原题：My assignment of credits for the proofs of two conjectures
I am among the first few people to express disagreement to the fabricated "Yang's assignment of credits", namely the famous 50-25-30. The following is my own assignment of credits.
老汉+阿佩=90%
Poincare Conjecture:
Hamilton and Perelman contributed 90%.
Geometrization Conjecture:
Similar to the Poincare Conjecture, Hamilton contributed 45%, and Perelman would have contributed 45% if he had posted his "fouth preprint"(see Milnor's article published in AMS Notices, 2003, page 1231). All others combined contributed 10%.
Note that Perelman's third preprint is for the Poincare conjecture only. So, I assign 15% to his first preprint, 15% to the second and 15% to the non-existing "fouth preprint".
Since Perelman failed to deliver his "fouth preprint" as he once promised, 15% goes to the people who solved that problem. 5% goes to Shioya-Yamaguchi, who proved the collapsing result in the special case when the manifold is closed and 10% goes to Cao-Zhu for using this weak result to finalize the proof of the geometrization conjecture.
Therefore, 45% goes to Hamilton, 30% goes to Perelman, 10% to Cao-Zhu for the completion of the collapsing result, 5% to Shioya-Yamaguchi, and 10% for all other contributions, including Cao-Zhu's other contribution, Kleiner-Lott (Cao-Zhu used their result in the proof of one theorem), Chen-Zhu for the uniqueness result, and Li-Yau, etc.
posted by sk08 at 1:58 PM 0 comments
Saturday, April 21, 2007
"the gun does not kill, people do"??
Somebody said:"the gun does not kill, people do".
One can also argue that "WMD in Iraq/Iran does not kill, people do".
Is there a reason to eliminate WMD from those areas?
posted by sk08 at 5:45 AM 0 comments
Saturday, April 07, 2007
Another way to tell the story.
Before 2002, like many other mathematicians, Dr. Perelman published many well written papers. Why he suddenly changed his style? In Nasar's words, he "was not just flouting academic convention but taking a considerable risk" for some untold purpose. Nasar wrote a story in favor of this "risk" taker. But this story can be written in another way:
In 2002, Perelman worked out an outline of the proof of the geometrization conjecture. He did not want other people to share credit with him and was afraid that somebody else would publish it quicker, so he posted two articles on the internet. Later, he found that his approach was wrong and could not get Theorem 7.4 proved. Instead of fulfilling his promise for the proof of Theorem 7.4, he wrote his third article devoted entirely to a special case of the geometrization conjecture, namely the Poincare Conjecture. Since then, he has been hiding. He only talked to story writers like Nasar, not the mathematicians.
No one can imagine how he would reply if the experts ask him about his "fouth preprint"(see Milnor, AMS Notices, Nov.,2003, page 1231).
posted by sk08 at 6:53 PM 0 comments
Thursday, January 18, 2007
Nature article, Aug., 2006
Perelman followed his first article with two further papers, and in the spring of 2003 he toured the United States to lecture about his work2. He has since retreated from the public eye, leaving other mathematicians to comb through his papers line by line, filling in details and searching for holes in his logic.
"How do you decide whether anything is correct?" asks John Ball, president of the International Mathematical Union and chair of the Fields medal committee. "All that can happen is that clever people, experts in the area, read it and come to an opinion."
Three pairs of respected mathematicians have produced written accounts filling in the details of Perelman's work.
Kleiner and John Lott of the University of Michigan, Ann Arbor, posted their most recent paper to the arXiv preprint server on 25 May. "There was a moment when I really thought there was a problem with the argument," says Kleiner. "But that state of mind persisted for only a week or two before the issue was resolved."
A 473-page paper4 by Morgan and Gang Tian of the Massachusetts Institute of Technology appeared on 25 July.
The third paper, from Huai-Dong Cao of Lehigh University in Bethlehem, Pennsylvania, and Xi-Ping Zhu of Zhongshan University in Guangzhou, China, was published in June. It claims to complete the proof of both conjectures, rather than simply fleshing out Perelman's work. This is justified, argues Shing-Tung Yau, an editor-in-chief on the journal, because Cao and Zhu follow a somewhat different argument to Perelman.
The appearance of these three papers has fuelled rumours that Perelman will receive a Fields prize. Up to four medals are awarded every four years to mathematicians no older than 40, making Perelman just eligible for this year's crop. Not that he will attend the Madrid meeting: the organizing committee received no reply when they invited him to give a plenary lecture.
posted by sk08 at 7:43 PM 0 comments
Friday, November 17, 2006
reply in the New Yorker forum.
Here is the complete sentence :"There is an apparent GAP in the proof of [40(Perelman's first preprint), Thm 12.2] , in the sentence(there is a little subtlety...)" (Kleiner & Lott, arxiv.org)
One supporter of Nasar said:"Notably, not one letter supports Yau's claims of credit for Cao-Zhu ...." The reply is simple: lawyers and Nasar are not the people who determine "the question of who gets credit". You and Nasar seem to forget this.
As for the Poincare, Prof. Atiyah said:"the final judgement is suspended until the COMPLETE PROOF has been written down, ...". These words clearly indicate that Perelman did not complete the proof.
posted by sk08 at 7:23 PM 0 comments
Thursday, November 02, 2006
See one of Nasar's "honest people"
Science Magazine, 9/22/2006
Frustrations Mount Over China's High-Priced Hunt for Trophy Professors
Chinese universities bask in the glow of top-gun scientists hired on part-time deals to share their wisdom. Critics say the money could be spent more wisely Mathematician Gang Tian did not expect a standing-room-only crowd last week when he gave a lecture at Beijing University (Beida) on the Poincaré conjecture. But not all were there for the math. Reporters and others had come for a glimpse of the man at the center of a tempest engulfing Chinese academia. Tian is a premier example of a controversial phenomenon: a Chinese-born researcher with a full-time faculty position overseas who gets paid handsomely for short working stints in his homeland.
Resentment against part-timers boiled over last July, when Shing-Tung Yau, a Harvard University mathematician and Tian's former mentor, dismissed the "majority" of Beida's overseas recruits as "jiade," or "fakes," in comments in the Chinese magazine Nanfang Renwu Zhoukan. Beida officials fired off a series of rebuttals in which they termed Yau's remarks "irresponsible" and a "distortion of facts" and rattled off achievements--papers in prestigious journals and patents, for instance--by talent returned from overseas.
The university's attempts at damage control, however, only intensified debate about professors such as Tian, who has been listed among Beida's full-time faculty for several years. Beida nominated Tian to membership in the Chinese Academy of Sciences (CAS), an honor reserved for scientists who expend at least half their effort in China. Thanks to Beida's backing, Tian--who was then also listed as a full-time professor at the Massachusetts Institute of Technology (MIT)--was elected in 2001 by a margin of one vote. Last spring, Tian left MIT to become a full-time professor at Princeton University.
After the Poincaré lecture, reporters pressed Tian about his employment status in China. He said that he now spends more than 4 months a year at Beida and "hopes to be a full-time professor later on," perhaps after Beida builds a $13 million international institute of mathematics, which Tian will direct.
Some proponents consider part-time academic appointments a critical means of stanching China's loss of scientific talent. Universities and government agencies are boosting quotas for part-timers and upping the ante to entice more top guns to return. Several universities have created "million-yuan professorships" with stratospheric--for China--annual salaries equivalent to $125,000. Most returnees are midcareer scientists who accept more modest offers (see sidebar on p. 1722).
Critics, however, contend that part-timers often are less important as professors than as tools in the battle for prestige and resources. Yau claims that researchers who parachute in can hardly contribute in a substantive way to China's scientific development. But the trend seems almost unstoppable, says Shigang He, a neuroscientist currently at CAS's Institute of Biophysics in Beijing: "I don't think universities will really seriously control this, because they benefit."
posted by sk08 at 5:10 AM 0 comments
Saturday, October 07, 2006
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
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