Thursday, August 17, 2006

Poincare Again

I wrote about the mathematics problem called the Poincare Conjecture a few days ago and Grigory Perelman's proof of it. Since Perelman published and lectured about his results in 2002 and 2003 I have been Googling the news each day about the problem and have gotten zero results. Now there is an avalanche of news stories about it. The stories are more about the man than the math problem.

And why not? Perelman is a certified mathematical genius who did post-doc work in the US until he returned to St. Petersburg, Russia in the mid-Nineties. Some thought he had given up mathematics until he published his stunning results on the Internet in November 2002. Mathematicians have been checking his proof of Poincare since. Several long papers recently published by other mathematicians have validated his proof.

Perelman is eligible for the Fields Medal this year. The Fields Medal is given to those mathematicians under 40 years of age who have done the most outstanding work in mathematics. Perelman turned 40 in June and is still eligible by the rules. People are speculating on whether Perelman, incredibly reclusive, will show up to receive his medal. Just to put the Fields Medal in perspective, it is the equivalent of the Nobel Prize. No lightweights need apply.

On top of that, the Clay Math Institute will award a million dollars to the person who proves or disproves the Poincare conjecture. The rules state that the proof must be published in a peer reviewed journal and withstand the scrutiny of the mathematics community for two years. Perelman has not published his proof other than on the Internet. Other mathematicians have filled in the details and published papers recently. They all give credit to Perelman and claim their papers are exposition and explanation of his proof. That in itself is more than a little humble on their part because their papers run to several hundred pages of arcane mathematics.

But at least Perelman and the Poincare Conjecture are finally making the news after a frustrating lull in the reporting of it. I am really excited. Some people hate math, but what is not to like about a field where you can actually prove something profound like Thurston's geometrization conjecture and hence the Poincare conjecture a special case of it?

Thanks, Mr. Perelman. And just in case you are reading this, Mr. Perelman, even though I know you never will, I think you should pick up the Fields Medal, the million dollars, and the thunderous applause you deserve.

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