Qu'est-ce qu'un cercle? Ce n'est point carré.*

Lately I've been engrossed by Mount Holyoke math professor Donal O'Shea's fascinating mathematical history, The Poincaré Conjecture. While the topological discussions are a little over my head (I never did learn much about topology), the writing is accessible and the story fascinating.

For those who aren't familiar with Henri Poincaré and his famous conjecture, here is one way to state it: That every simply connected, compact three-dimensional manifold without boundary is homeomorphic to the three-dimensional sphere. The proof of this conjecture would have a lot to say about the shape of the universe, thus it has fascinated mathematicians and physicists for a century. The Clay Institute even declared it to be one of their seven Millennium Prize Problems, meaning one million dollars is on the line for whoever could offer a proof.

Though many tried and failed, it seems fairly certain that a relatively unknown Russian mathematician, Grigori Perelman, has finally proved the conjecture. Shy and reclusive, Perelman is the perfect hero for this 100-year story of alternately smugly or endearingly obsessed mathematicians. There is a two year period of review before the Clay Institute makes its prize offering official, but those in the know seem confident in Perelman's work. It's a shame Perelman seems to have quit math due to concerns about mathematical ethics and the high level of unwanted publicity he and his discovery received. Still, one Millennium Problem down, six to go.

*A play on words oft-repeated by adolescent French math nerds: What is a circle? It's not a square.