Do you want to be a mathematical millionaire? The Poincare conjecture

Last May in Paris, the Clay Institute announced $1,000,000 prizes for each of seven ``Millenium problems" of mathematics. This is the first in a series (by different speakers) to discuss these problems in a way that is hopefully accessible to the rest of us.

The Poincare conjecture is a century old, and a solution seems as far away as ever. The conjecture -- deceptively simple to state -- is that the 3-sphere is the only simply-connected closed 3-dimensional manifold. I will explain all these terms, some of the conjecture's fascinating history, partial results, and its importance in the program of classification of 3-manifolds and understanding the possible shapes of our universe.