流形的命运

维基百科，自由的百科全书

流形的命运正在校对翻译。
歡迎您積極參與校對與修訂，原文在"http://en.wikipedia.org/wiki/Manifold_Destiny"。

《流形的命运》^[1]是一篇由Sylvia Nasar和David Gruber撰稿，于2006年8月28日刊登在《纽约客》杂志上的文章。此文在2006年8月21日左右就已由《纽约客》杂志刊登上网^[2]。

"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.

此文詳細描述了圍繞龐加萊猜想之Grigori Perelman證明所發生的一些背景，并追蹤了三組數學家試圖驗證Perelman證明的過程。

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.

[编辑] 文章的視角

文章描述了Grigori Perelman對數學界的幻灭和退出，并描繪了1982年菲爾茨獎得主丘成桐的一幅不敢讓人恭維的肖像。

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.

文章的副标题是“一道传奇的问题以及誰是其解决者的争斗”。文章专注于描述三组独立的数学家对庞加莱猜想（也可能还有Thurston的几何化猜想）之Perelman证明的验证过程中所发生的人间戏剧。作者們追蹤到了隱居于其母在圣彼得堡的公寓中的Grigori Perelman，并將此次面談穿插在本文中。

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.

[编辑] 面談采訪者列表

(按文中出現順序排列)

丘成桐
Grigori Perelman
John Morgan，哥倫比亞大學數學教授，田剛驗證Perelman證明的合作者。
Yuri Burago，Perelman的博士導師，圣彼得堡的Steklov數學研究院成員。
Daniel W. Stroock，麻省理工學院Simons數學講座教授。
田剛，普林斯頓大學數學教授，丘成桐的前學生，但已鬧翻，見田丘之爭，John Morgan驗證Perelman證明的合作者。
Barry Mazur，哈佛大學數學教授。
Phillip Griffiths，普林斯頓高等研究院前院長。
陳省身（丘成桐博士導師）的一個未具名的親屬。
丘成桐和Richard Hamilton的一個未具名的朋友。
Mikhail Gromov，法國高等科學研究院（IHÉS）終身成員，紐約大學Jay Gould數學講座教授。
Michael Anderson，紐約州立大學石溪分校數學教授。
Alexander Givental，加州大學伯克利分校數學教授。
Vitali Kapovitch，馬里蘭大學數學教授。（實際上并沒有面談采訪，但他發給Perelman的一封電子郵件在文中被引用）
Fedor Nazarov，密西根州立大學數學教授。
Frank Quinn，弗吉尼亚理工大学數學教授。
Joseph Kohn，普林斯頓大學數學教授。

[编辑] Summary

The article begins with a description of Yau lecturing on a paper^[3] by his students, Huai-Dong Cao and Xi-Ping Zhu, in Beijing, on the occasion of Strings 2006^[4], 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 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 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:^[5]

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 above-mentioned work of Zhu-Cao, which Yau promoted in the Beijing conference.^[6] 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.

[编辑] 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.^[7]^[8] 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. ^[9]

Three of the mathematicians interviewed — Stroock, Anderson and Kohn — have allegedly issued statements of clarification online, after the article became available online.^[10] These statements appeared to be in the form of emails to Yau and some graduate students. ^[11] On Oct 6, 2006, the statements from Stroock and Andersen were posted on Yau's website.^[12]^[13]. Stroock stated in his letter about the article's controversy:

Having seen Yau in action during his June conference on string theory, Nasar led me to believe that she was fascinated by S.T. Yau and asked me my opinion about his activities. I told her that I greatly admire Yau's efforts to support young Chinese mathematicians and to break down the ossified power structure in the Chinese academic establishment. I then told her that I sometimes have doubts about his methodology. In particular, I told her that, at least to my ears, Yau weakens his case and lays himself open to his enemies by sounding too self-promoting. As it appears in her article, she has purposefully distorted my statement and made it unforgivably misleading.

On September 25, 2006, a letter from Richard Hamilton was posted on Yau's website.^[14] 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.^[15]

On Oct 17, 2006, a profile of Yau in the New York Times devoted about half its length to the Perelman dispute. ^[16] 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."

[编辑] Erratum to Cao/Zhu article

Lemma 7.1.2 and its proof in the Cao-Zhu paper^[3] is nearly identical to Lemma 43.3 in a June 2003 note posted online^[17] by Bruce Kleiner and John Lott. After the publication of the Cao-Zhu paper, Sujit Nair, a post-doctoral researcher at Caltech, discovered the similarity and wrote a side-by-side comparison of the Cao-Zhu paper and the Kleiner-Lott note. Based on this comparison, Nair and New York Times^[18] accused Cao and Zhu of having committed plagiarism. In reaction to these charges, Cao and Zhu published an erratum^[19] that confirmed that the material was by Kleiner and Lott, stated that its uncredited appearance in the Cao–Zhu paper was due to an oversight, and apologized to Kleiner and Lott.