In the early 20th Century, Henri Poincare conjectured that the three-dimensional sphere is the only compact three-dimensional manifold which is simply connected. This is now called the Poincare Conjecture.

This conjecture is the dimension three case of the Generalized Poincare Conjecture, which makes a similar assertion for manifolds in an arbitrary dimension. Amazingly, the dimension three case (which the original case conjectured by Poincare) is the only one which has not yet been solved.

This conjecture is one of the seven Millenium Prize Problems proposed by the Clay Mathematics Institute.

It appears that topologist Martin Dunwoody has proposed a general proof for the Poincare Conjecture. As of April 7, 2002, this proof is in preprint, available for now at
As I am not a mathematician, I will not attempt to provide a layman's explanation of the conjecture. It is worth noting that if the proof stands, Dr. Dunwoody may be a very wealthy man - the Clay Institute prize is one million dollars!

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