Manifold Destiny

Grigori Perelman by Antonio Guzman

Manifold Destiny‘ is a 2006 article in ‘The New Yorker’ written by Sylvia Nasar (known for her biography of John Forbes Nash, ‘A Beautiful Mind’) and David Gruber. It gives a detailed account (including interviews with many mathematicians) of some of the circumstances surrounding the proof of the Poincaré conjecture, one of the most important accomplishments of 20th and 21st century mathematics, and traces the attempts by three teams of mathematicians to verify the proof given by Grigori Perelman.

Subtitled ‘A legendary problem and the battle over who solved it,’ the article concentrates on the human drama of the story, especially the discussion on who contributed how much to the proof of the Poincaré conjecture. Interwoven with the article is an interview with the reclusive mathematician Grigori Perelman, whom the authors tracked down to the St. Petersburg apartment he shares with his mother. The article describes Perelman’s disillusionment and withdrawal from the mathematical community and paints an unflattering portrait of the 1982 Fields Medalist, Shing-Tung Yau.

The article begins with a description of Yau lecturing on a paper by his students, Huai-Dong Cao and Xi-Ping Zhu, in Beijing, on the occasion of ‘Strings 2006,’ 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 mathematician Grigori Perelman. The interview touches on the Fields Medal, Perelman’s life prior to his proof of the Poincaré 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. Nasar and Gruber write, ‘he was increasingly anxious … [that] a younger scholar could try to supplant him as Chern’s heir.’

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 such as 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 a conflict in 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: ‘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 a week after this April email, the title of the paper dramatically changed to ‘A Complete Proof of the Poincaré and Geometrization Conjecture — Application of the Hamilton–Perelman Theory of The Ricci Flow’ (this title was later retracted).

This paper was the result of the above-mentioned work of Zhu and Cao, which Yau promoted in the Beijing conference. ‘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. As for Yau, Perelman is quoted saying, ‘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.’

The article concludes with a quote from Mikhail Gromov (who earlier in the article compares Perelman’s mathematical approach to that of Isaac Newton): ‘To do great work, you have to have a pure mind. You can think only about the mathematics. Everything else is human weakness. Accepting prizes is showing weakness.’

The article, and an included full-page color illustration of Yau grabbing the Fields Medal hanging around Perelman’s neck, 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 past controversies.

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