下面抄自Jeremy（俺估計是漢密爾頓）在反弦博上的發言，與漢密爾頓在2006年國際數學大會的發言觀點一致。博主Woit明顯偏袒摩根/田剛一方，但卻不敢刪Jeremy關於“田剛是腐敗的中共官員”的博文，自那時起俺就知道Jeremy肯定是哥大數學系的，從而肯定是漢密爾頓。 另外，Jeremy當時似乎不知道，克-洛也是克雷研究所資助的（見克-洛在2008年發表的論文）。 俺特別贊同下面兩點： 1。是克洛曹朱摩田完成了龐猜的證明(are the ones who really completed the proof)。 2。克雷研究所是大輸家。它並非組織研討會、出版相關論文，而是直接資助個別人。因此它不是個仲裁機構，而是參賽者之一，而且它資助的數學家跑在最後。 但Jeremy說龐猜可以命名為“佩氏定理”，俺以前說過，俺覺得應該是“漢佩定理”。 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. |
