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

User Review - Not Available - Book VerdictIn 1904, Henri PoincarÃƒÂ¯Ã‚Â¿Ã‚Â½ (1854-1912) challenged the world to solve one of the 20th century's most famous mathematical problems, collectively named the PoincarÃƒÂ¯Ã‚Â¿Ã‚Â½ Conjecture and ... Read full review

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

User Review - Erickson Tjoa - GoodreadsGood introduction to Poincare Conjecture as well as some mathematics surrounding it. However, it contains a little too much of historical accounts and contexts in which the conjecture was made, thus making this book less informative mathematically than expected. 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 non-Euclidean 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 three-dimensional manifold three-manifolds three-space three-sphere Thurston tions topologist topology translation triangle two-dimensional manifold two-dimensional sphere two-holed torus universe Veblen wrote