professor proof proved Ptolemy Pythagoras Pythagorean real numbers region result Ricci flow Riemann Russian shape simply connected solid balls spherical straight lines student surface theorem theory threedimensional manifold threemanifolds threespace threesphere Thurston tions topologist topology tori translation triangle twodimensional manifold twodimensional sphere twoholed torus universe Veblen wrote