Thursday, February 15, 2007

When Mathematicians Rumble

There's nothing like watching a rousing good fight, even when it's among a bunch of egghead mathematicians rumbling over who gets credit for the geometrization conjecture which substantiated that Russian mathematician Grigori Perelman had, indeed, proved the Poincaré conjecture.
In 2003, when Perelman revisited the United States to lecture on his work, many mathematicians doubted that he could have pulled off all of these feats. By 2006, however, the mathematical community had finally caught up. Three separate manuscripts, each more than 300 pages in length, filled in key missing details of Perelman's proof.

Two of the papers -- one authored by Bruce Kleiner and John Lott of the University of Michigan, Ann Arbor, the other by John Morgan of Columbia University and Gang Tian of the Massachusetts Institute of Technology in Cambridge -- stopped short of the geometrization conjecture, because Perelman's explanation of the final step had been too sketchy. (Both groups are still working on it.) They did, however, include enough math to nail down the Poincaré conjecture.

The third paper, by Huai-Dong Cao of Lehigh University in Bethlehem, Pennsylvania, and Xi-Ping Zhu of Zhongshan University in Guangzhou, China, was less circumspect. Cao and Zhu claimed to have "the first written account of a complete proof of the Poincaré conjecture and the geometrization conjecture of Thurston." This summer, the International Mathematical Union (IMU) decided to award Perelman the Fields Medal, traditionally considered the highest honor in mathematics.
* * *
Since then, the rosy glow of triumph has taken on darker hues. * * *Perelman declined the Fields Medal. * * * In an interview in The New Yorker, the reclusive mathematician said he was retiring from mathematics, disenchanted by unspecified lapses in "ethical standards" by colleagues. The New Yorker article also painted an unflattering portrait of Yau, intimating that he had claimed too much credit for his protégés Cao and Zhu.

In the ensuing months, hard feelings have abounded. Certain mathematicians claimed that their quotes were distorted in the New Yorker, and Yau threatened to sue. Kleiner and Lott complained that Cao and Zhu had copied a proof of theirs and claimed it as original, and the latter pair grudgingly printed an erratum acknowledging Kleiner and Lott's priority.

This fall, the American Mathematical Society attempted to organize an all-star panel on the Poincaré and geometrization conjectures at its January 2007 meeting in New Orleans, Louisiana. According to Executive Director John Ewing, the effort fell apart when Lott refused to share the stage with Zhu.

Got that? Pop quiz soon.

Poor New Orleans. They can't even host a peaceful mathematics convention.

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