赛昆

前几天（2022年7月3日）在新闻版《环球大观》栏目读到一篇文章：《顶级数学家有多厉害？厉害到你会觉得我在胡说…》，作者署名“知乎”。

俺作了下面的评论：

“该文谎话连篇。

克雷所确实通知佩雷尔曼获奖，但拒绝的原因却不是文中所说‘对钱不感兴趣’，而是指责克雷所‘不公平’。至于‘面对记者的提问’则纯属杜撰，他获克雷奖后没有记者报道过对其的采访。事实上，佩雷尔曼对钱感兴趣，因为他在‘庞加莱猜想’事件前领过奖。

佩雷尔曼共发表了三篇网文(preprint)，第二篇网文叙述了一个定理（7.4)却没给出证明，只是说在下一篇preprint中给出证明。前两篇论文的目标是瑟斯顿猜想（其结果包含了庞加莱猜想）。但是，他的‘下一篇’却没有给出所预报的证明，而是给出庞加莱猜想所需的一些引理。

也就是说，佩雷尔曼第二篇论文的定理7.4至今仍未有证明。俺认为，这是他避不见人的主因。否则，内行问起‘定理7.4’，他如何回答？”

这里简单说说整个争端的来龙去脉。2002年，佩氏贴出两篇论文，其中第二篇有个定理7.4，从三个条件推导出一个结论。但佩氏随后说：“第三个条件可以去掉，具体证明将在下一篇文章中给出”。他随后到美国讲学，说这些方法证明了瑟斯顿猜想（比庞加莱猜想更大的猜想）。回到俄国后，他贴出第三篇论文，并没有前述定理7.4的证明，只有针对庞加莱猜想的几个定理。从2002年到2006年，有三个团队在解读佩氏的论文：曹-朱、克-洛、摩-田。其中，克-洛在其论文写道：佩氏的定理7.4，如果用三个条件，证明就简单得多，但实用性不大（“it is NOT clear this strong condition” can be applied）。最后，丘成桐在2006年4月26日宣布，曹-朱的论文将在6月发表，给出完整证明。另外两组相继于5月贴出了他们匆忙赶制的论文。有兴趣者可以对比他们在2006年5月贴的论文与最后定稿版的区别。《科学》杂志年终文章说道：庞加莱猜想在2006年得到解决，三组数学家填补了佩雷尔曼文章的漏缺（gap)。

上面是基本事实。然而《纽约客》作者纳萨写了篇故事《流形上的命运》，指责丘成桐的学生曹-朱抢功。据《流形上的命运》，佩雷尔曼本人指责“有些人不诚实”。

俺也写了个故事：2002年佩氏到美国研讨后，发现自己的定理7.4（两条件版）有错，回国后马上把大猜想（瑟斯顿猜想）放下，写出第三篇论文专攻小猜想（庞加莱猜想）。此后就不敢见人，怕人问“定理7.4”。

俺在blogspot找到2006年在《纽约客》论坛的辩论，贴到这里，多一个地方保留。

俺的《致佩雷尔曼博士的公开信》贴出后次日，在《纽约客》论坛读到一篇文章，作者自报为数学教授，但不在微分几何方向。他说：“原本到此坛的目的是支持纳萨。有人指控她对丘的措辞过严，我当时认为还不够严。但看了一下争论之后，我认为事实完全与纳萨所编的故事相反。”在这位教授贴出网文的第二天，《纽约客》关闭了论坛。很可惜，教授的帖子没抄下来。

- - - -
下面是俺的两份公开信（分别致纳萨和佩氏）。
大致翻译给佩氏的信：

亲爱的佩博士：
从您朋友纳萨的文章《流形上的命运》知道，您为了某种不可告人的目的在数学研究中“冒了巨大的风险”。虽然俺很反对这种行为，但仍认为您与汉密尔顿教授对证明庞加莱猜想作出90%的贡献，而且很赞赏两位的贡献。

…缪纳教授在美国数学会会刊《通知》上发表文章，说您“宣布了一个解决办法，并保证会在第四篇论文给出定理7.4的证明”（见《通知》2003年11月号，第1231页）。如今，瑟斯顿猜想已经被证明，而证明者被您及其支持者包括这位缪纳教授攻击为“不诚实、抢功”。

请问，是否能通过“宣布”和“保证给出证明”来获取数学定理的证明权？

Letters to Ms. Nasar and Dr. Perelman
Dear Ms. Nasar:

I would like to report two obvious mistakes you made in your article entitled "Manifold Destiny".

1. Your article reads:"Yau added, 'Given the significance of the Poincare, that Chinese mathematicians played a 30% role is by no means easy.'" However, the Chinese official news website attributed the quoted words to Yang. [To verify, you can use google to search "content_4644722" +"2006-06", then click translation]. So, you made an undeniable mistake. By the way, on June 9, Yang publicly denied he said that.

2. Cao-Zhu indeed said that they "substitute several key arguments" for "the completion of the geometrization program." It does not contradict with Morgan's comments about "the Poincare". Note that the geometrization conjecture is not "the Poincare" and your words about "the idea that Zhu and Cao had contributed significant new approaches to the Poincaré" are wrong.

For your info: Prof. Milnor wrote:"Perelman has announced a resolution of these difficulties and promised a proof of the Thurston (geometrization) conjecture based on Hamilton's ideas, with further details to be provided in a fourth preprint." (AMS Notices, Nov. 2003, Page 1231). The "fouth preprint" has not been posted yet. You and Morgan should see the difference now: Perelman "announced" and "promised a proof", but Cao and Zhu provided a proof, although their proof was described by Prof. Milnor as "throwing 'a monkey wrench' into the question of who gets credit" (see Wall Street Journal).

"Politics, power, and control have no legitimate role in our community, and they threaten the integrity of our field,"Phillip Griffiths said and we all should remember these.

3. I would appreciate if you would do me a favor to pass the following message to Dr. Perelman, since you are a friend of this "risk" taker and he refuses to receive mails.
Thank you.

Sincerely,
SK

sk08.blogspot.com
cc: Ms. Rosenberg, Mr. Gruber, Mr. Cooper and Dr. Yau

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Open letter to Dr. Perelman.

Dear Dr. Perelman:

From the story “Manifold Destiny” written by your friend Ms. Nasar, I found that you took “a considerable risk” in your math research for some untold purpose. Although I strongly disapprove this kind of action, I think that you and Hamilton contributed at least 90% in the Poincare and admire your contribution.

Prof. Milnor wrote: "Perelman has announced a resolution of these difficulties and promised a proof of the Thurston conjecture (TC) based on Hamilton's ideas, with further details to be provided in a fourth preprint." (AMS Notices, Nov. 2003, Page 1231) . Three years have passed and your “fourth preprint” has not been posted yet. Now, two teams have provided those “further details”, but one of them was blamed as “not honest” by you and “stealing credit from Perelman” by your backers. Do you think that one can claim full credit by “announced” and “promised a proof”? I believe people will know who is the one that is “not honest” when they know the truth.

Many people believe that you can prove TC. Now, since two teams provided proofs that circumvented your Thm. 7.4, you still have two ways to prove that you are able to realize your promise:
(i) prove Thm 7.4 with only the first two conditions; or
(ii) prove Thm 7.4 with all three conditions and use it to complete the proof of TC. Note that Kleiner & Lott said that “it is not clear this strong condition” can be applied. You may give them a lesson.

So, finish your job and don’t let your backers down.

Sincerely yours,
SK