Manifold Destiny

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

The article gives a detailed account (including interviews with many mathematicians) of some of the alleged circumstances surrounding Grigori Perelman's proof of the Poincaré conjecture, and traces the attempts by three teams of mathematicians to verify that proof.

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

[edit] Perspective of the article

The article describes Perelman's disillusionment and withdrawal from the mathematical community and paints an unflattering portrait of the 1982 Fields Medallist, Shing-Tung Yau.

Subtitled "A legendary problem and the battle over who solved it", the article concentrates on the human drama surrounding the attempts, made by three separate teams of mathematicians, to verify 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 he shares with his mother.

[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, College Park. (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] Summary

The article begins with a description of Yau lecturing on a paper^[2] by his students, Huai-Dong Cao and Xi-Ping Zhu, in Beijing, on the occasion of Strings 2006^[3], an international conference on string theory. That paper described their effort to verify Perelman's proof. Zhu and Cao were one of the three teams that had undertaken this task.

The article then moves on to an interview with the reclusive Perelman. The interview touches on the Fields Medal, Perelman's life prior to Perelman's proof of the Poincare Conjecture, 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 also 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 Nasar and Gruber, "he was increasingly anxious ... [that] a younger scholar could try to supplant him as Chern's heir."^[1]

Interweaving comments from many mathematicians, the authors present a complex narrative that touches upon matters peripheral to the Poincaré conjecture but reflective of politics in the field of mathematics:

Yau's supposed involvement in the 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 tussle between him and the Chinese mathematical community that allegedly resulted; and
the Tian-Yau conflict of 2005, in which Yau allegedly accused his student Gang Tian (a member of another team verifying Perelman's proof) of plagiarism and poor scholarship while criticizing Peking University in an interview.

In discussing the Poincaré conjecture, Nasar and Gruber also reveal an allegation against Yau that had apparently not been reported in the press before their article appeared:^[4]

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.

The authors also report that sometime after this April email, and before publication, the title of the paper dramatically changed to "A Complete Proof of the Poincare and Geometrization Conjecture--Application of the Hamilton-Perelman Theory of The Ricci Flow" (this title was retracted on December 3, 2006). This alleged incidence with the journal has not been confirmed by an outside source, however, no one involved has yet made a statement claiming that it is false.

This paper was the result of the above-mentioned work of Zhu and Cao, which Yau promoted in the Beijing conference.^[5] The New Yorker article concludes by linking the alleged actions of Yau with Perelman's withdrawal from the mathematical community, stating 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 has seen much worse behaviour than Yau's. The article is accompanied by a controversial full-page cartoon, described below.

[edit] Controversy

The article, and an included full-page color illustration of Yau grabbing the Fields Medal hanging around Perelman's neck [1], has garnered controversy. It has been the subject of extensive commentaries in blogs. The controversy revolves around its 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 August 22, 2006, Sir John M. Ball, president of the International Mathematical Union, made reference to the article and rushed publication of the Cao/Zhu paper at a speech given at the opening ceremony of the International Congress of Mathematicians.

Mathematics is a profession of high standards and integrity. We freely discuss our work with others, without fear of it being stolen, and research is communicated openly prior to formal publication. Editorial procedures are fair and proper, and work gains its reputation through merit and not by how it is promoted. These are the norms operated by the vast majority of mathematicians. The exceptions are rare, and they are noticed....[2]

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.^[6]^[7] 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 the following response to the letter:

"’Manifold Destiny,’ a 10,000-word article by Sylvia Nasar and David Gruber published in the August 28, 2006 issue of The New Yorker, is the product of more than four months of thorough, careful reporting and meticulous fact-checking. Ms. Nasar and Mr. Gruber spent over twenty hours interviewing Dr. Yau; they conducted approximately 100 other interviews with people in the field; corresponded by email with Dr. Yau and many others; and traveled to China where they conducted interviews and attended speeches and events discussed in the article. In addition, the magazine’s fact-checkers spoke with Dr. Yau for approximately eight hours, they examined notes, tapes, and documents gathered by the authors, and the checkers conducted their own thorough research. Contrary to Dr. Yau’s assertions, the article is nuanced and fair, and was prepared using ethical standards of journalism. Dr. Yau, his supporters and his point of view were given ample space in the article. We stand by the piece and the journalists." ^[8]

Two of the mathematicians interviewed — Stroock and Anderson— have allegedly issued statements in opposition to the New Yorker article, after it became available online. On Oct 6, 2006, the statements attributed to Stroock and Andersen were posted on Yau's website.^[9]^[10]. It has not been confirmed if these mathematicians actually wrote the statements since they are not posted on their own websites and Stroock's "official" letter in the September 11, 2006 issue of The New Yorker is not critical of the article.

On September 25, 2006, a letter from Richard Hamilton was posted on Yau's website.^[11] 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 web site.^[12]

On Oct 17, 2006, a profile of Yau in the New York Times devoted about half its length to the Perelman dispute. ^[13] The article said that Yau's promotion of the Cao-Zhu paper "annoyed many mathematicians, who felt that Dr. Yau had slighted Dr. Perelman," but also said about 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."

On Dec 26, 2006, National Public Radio (NPR) released an account of the Poincare conjecture and the controversy surrounding the New Yorker article. ^[14] In his interview with NPR, Yau called Perelman’s work “truly original and genius”, and the New Yorker article as inaccurate, denying having given a quote concerning credit contributions at a specific press conference referenced by the New Yorker. He did not directly answer if he had ever made such a statement. An analysis by NPR of an audiotape "provided by Yau" and "translated by NPR" is in agreement with Yau's statements. Sylvia Nasar was said to have declined multiple attempts for interview by NPR. ^[15]

[edit] Erratum to Cao/Zhu article

Lemma 7.1.2 and its proof in the Cao–Zhu paper^[2] is nearly identical to Lemma 43.3 in a June 2003 note posted online^[16] by Bruce Kleiner and John Lott. After the publication of the Cao–Zhu paper, Sujit Nair, a post-doctoral researcher at Caltech, posted a side-by-side comparison of the Cao–Zhu paper and the Kleiner–Lott note on his blog. The New York Times^[17] also carried an article pointing out to the flaw in Cao-Zhu paper. Cao and Zhu have published an erratum^[18] confirming that the material was by Kleiner and Lott, stating that its uncredited appearance in the Cao–Zhu paper was due to an oversight, and apologizing to Kleiner and Lott.

On December 3, 2006, in response to plagiarism charges, Cao and Zhu retracted their original paper titled, “A complete proof of the Poincaré and geometrization conjectures — application of the Hamilton-Perelman theory of the Ricci flow” and renamed it more modestly, "Hamilton-Perelman's Proof of the Poincaré Conjecture and the Geometrization Conjecture." [3]. They also took out the word "crowning achievement" from the abstract.

At present, Yau's legal efforts have not progressed beyond his September letter. The New Yorker has stood firmly by its story. In a twist, after the publication of Manifold Destiny, plagiarism was discovered in Cao and Zhu's paper. [4]. This led to an Erratum being issued [5] in the December 2006 issue of the Asian Journal of Mathematics. In the same issue, the AJM editorial board issued an apology for what it called "incautions" in the Cao/Zhu paper [6]

[edit] Reaction from the mathematics community

Reactions to the article among research mathematicians has been mixed. Joan Birman, in a letter to the Notices of the AMS, cited the events to argue for higher standards and better self-policing in the mathematics community, pointing out that mathematicians' tolerance for eccentricity also sometimes leads to tolerance of bad behavior, especially when the individuals in question are highly talented. In particular, she mentioned that "the manner in which the normal peer review process, essential to the integrity of the profession, was tossed out the window when the paper of Cao and Zhu was accepted for publication in the Asian Journal of Mathematics" and that "those who were in a position to say 'wait a minute, we will not let our names be used in this way' remained silent. This was just one of the many moments in this sad tale when there were no whistle blowers. As a result the entire profession has a received a very public and very bad black mark."^[19]

Some have claimed that the portrayal of S. T. Yau as "Chern's successor" or "Chern's heir" played deliberately to stereotypes of Asian Americans^[20]. In a letter to the Notices of the AMS, Bun Wong and Yat Sun Poon contend that the article reveals an underlying bias against Asian mathematicians: "For the Asian Americans below the glass ceiling, it is disheartening to see such a successful and dedicated academic being subjected to the smear of popular press," although it should be noted that none of the other Asian mathematicians in the article were portrayed similarly.

This and other articles reporting on the events surrounding the proofs of the Poincaré Conjecture have led to discussion among researchers in academia as to whether large cash prizes are good or bad for the profession. Anatoly Vershik writes that million dollar prize offered for the Clay Millennium Prize Problems is not the best way to promote a healthy mathematics community and "the topic of the “millions” only inflames such passions and guides them in the wrong direction."^[21] Others feel that, on the contrary, the media attention will help generate public interest in mathematics and perhaps research in the area.^[22]