This video gives an explanation of the Poincaré Conjecture from ABC science program Catalyst.
In mathematics, the Poincaré conjecture is a theorem about the characterization of the three-dimensional sphere among three-dimensional manifolds.
The Poincaré Conjecture tries to answer how multi-dimensional shapes behave in space.
Jules Henri Poincaré (29 April 1854 – 17 July 1912) was a French mathematician, theoretical physicist, and a philosopher of science. He is often described as a polymath, and in mathematics as The Last Universalist, since he excelled in all fields of the discipline as it existed during his lifetime. He was responsible for formulating the Poincaré conjecture, one of the most famous problems in mathematics.
Grigori Yakovlevich Perelman (born on 13 June 1966) is a Russian mathematician, who has made landmark contributions to Riemannian geometry and geometric topology. In particular, he proved Thurston's geometrization conjecture. This solves in the affirmative the famous Poincaré conjecture, posed in 1904. Grigori Perelman presented a proof of the conjecture in three papers made available in 2002 and 2003 on arXiv.org. The proof followed the program of Richard Hamilton.
Clay Mathematics Institute, $1,000,000 Prize
The Poincaré conjecture, before being proven, was one of the most important open questions in topology. It is one of the seven Millennium Prize Problems, for which the Clay Mathematics Institute offered a $1,000,000 prize for the first correct solution. Perelman's work survived review and was confirmed in 2006. Perelman was awarded the Millennium Prize on 18 March, 2010. On 1 July, 2010, the Clay Mathematics Institute in Cambridge, Mass. announced that Perelman, once again, declined the $1,000,000 prize stating his "disagreement with the organized mathematical community" and that he doesn't "like their decisions", considering them unjust.