The Clay Prizes

The Committee offers prizes (comparable in monetary value to the Nobel prizes) for solving any of seven major problems in mathematics.

One of the topics offering $1M is to prove the Poincaré conjecture. This concerns the equality of the homotopy group of a general manifold: if the first and second homotopy groups are the same as those for the 3-sphere, then Poincaré conjectured that the manifold is isomorphic to the 3-sphere. This conjecture has now been proved.