Manifold Destiny

From Wikipedia, the free encyclopedia

"Manifold Destiny"^[1] is an article in The New Yorker written by Sylvia Nasar and David Gruber, published in the August 28, 2006 issue of the magazine, but made available online around August 21, 2006.

The article gives a detailed account, with interviews of many mathematicians, of some of the alleged circumstances surrounding Grigori Perelman's proof of the Poincaré conjecture and the attempts at its verification by three teams of mathematicians.

1 Perspective of the article
2 Summary
3 List of interviewees
4 Controversy
5 Erratum to Cao/Zhu Article
6 See also
7 References
8 External links

[edit] Perspective of the article

It describes Perelman's disillusionment and withdrawal from the mathematical community (with the only extensive media interview of Perelman) and paints an unflattering portrayal of the 1982 Fields Medallist, Shing-Tung Yau.

Subtitled "A legendary problem and the battle over who solved it", the article concentrates on the depiction of the human drama surrounding the attempts, made by three separate teams of mathematicians, at verifying Perelman's proof of the Poincaré (and possibly, Thurston's Geometrization) conjecture. Interwoven with the article is an interview with the reclusive Perelman, whom the authors tracked down to the St. Petersburg apartment that he shared with his mother.

[edit] Summary

The article begins with a description of Yau lecturing on the work of his students, Xi-Ping Zhu and Huai-Dong Cao, in Beijing, on the occasion of Strings 2006^[2], an international conference on string theory. The work in concern was their effort in verifying Perelman's proof. Zhu and Cao were one of three teams that had undertaken this task.

The article then moves to an interview with the reclusive Perelman, discussing the Fields Medal, Perelman's life before the proof, Richard Hamilton's formulation of a strategy to prove the conjecture, and William Thurston's geometrization conjecture. Yau's long collaborative friendship with Hamilton, which started after Yau learned of the latter's work on the Ricci flow, is mentioned.

Subsequently, the article describes Yau in relation to the late Shiing-Shen Chern, his PhD advisor and the acknowledged top Chinese mathematician; as well as Yau's activities in the Chinese mathematical community. In the words of the authors, "he was increasingly anxious ... [that] a younger scholar could try to supplant him as Chern's heir."^[1]

Interweaving comments by many mathematicians, Nasar and Gruber present a complex narrative that touches upon matters peripheral to the Poincaré conjecture but reflective of the politics of the mathematics field:

Yau's supposed involvement in controversy surrounding Alexander Givental's proof of a conjecture in the mathematics of mirror symmetry;
his alleged attempt (which he denied, according to the article) to bring the ICM 2002 to Hong Kong instead of Beijing, and the alleged tussle that resulted between him and the Chinese mathematical community;
and the Tian-Yau affair of 2005, in which Yau allegedly accused his student Gang Tian (who was also one of the members of a team verifying Perelman's proof) of plagiarism and poor scholarship while criticizing Peking University in an interview.

In relation to the Poincaré conjecture, however, Nasar and Gruber also reveal an allegation against Yau that had apparently not been reported in the press prior to the (online) appearance of their article:^[3]

On April 13th of this year, the thirty-one mathematicians on the editorial board of the Asian Journal of Mathematics received a brief e-mail from Yau and the journal’s co-editor informing them that they had three days to comment on a paper by Xi-Ping Zhu and Huai-Dong Cao titled “The Hamilton-Perelman Theory of Ricci Flow: The Poincaré and Geometrization Conjectures,” which Yau planned to publish in the journal. The e-mail did not include a copy of the paper, reports from referees, or an abstract. At least one board member asked to see the paper but was told that it was not available.

This paper was the result of the abovementioned work of Zhu-Cao, which Yau promoted in the Beijing conference.^[4] The New Yorker article concludes by linking the alleged actions of Yau with Perelman's withdrawal from the mathematical community, alleging that Perelman claimed not to see "what new contribution [Cao and Zhu] did make," that he had become disillusioned by the lax ethical standards of the community, and that he had seen much worse behaviour than Yau's. The article is accompanied by a controversial full-page cartoon, described below.

[edit] List of interviewees

(In order of appearance)

Shing-Tung Yau.
Grigori Perelman.
John Morgan, Tian's collaborator in verifying Perelman's proof, and a mathematician at Columbia University.
Yuri Burago, Perelman's PhD advisor, and a mathematician at Steklov Institute of Mathematics in St. Petersburg.
Daniel W. Stroock, a mathematician at MIT.
Gang Tian, a mathematician at Princeton University.
Barry Mazur, a mathematician at Harvard University.
Phillip Griffiths, a former director of the IAS.
An unnamed relative of S. S. Chern.
An unnamed friend of Yau and Hamilton.
Mikhail Gromov, a permanent member of IHÉS, and Jay Gould Professor of Mathematics at New York University.
Michael Anderson, a mathematician at SUNY Stony Brook.
Alexander Givental, a mathematician at UC Berkeley.
Vitali Kapovitch, a mathematician at the University of Maryland. (Not actually interviewed, but email from him to Perelman was quoted.)
Fedor Nazarov, a mathematician at Michigan State University.
Frank Quinn, a mathematician at Virginia Tech.
Joseph Kohn, a mathematician at Princeton University.

[edit] Controversy

The article, and an included full-page color illustration of Yau grabbing the Fields Medal hanging around Perelman's neck [2], has garnered controversy. It has been the subject of extensive commentaries in the blogosphere. The controversy revolves around: emphasis on Yau's alleged stake in the Poincaré conjecture; its view that Yau was unfairly taking credit away from Perelman; and its depiction of Yau's supposed involvement in unrelated past controversies.

On September 18, 2006, a few weeks after publication of the article, Yau's attorneys released a letter accusing The New Yorker and the article's authors of defaming Yau. In the letter, the reporters are accused of fabricating quotes and deliberately molding facts into a narrative they knew to be inaccurate.^[5]^[6] The letter also asks for a public apology from The New Yorker. The letter appeared online on Yau's website, apparently created in response to the controversy. The New Yorker has issued a response to the letter, stating they stand by the piece and the journalists and citing the amount of time its staff put into the research, interviews, and fact-checking for the article. ^[7]

Three of the mathematicians interviewed — Stroock, Anderson and Kohn — have allegedly issued statements of clarification online, after the article became available online.^[8] These statements appeared to be in the form of emails to Yau and some graduate students. ^[9] On Oct 6, 2006, the statements from Stroock and Andersen were posted on Yau's website.^[10]^[11]

On September 25, 2006, a letter from Richard Hamilton was posted on Yau's website.^[12] Hamilton detailed a personal account of the history of the Ricci flow approach to the Poincare conjecture, saying he was very disturbed by the unfair manner in which Yau had been portrayed in the New Yorker article.

As of Oct 16, 2006, eight mathematicians in total have posted letters expressing support for Yau on his website.^[13]

On Oct 17, 2006, a profile of Yau appeared on the New York Times that devotes about half of its length to the Perelman affair. ^[14] The article acknowledges that Yau's promotion of the Cao-Zhu paper "annoyed many mathematicians, who felt that Dr. Yau had slighted Dr. Perelman," but it focuses more on Yau's position, which is that Perelman's proof was not understood by all and he "had a duty to dig out the truth of the proof."

[edit] Erratum to Cao/Zhu Article

The New York Times article [3] also uncovered that a key argument in the Cao-Zhu paper was copied almost word-for-word from a 2002 paper by Kleiner and Lott. A side-by-side comparison can be viewed here [4]. This led to an Erratum in the Cao-Zhu paper [5].