poincare conjecture
Poincare Conjecture And Mathematics Complete Details
In mathematics, the Poincaré conjecture is a theorem about the characterization of the three-dimensional sphere among three-dimensional manifolds. Originally conjectured by Henri Poincaré, the claim concerns a space that locally looks like ordinary three-dimensional space but is connected, finite in size, and lacks any boundary (a closed 3-manifold). The Poincaré conjecture claims that if such a space has the additional property that each loop in the space can be continuously tightened to a point, then it is necessarily a three-dimensional sphere. An analogous result has been known in higher dimensions for some time.
The Poincaré conjecture concerns the three-dimensional equivalent of this situation. It asserts that if any loop in a closed three-dimensional space without boundary can be shrunk to a point without tearing either the loop or the space, then the space is equivalent to a three-dimensional sphere.
In March 2010, the Clay Mathematics Institute (CMI) of Cambridge, Massachusetts, announced that Perelman, 43, would be awarded the prize for proving the Poincare conjecture, one of seven problems on the institute’s Millennium Prize list.
In June, Perelman did not appear at a ceremony in Paris to collect the prize and did not inform CMI about his decision regarding the money.
The Poincare conjecture, which was first proposed by Henri Poincare in 1904, says that a three-sphere is the only type of bounded three-dimensional space possible that contains no holes.
Perelman presented proof on the conjecture in 2002 and 2003. Several high-profile teams of mathematicians have since verified the correctness of his proof.
In 2006, Perelman refused to attend a congress in Madrid where he was to receive a Fields Medal, often called the Nobel Prize of mathematics.
Perelman, who lives in a small apartment in St. Petersburg with his elderly mother, is unemployed and neighbors say he lives in poverty. He has rejected job offers at several top U.S. universities.
