Interesting Math Article

by DPatrick, May 21, 2010, 4:30 PM

We're hoping to use this blog not just for AoPS announcements and such, but for some math entries too! Such as:

Discover magazine has this month an interesting interview with S-T Yau, who is one of the major contributors to the mathematics behind string theory. String theory is one of the "hottest" areas of current mathematics and physics research, though not without controversy. The interview is fascinating: Yau is one of the giants of mathematics in the past 50 years, and he shares many personal anecdotes in the article. (The photo in the article is pretty bizarre, though.)

Yau has recently been in the mathematical news regarding the proof of the Poincaré conjecture, one of the 7 Millennium Problems. From the interview:
Quote:
Most people don’t realize how political math can be: In 2006 The New Yorker accused you of taking credit from the Russian mathematician Grigory Perelman after he proved the famed Poincaré conjecture. What happened there?
In a process as intricate and daunting as proving the Poincaré conjecture, it is understandable that Perelman released his manuscript with several key steps merely sketched or outlined. One of my students tried to fill in some of the details, and I supported that. I also said that my friend Richard Hamilton, a geometer at Columbia University, laid much of the groundwork that Perelman ultimately relied on to construct his proof. For these things The New Yorker tried to accuse me of stealing credit, but that is ridiculous. What I think of as the Hamilton-Perelman proof of the Poincaré conjecture is a great triumph for mathematics, and I fully support the award of the Fields Medal to Perelman. Hamilton deserved the Fields Medal too, but he was ineligible because of the age restriction [you must be under 40]. To suggest that my position has ever been any different is completely untrue.

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I still don't know if Yau actually tried to gain some credits on Pereleman's proof of Poincare conjecture. The main thing about this issue that bothers me is that Pereleman didn't care about these things, so he didn't publicly fight back to gain fully his credits. However, Yau was right that Hamilton set a foundation by merely connecting some theorems about Ricci flows to the Poincare conjecture, which indeed worked and set up the foundation for Pereleman's proof. Unfortunately, Hamilton got stuck forever on an important statement in his proof, and was never able to prove that statement(conjecture, I think) . Pereleman came up, used his own "theorems", which he found out while working alone on Poincare conjecture, and proved Hamilton's conjecture completely. As a result, Pereleman went on and blew off the Poincare conjecture(Hamilton should have gotten the Field Medals if he accepted Pereleman's suggestion on collaborating to prove Poincare conjecture, but he didn't! :wink:)

by ghjk, May 27, 2010, 6:10 PM

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