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赛昆  
俺的第二家铺子  
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佩雷尔曼的死穴命门 2022-07-07 17:39:06

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,但却因条件太强而实用性不大(“it is NOT clear this STRONG condition” can be applied,原文是小写字母)。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——最重要的一条:定理7.4是佩氏的死穴(!!),20年过去了,证明仍没给出。2005年,Shioya和Yamaguchi修改了佩氏定理7.4的条件,在无界流形条件下证明了该定理的结论(两版定理的在本文下面给出,以供比较)。曹-朱以此证明了瑟氏猜想。这足够说明:佩氏对瑟氏猜想的解决思路完全错了,他根本没有想到“无界流形条件”也能解决这一猜想。

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,贴到下面,多一个地方保留。

俺的《致佩雷尔曼博士的公开信》贴出后不久,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,而我认为对丘的指责再严也不过分。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——显然是觉得真相不在他们一边。很可惜,教授的帖子没抄下来。

- - - - -
下面给出两份资料。

1,俺贴到《纽约客》的两份公开信(分别致纳萨和佩氏);

2,最后给出佩氏的“定理7.4”和Shioya/Yamaguchi给出并证明了的“弱版”定理(发表在1868年创刊的 Mathematische Annalen)。曹-朱利用“弱版定理”完成了瑟斯顿猜想的证明——如果说有人“抢功”,那就是Shioya/Yamaguchi抢功,把关键的“定理7.4”抢到手,而且合法合理。

- - - - -

附1:在《纽约客》的两份公开信

摘要翻译给佩氏的信:

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

===========

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

- - - - -

附2:佩氏的定理7.4和Shioya/Yamaguchi随后发表在学刊上的定理。Shioya/Yamaguchi证明的结果是佩氏定理的一个特例(closed manifolds)。

这是证明瑟斯顿猜想的重要定理。佩氏开了头,但做错了。他给了两个版本:(1)用三个条件推结论——条件太多,很难应用(这是佩粉克-洛说的);(2)只用两个条件推结论,他自己至今十几年证不出来。

佩粉是否要说Shioya/Yamaguchi“抢功”?

其实,懂英文的看看就知道,Shioya/Yamaguchi的定理与佩氏定理7.4几乎一样。俺用红线标出两个定理条件的不同之处。而最重要的不同之处是:佩氏定理没有证明,而Shioya/Yamaguchi的弱版定理有证明。

其实也可以说,Shioya/Yamaguchi确实是从佩氏那里合法地“抢”到了这个定理(而且被证明有用),谁叫佩氏耍赖?

从两个定理之区别可以看出,佩氏认为:证明瑟斯顿猜想必须要“闭流形或者有凸边界”。而Shioya/Yamaguchi把边界条件去了,曹-朱用这个弱版定理证明了瑟斯顿猜想。所以,非常显然,佩氏对瑟斯顿猜想的思路错了。

最后要指出,克-洛、摩-田的研究由克雷研究所资助。克雷研究所就庞加莱猜想颁发的大奖却被获奖人称为“不公平”而拒绝领奖(这是佩氏在此事件中唯一值得称赞之处),克雷研究所丢人丢姥姥家了。

THM7_4.jpg







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作者:赛昆 留言时间:2022-07-16 07:33:57

下面抄自Jeremy(俺估计是汉密尔顿)在反弦博上的发言,与汉密尔顿在2006年国际数学大会的发言观点一致。博主Woit明显偏袒摩根/田刚一方,但却不敢删Jeremy关于“田刚是腐败的中共官员”的博文,自那时起俺就知道Jeremy肯定是哥大数学系的,从而肯定是汉密尔顿。

另外,Jeremy当时似乎不知道,克-洛也是克雷研究所资助的(见克-洛在2008年发表的论文)。

俺特别赞同下面两点:

1。是克洛曹朱摩田完成了庞猜的证明(are the ones who really completed the proof)。

2。克雷研究所是大输家。它并非组织研讨会、出版相关论文,而是直接资助个别人。因此它不是个仲裁机构,而是参赛者之一,而且它资助的数学家跑在最后。

但Jeremy说庞猜可以命名为“佩氏定理”,俺以前说过,俺觉得应该是“汉佩定理”。

Jeremy Says:August 7th, 2006 at 10:49 pmPeter,What happens if Hamilton had claimed that he had given outline of a proof to the Poincaré and the geometrization conjectures in 1982, when he first introduced the Ricci flow approach, then he would leave it to the others to fill in the details (gaps)? Of course, he didn't. He went on to fill in the details and faced some serious difficulties. But if he did, would Perelman's work also be considered as filling the details?Hamilton started the program. He did not finish it, probably because he didn't know how to fill in some the details. Is it possible that Perelman also didn't know how to fill in some of the details of his outline?Perelman is a great mathematician. So is Hamilton. Their work has shown that. But it does not mean that they know how to complete the proof of the conjectures.Kleiner-Lott devoted much of their almost 200 pages paper to fill in Perelman's gaps; Morgan-Tian devoted a large part of their more than 400 pages paper to fill in some of Perelman's gaps (not including geometrization); Cao-Zhu devoted a large part of their more than 300 pages paper to fill in some Perelman's gaps and some Hamilton's gaps (Cao-Zhu do have some of their own ideas to fill in Hamilton's gaps). Obviously, these are not small gaps. Are they?Cao-Zhu, Kleiner-Lott and Morgan-Tian must have faced and solved many serious difficulties too. Kleiner-Lott did not write up a complete proof,but Cao-Zhu (for Poincaré and geometrization) and Morgan-Tian (for Poincaré) did. I believe that they all should share the credit with Hamilton and Perelman for completing the proof of the Poincaré conjecture. In fact,if there is nothing wrong in their papers. They are the ones who really completed the proof. Right?As for the prize money. None of the U.S. based professors really need it. Do they?=============August 18th, 2006 at 2:40 amAfter collecting information from the Hamilton's paper (1982), Perelman's three papers (2002, 2003), Cao-Zhu paper (2006), Kleiner-Lott paper (2006), Morgan-Tian paper (2006), as well as the articles by Sharon Begley (The Wall Street Journal), Allyn Jackson (AMS) and Dennis Overbye (The New York Times), a theory of the winners and losers in the proof of Poincare conjecture and the geometrization conjecture has been formed. The theory is described as follows:

Theorem (Winners-Losers): There are winners and losers in the proof of Poincare conjecture and geometrization conjecture.

The winners are: Hamilton, Perelman, Cao-Zhu, NSF, JSG Memorial Foundation, NSF of China, Harvard University and Tsinghua University in Beijing.

The losers are: Kleiner-Lott, Morgan-Tian and Clay Mathematics Institute.

The biggest loser: Clay Mathematics Institute. ||

A complete proof of the Winners-Losers Theorem is given in the Appendix.

Corollary: Losers speak first. Winners speak last. ||

This corollary arrives naturally and it is even true in sports and politics.

Appendix

For later reference, we start by introducing the well-known Theorem of Publication.

Theorem: Publish after the publication of others on solving the same problem equals publishes nothing, i.e.

P(t) = 0 for t > t_(P of others).

Here P stands for publication and t is time. ||

Now we proceed to the details of the winner-loser theory.

Hypothesis: All statements and claims made in the Cao-Zhu paper, Kleiner-Lott paper and Morgan-Tian paper are accurate and correct. ||

The following is the proof of the Winners-Losers Theorem.

Proof

We first give proof of the winners.Hamilton had the vision to first introduce the equation of Ricci flow to the proof of the geometrization conjecture and laid the foundation for the Hamilton program. He has many mathematicians believed in and participated in the program. Perelman agreed that his own work was to carry out the Hamilton program. Cao-Zhu also acknowledged that their work is part of the Hamilton program. The final proof of the conjectures has vindicated Hamilton's vision. Therefore, a winner. (Very likely, the Ricci flow equation will be renamed as the Hamilton Equation.)

Perelman shared Hamilton's vision and made the most critical contribution to push through the Hamilton program by bring in new ideas and new techniques, which made others realize that his claim to the proof of the geometrization conjecture, therefore the Poincare conjecture, could very well be true. Probably more importantly, the new techniques he developed will help the future development of mathematics. Although he left many less critical issues unsolved, some of those can be considered as details, the final proof of the conjectures has proved that his statement was accurate. Therefore, a winner. (The Poincare Conjecture will almost definitely be renamed as Perelman Theorem.)

Cao-Zhu worked on the conjectures in secrecy, except to the Harvard mathematicians. They used much of the Perelman's work, but did not limit themselves only on filling Perelman's details, which enable them to keep a broader vision in pushing through the Hamilton program. After combining other people's work with their new ideas, they could first publish a complete proof for the Poincare and geometrization conjuctures. Therefore, winners. (The geometrization conjecture may very well become Perelman-Cao-Zhu Theorem.)

Cao-Zhu has certainly pulled off a coup when the publication of their paper was first announced in April 2006.

NSF and JSG Memorial Foundation have been funding the work of Cao; NSF of China has been funding the work of Zhu. Obviously, funding winners makes them winners.

Harvard University supported Zhu's work; Tsinghua University in Beijing supported Cao's work. Winner's supporters are clearly winners.

Now we give proof of the losers.

Kleiner-Lott have been narrowly following Perelman's work, but posted their findings for everyone to use. Unfortunately, they lost their concentration on the larger picture, the relationship of Perelman's work with other people's work. Filling in Perelman details has been proved not to be easy. The announcement of the forthcoming Cao-Zhu paper in April 2006 has been a surprise and total shock. Unable to complete their paper in time and were very much aware of the implication of the Theorem of Publication, Kleiner-Lott posted their unfinished paper on the non-refereed arXiv at the end of May, a few days before the appearance of the Cao-Zhu paper. Kleiner-Lott still plan to publish their paper, but after the publication of the Cao-Zhu paper and the Morgan-Tian paper, (Morgan-Tian paper uses many Kleiner-Lott's results), the publication of their paper becomes much less meaningful considering the Theorem of Publication. Therefore, losers.

Morgan-Tian have also been narrowly following Perelman's work and busying on filling Perelman's details. At the April 2006 announcement of Cao-Zhu paper's publication, they haven't even filled the details for a part of the Perelman's work. Fully understood the implication of the Theorem of Publication, they sent a preliminary version (i.e. unfinished version) of their paper for refereeing in May, just before the Cao-Zhu paper's June appearance, to show that their work was independent. The final version of their finished paper was posted on the non-refereed arXiv more than a month after the publication of the Cao-Zhu paper. By the implication of the Theorem of Publication, there will always be suspicion that the final version of the Morgan-Tian paper has been inspired and has benefited from the Cao-Zhu paper. Therefore, losers.

The final version of the Morgan-Tian paper is more than 400 pages and only filled the details of a part of the Perelman's work. Among other things, it certainly has proved that “the details for a genius could be major problems for common men”.

As the supporter of the losers, Clay Mathematics Institute is obviously a loser.

Finally, we give proof of the biggest loser.

Clay Mathematics Institute has a big treasure chest to back up its list of millennium prize problems. However, whenever the millennium problems are concerned, Clay Institute should support the mathematics community as a whole (support its conferences, workshops etc.), rather than support individual mathematician(s). Its role should be of a referee rather than a player. Once it starts to support individual mathematician(s), it may be viewed as playing favoritism. Perelman might very well consider that Kleiner-Lott and Morgan-Tian are taking advantages of his work, under the support of Clay Institute. Other mathematician may think that Clay Institute intended to give the prize to mathematician(s) of their choice even before the problem is solved. The prize money may then be considered as “tainted”. The honor of the prize is therefore completely lost. The only thing that left is money. Giving out money that does not have widely recognized honor is truly meaningless. (There are people who really do not care about money!) Therefore, Clay Mathematics Institute is the biggest loser.

End of proof.===If you ask Atiyah the same question now, he, as any other responsible mathematicians, will probably give you the same answer.

The world, as far as Poincare conjecture is concerned, has not changed at all, even with the recent media storm. After all the dust settled, the mathematics community will have to do exactly what Atiyah said in his interview. Otherwise, mathematics as we know it will no longer exist. I personally have faith that the final conclusion of a mathematical problem will only be given by the mathematics community, not by the media.

However, from what has happened in the last two months, we have learnt a great deal about mathematicians. These guys can behave exactly like politicians. Their skill of personal attacking and backstabbing is certainly no worse than the ordinary politicians. They probably played politics and media better than the politicians from their own district. I have to congratulate them for that.

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作者:赛昆 留言时间:2022-07-08 04:32:28

下面是俺在《纽约客》与对手的争论,也抄过来。那个“某人(somebody)”很可能是纳萨《流形上的命运》的合作者。

从对方的反驳可见,对方对俺指控佩雷尔曼耍赖的事实没有一个字的反驳(俺的指控都是板上钉钉的事实,还有美国数学会《通知》为证),只是反控丘成桐以前的所作所为。此人的其他反驳还有:用贴网文的方式获得“优先权”的并非佩氏一个,总之,就是不敢回答"定理7.4"——这是佩氏最大的死穴。

佩氏最后一次回答数学问题是:大约在2004年指出某篇文章对其定理7.4的改编版的证明是错的。这显示佩氏一直在关注这个定理。

*
SK:

I believe that Nasar likes to praise those "ill people" like Nash;
and this time she was cheated by a clever person. Unfortunately, some
Chinese mathematicians got involved. Actually, from Nasar's article, one
can reveal Perelman's real intention.

Writing sketchy drafts is not how
centuries of math/theoretical physics research has been done, and
Perelman himself had not acted that way before 2002.Nasar's article
describes this as taking a "risk". Clever people take risk for
something, so did Perelman.I think that the person who "grab credit" is
not Yau but this clever person. (some sentences were borrowed from
another post)

* Somebody's reply:

Perelman's "cleverness" asyou call it,
is irrelevant to Yau. Either Perelman gets 100 percent credit for
solving the Poincare conjecture, or Kleiner, Lott, Morgan,Tian, Cao and
Zhu all share credit for producing completed proofs of the conjecture.
The problem that Yau will have trouble explaining is that in either case
he ignores or minimizes the contributions from people whoare not
connected to Yau or China.

* My rebuttal:

Perelman's cleverness is
relevant to Nasar's story. Nasar said:"only true mathematical
gaps--missing or mistaken arguments--can be the basis for a claim of
originality". I wonder if she consider the proof of Perelman's "Theorem
7.4" (page 19-20 in Perelman's second preprint) as missing.Three and
half years have passed since he announced that another paper would be
given. If it is not "MISSING", then what is the definition of "MISSING"?

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· 白川粉与黄右的故事(图)
· 川普辩赢了?Fox总裁:“网络投票
【1950-1966】
· 中共自称“全歼北极熊团”闹大笑话
· 草包毛主席害了儿子性命
· 扒虚构的“白虎团”故事:《环时》
· 1949年以后中共割让和丢失的国土
· 朝鲜战争时期美军的死亡人数
· 毛主席自慰曝光
【1945-1949】
· 评潇潇飞云博的《内战双雄》
· 驳《美国百年两次痛失中国》——满
· 驳《郝柏村研究蒋公日记》
· 1946年中共俄杂党的“军事家、间
· 扒“七战七捷”:苏中战役的参战人
· 中共“元帅、大将”最大的本事
· 中共外援和国军外援的根本区别。
· 扒黄俄所谓国民党“在地图上重新
· 外蒙独立的几个重要史实
· 汉奸大游行
【1937-1945】
· 评《中国事变陆军作战史》和《吴
· 黄桥战役和曹甸战役的真实伤亡数
· 防卫厅《益子战斗概要》揭示黄俄
· “地图开疆”典范:1941年《中英滇
· 揭《从八路军和国军俘虏日军数量
· 俄国杂种《红旗文稿》篡改《中国
【1911-1937】
· 俄杂狗“飞夺泸定桥”谎言的三个相
· 外蒙丢失简述(据《东北边防与外
【闲谈】
· 《国际法医》朱令头发分析的一道
· 评《2018年检测朱令头发》:暑假
· 关于朱令案的几个旧帖
· 陈维健很无知:“首战即终战”最先
· 俄杂卖国贼衙内笑料集(不断更新
· 佩雷尔曼的死穴命门
· 黄川粉笑料集(不断更新)
· 红卫兵大批判范文——作者川粉何请
· 自称“反共”者当川粉,就是真共党
· 从戏子们终止与西方公司合作,可
【deleted】
· 删除不了。
· 火狐不行?
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