We’ve started work on some histograms of the orbits under the logistic family. Code and more pictures at viz.

via butdoesitfloat

Super nice video of the Hopf Fibration.

via imgfave

I was trained as a topologist. Since 1904, the Poincare conjecture has been the greatest unsolved problem in topology. In 2002-2003 a Russian mathematician, Grigory Perelman, essentially solved the Poincare conjecture. For his research he was awarded the Field’s medal, which is basically the Nobel prize of mathematics. He was also the first person to solve a Millennium Prize Problem and so he was awarded $1,000,000 from the Clay Math Institute. Grigory then TURNED DOWN both the Field’s medal and the $1,000,000. Grigory hasn’t been too stoked about talking to the media but he basically gave three reasons:

- Mathematical research is collaborative. Grigory couldn’t have solved the Poincare conjecture without the work of hundreds of fellow mathematicians. In particular, Grigory’s research relied heavily on the work of Richard Hamilton whom Grigory thought should be a co-recipient of any prizes. “To put it short, the main reason is my disagreement with the organized mathematical community,” Perelman, 43, told Interfax. “I don’t like their decisions, I consider them unjust.”
- Grigory did it for the math, not the fame or the money. Topology is an obscure and difficult subject. Grigory was offered fancy jobs at prestigious universities, but he was happier doing research in his hometown of St. Petersburg. The dude just wanted to chill at home with his moms and think about math. “I’m not interested in money or fame,” he is quoted to have said at the time. “I don’t want to be on display like an animal in a zoo. I’m not a hero of mathematics. I’m not even that successful; that is why I don’t want to have everybody looking at me.”
- Grigory was pissed at the biters. In 2006 Cao and Zhu published their own “proof” of the Poincare conjecture and declared it “the crowning achievement of the Hamilton-Perelman theory of Ricci flow.” A few months later they published various errata and retracted that “crowning achievement” statement. Grigory tried to keep his cool but made a variety of statements like, “I can’t say I’m outraged. Other people do worse. Of course, there are many mathematicians who are more or less honest. But almost all of them are conformists. They are more or less honest, but they tolerate those who are not honest.”

After all this drama, Grigory has reportedly QUIT professional mathematics. He’s now just another unemployed topologist living with mom. Since this is the last year of my contract with UConn, I’ll probably be following in Grigory’s footsteps next year – minus the prizes and all…. As a stupidier and less successful topologist, I basically agree with Grigory on all his beefs. But I think he should have given the $1,000,000 to charity. There’s alot of hungry babies out there. Anyway, overall I salute you, Grigory! Keepin it real. 1luv.