PINWHEELS FOR PERELMAN

Esoteric is far too weak a word for the work of Grigori Perelman. It’s like he sees mathematics on an entirely different plane of existence. One of his major accomplishments is proving the soul conjecture which goes like this:

“Suppose (M, g) is complete, connected and non-compact with sectional curvature K ≥ 0, and there exists a point in M where the sectional curvature (in all sectional directions) is strictly positive. Then the soul of M is a point; equivalently M is diffeomorphic to Rn.

Proof: In the general case K ≥ 0, Sharafutdinov’s retraction P : M → S is a submersion.”

I have no idea what that means either.

Perelman subsequently turned down the $1 million Clay Millennium Prize for the contributions his work had made to prove the Poincaré conjecture because he felt other’s work was more worthy.

Mr. Perelman, these mathematical pinwheels are dedicated to you and the breath of fresh air your ethics bring to the world.