The winners of the 2006 Fields Medals are Terence Tao and Grigori Perelman (as widely predicted), also Andrei Okounkov, and Wendelin Werner. For some more information, see the press releases at the ICM site.
Okounkov’s mathematical work has been in the area of representation theory and its links to combinatorics. His work in mathematical physics is well-known, relating random partitions and the statistical mechanics of certain crystals to Gromov-Witten and Seiberg-Witten theory (counting holomorphic curves and instantons). For some nice expository papers of his about this, see here, here, and here.
Wendelin Werner I know little about, his work involves 2d random walks and is related to CFT. There has been a lot of activity recently in this field, and there’s a related program going on this semester at the KITP. A friend wrote to me this morning to speculate that this is the same Wendelin Werner who at age 12 appeared in the film “La Passante du Sans-Souci”.
Update: Luca Trevisan is blogging from the conference.
Today the arXiv servers contain the message ” arXiv.org servers are currently under very heavy load due to demand for Grisha Perelman’s papers, published only as arXiv.org e-prints, which are available below.”
tg wrote:
(3) The feeling that Perelman’s work has “killed” the field, so new graduate students and others are loath to bother continuing on.
I’m not sure this is true. As MathLover pointed out, there’s probably quite a lot that can be done with Perelman’s techniques. Geometrization can probably help us understand 3d TQFT and knot theory, for example. The problem is that these techniques are really hard to use. That’s why it took several years for the ideas to be accepted as true (although I seem to recall Hamilton saying a few years ago that the ideas were probably correct), that’s why the full proofs are hundreds of pages long, and it’s why we haven’t seen the same rush of theorem proving that came after Seiberg-Witten.
Chern and Yau are Chinese mathematicians. Over one billion Chinese understand this obvious fact. Both were born,raised and educated-excluding Yau’s Berkely years- in China and Hong Kong.
Yau clearly wants his accomplishments to seen as a great of achievement for the Chinese people. Americans of European descent are not interchangeable with one billion Chinese living in China.
I would rather have my tax dollars spent on developing home-grown mathematical talent(like my own three daughters)
One last thing. Peter, thank you for this website. You are performing a great civic duty for the general public.
Lubos hasn’t pulished a scentific paper in nearly three years. There is something very weird going on over at the Harvard physics departement. Or maybe Lubos is working on something very top secret.
Dear ordinaryamerican,
You say:
“Americans of European descent are not interchangeable with one
^^^^^^^^^
billion Chinese living in China.”
Thank you for proving my point; I presume you enjoyed Nasar and Gruber’s article.
Dear A.J.,
“”(3) The feeling that Perelman’s work has “killed” the field, so new graduate students and others are loath to bother continuing on.”
I’m not sure this is true. As MathLover pointed out, there’s probably quite a lot that can be done with Perelman’s techniques.”
I should have called my “reasons” for why more isn’t being done by “general/plausible reasons”. Sure, I believe a lot can be done — but how convincing is the situation to an incoming grad student, with there being so much math available to be done?
“Geometrization can probably help us understand 3d TQFT and knot theory, for example.”
This sounds nice to me!
ordinaryamerican,
Please take the nationalism and racism elsewhere. I’ll delete anymore of it that people try and introduce here, but I have to admit you do give credence to those commenters worrying that anti-Chinese prejudice is an issue.
Hoping to be on-topic, I would like to ask: before that the Poincare conjecture was proofed, somebody doubted about its validity, or it is one of these statements that physicists consider true for obvious intuitive reasons?
There’s no “obvious intuitive reason” for the Poincare conjecture to be true, and because it was so hard to prove, their certainly had been mathematicians who speculated that there could be a counterexample and looked for it.
Peter,
Would you say or have you heard other mathematicians speculate on whether there is something specially about 3 dimensions that made it the last and most difficult case to solve the Poincare conjecture in?
TheGraduate,
The standard explanation is that in higher dimensions there’s so many ways to move things around that things simplify. The conjecture was proved in dimension 5 and above during the sixties. dimensions 1 or 2 are easy, because there’s not that much that can happen. The worst cases are dimensions 3 and 4, because there’s enough room for a lot of complicated things to happen, but not enough to move things around and simplify.
I don’t know of a particular reason why 3 should be worse than 4. Actually, the “smooth Poincare conjecture” still remains unsolved in 4 dimensions, this says that there is only one “smooth structure” on the four-sphere.
Graduate,
You asked Peter
**Would you say or have you heard other mathematicians speculate on whether there is something specially about 3 dimensions that made it the last and most difficult case to solve the Poincare conjecture in?**
I can tell you one special thing about 3D that you can think about while waiting for an authoritative answer. This is just something that comes to mind about 3D that might not actually address your question. A fun thing though.
You can tie knots in 3D.
whereas in 2D it is hard to tie knots, and in more than 3D the knots tend to come untied and turn out not to be knots.
Thanks for the answers Peter and Who.
A few months ago, I had been reading an overview of past fields medal work by Michael Monastyrsky and I was struck by the following:
“From the time of Cayley, the following division algebras were known: real numbers, complex numbers, quaternions, and Cayley numbers … A natural question to ask is: Are there other division algebras? The negative answer was obtained only in the 1960s and proved to be closely related to the following topological question: find all spheres on which the number of independent, continuous vector fields is equal to its dimension. There are only three such: S1, S3, S7.”
I can’t even begin to claim I understand all the ideas in that quote, but… it seemed to suggest something special about these sorts of spaces: reals, complex numbers etc that have proven so useful in physics.
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To expand on Peter’s explanation of why higher dimensions have been easier for the purposes of the Poincare conjecture, the point is that an important tool in the higher-dimensional case (both for Poincare and for related results, like the h-cobordism theorem) is something called the “Whitney trick,” which is used to ensure that if two transverse submanifolds P and Q of complementary dimension in a simply-connected manifold have homological intersection number zero (which ordinarily just ensures that their intersection points come in oppositely-signed pairs) then one can isotope them to not intersect at all. To perform the trick, given any algebraically-cancelling pair x,y of intersection points between P and Q one needs to find an embedded 2-dimensional “Whitney disk” with the left half of its boundary being a path in P from x to y and the right half of its boundary being a path in Q from x to y. By simply-connectedness, one can always find a map of a disc into the manifold with the right boundary conditions–and if the dimension of the manifold is at least 5 then after a little jiggling the disc will become embedded and so the Whitney trick works. If the dimension is three or four, the disc can be jiggled to be immersed, but it will tend to intersect itself and thus not be embedded.
The failure of embeddedness isn’t as bad in dimension four, since genericaly all the self-intersections are single points. Because of this, Andrew Casson had the bright idea of using a complicated kind of infinite-dimensional handlebody now called a Casson handle as a replacement for a Whitney disc; Michael Freedman’s big technical result was that a Casson handle is homeomorphic to a standard handle, and this enabled him to prove that all the 5-or-higher-dimensional techniques for the h-cobordism theorem and Poincare still work in dimension 4 if one is willing to work up to homeomorphism rather than diffeomorphism. My understanding is that at the time he thought that if only one were cleverer one could extend his result to the smooth category, but within a year it became clear that that wasn’t the case: although we still don’t know whether the smooth Poincare conjecture is true in dimension 4, we do know via Donaldson’s results that the h-cobordism theorem does fail in that dimension–so Freedman’s technical result was actually as good as one could hope for.
In three dimensions a prospective Whitney disc would intersect itself in a one-dimensional submanifold, so there’s nothing analogous to Casson handles that one could try to use. In that regard, it’s fair to say that the proof of Poincare in dimension four is very much in the spirit of that in higher dimensions–although showing that the ideas from the higher-dimensional case actually extended to dimension four required hard, Fields-medal-deserving work. The proof in the three-dimensional case uses a completely different approach.
q2, this was wonderfully informative, thank you very much.
Thanks q2. I don’t quite understand all the terms but it’s good to at least know what the relevant ideas and mathematical objects involved would be.
I just read the Nasar article last night. As a lover of geometry, and as a Chinese woman, it left me sad and disgusted and angry. All the more so because I knew the New Yorker was running a story about Perelman, and I had so looked forward to reading it — it’s not every day that I get to read about math in the New Yorker! I had expected a detailed biography of Perelman, with detours into the world of modern mathematicians and their work, a sketch of the historical background to the Poincare conjecture, a depiction of the working life of mathematicians in the 21st century. ….I don’t know how one explains the pursuit of abstract mathematics to a lay audience, but I was greatly looking forward to the attempt.
Instead, as I read on and on, I could not believe how she was turning this beautiful story, this “landmark not just of mathematics, but of human thought” into a petty, racist soap opera.
Her descriptions of Yau as a washed-up uncreative techno nerd, and her implication that the Chinese are trying to improperly take credit, were painful to me. It seemed like such an exaggeration and distortion of Yau’s motives, work, and personality, and in a more anodyne but nevertheless insidious fashion, of Perelman’s motives, work, and personality (basically, he’s given the personality of a paranoid sheep). The subsequent comments of mathematicians quoted in the article indeed prove without a doubt that she was distorting their comments re Yau. Yet, even with all her deceptions, she couldn’t hide the fact that Yau *had* with his sharp mathemactical nose identified a critical problem and the right approach, as demonstrated by how hard he was encouraging Hamilton to follow up on his Ricci flow method.
This is a great story and Perelman is a true hero. Unfortunately, even though Sylvia Naser has a good command of English and rhetoric, she clearly doesn’t love math or have any inkling of its walk-on-air beauty, to do justice to the story. Otherwise, I’m sure she would have been able to communicate a shred of that beauty in her long-winded article.
By the way, the quote about the 50/25/30 breakdown in credit made at a speech in China, which Naser turns her nose at (“Even mathematicians can sometimes forget how to add”) was obviously an ironic joke by Yau, a self-deprecatory laugh at the unseemliness of China taking a percentage of the credit in this case, and indeed, the futility of ever apportioning credit exactly (yet it is completely understandable that China, a developing country, would want to celebrate its small but impressive contrbution to this discovery and it is touching of Yau to cheerlead this effort; I for one am proud that Chinese mathematicians living and working in China and publishing in Asian journals are able to do world-class mathematics). It might also be a geometry joke, since geometry is all about getting rid of numbers and not having to use coordinates.
Grigory Perelman got it exactly right when he said “journalists should have better taste.”
dt,
Please calm down.
From everything I’ve read, the 50/25/30 breakdown was not intended as a joke. Someone made a silly mistake. That’s all.
Further, S T yau is very well known to be notoriously competitive. There are many, many stories circulating about him to this effect since many years.
On the other hand, we all know of (born and bred in the) US scientists who are at least as competitive as Yau, so this not a particularly Chinese characteristic.
Dear dt,
I support your finely written comment.
At a recent ICM interview Cao said that Yau never talked about “50/25/30 breakdown”, and does not agree to any such breakdown.
(I think this is in ICM daily news of August 29).
Now this is interesting because the quote in Nasar’s paper (from a press conference at the math institute in Beijing) is very precise and clear. I am sure someone must have the whole press conference on tape. I wonder who is lying here?
dt:
I am glad you and other Chinese had chosen to share your opinions here.
I thought perhaps Nasar and Gruber were looking at things through the prism of American foreign policy. Through that prism, the rise of China would be potentially threatening.
One of the reasons that I do not think it rises to the level of racism is that I do not think they would have reacted to a similar situation with a Japanese person in the same way. I think this is because Japan is a strong partner of the US.
For me also, the article was not what I had expected it would be.
One question I did have for you or any other Chinese speakers that might care to comment: quite a few people who have identified themselves as Chinese have said things along the lines of Yau being brave or noble or caring etc. I was curious about what these comments were based on. Are these based on assumptions or are they based on things you know about Yau that non-Chinese speakers would not know?
For instance, How did you come to this conclusion: “obviously an ironic joke by Yau, a self-deprecatory laugh at the unseemliness of China taking a percentage of the credit in this case, and indeed, the futility of ever apportioning credit exactly”?
geometer:
Where did you hear/see the interview? Can you provide a link or reference to the source?
page 2 of http://www.icm2006.org/dailynews/dailynews29.pdf
Dear TheGraduate,
You said:
“One of the reasons that I do not think it rises to the level of racism is that I do not think they would have reacted to a similar situation with a Japanese person in the same way. I think this is because Japan is a strong partner of the US.”
The notion that Japanese and Chinese are not treated the same does not mean to me that there is no racism involved!
You also asked:
“Where did you hear/see the interview? Can you provide a link or reference to the source?”
Look at http://www.icm2006.org/dailynews/
I actually had some problems reading the files. But I did notice an interview with Cao who asserts that Perelman’s work was clearly the central (final) step in Poincare. Interesting Cao also seems to suggest that Yau has said the same to Nasar during her research into her biased, anti-China article. But this never seems to appear in her write up.
It should also be noted that even with regards to Nasar’s “A beautiful mind”, I’ve heard that a number of mathematicians have been angered by how she’s twisted/exploited their words to achieve effect. I ignored that feature of her journalism until recently, since the text was so nicely written.
So while previously, I believed what she said was true, but not given proper context — I now how reason to suspect that what she’s said in her article includes crucial falsehoods.
In retrospect I’m embarrassed as follows. As a mathematician, I so rarely see my field portrayed in media — so when it does happen, I’m quick to read/see it and enjoy it. I think I’ll be more discerning in the future.
tg:
Another reason I do not consider race as the dominant factor is that if Yau had been born and raised in America then they probably would also not treat that situation the same way. Do you perhaps mean some form of discrimination besides race-based discrimination?
I don’t think there is any reason to be embarassed for mathematics. Everyday people care more about politics than they do about computations. This kind of controversy will probably be more attractive to young people as it shows mathematics matters and also it shows mathematians as strong, socially aware characters in the form of Yau. It also shows Perelman as a detached guru-type … which is probably also appealing for some young people. Something for everyone …
I had a brief conversation with Nasar when she signed my copy of “A beautiful mind”. She was pretty friendly. I don’t think she is a saint though. It was always fairly obvious to me that she wasn’t a pushover. She gathered a lot of information on Nash for a long time against his will. She documented a lot of things on Nash that he probably didn’t want in print.
tg and geometer:
Also, thanks to you both for the link to the interview.
There are way too many half-truths, and extrapolations here for my taste. I’m surprised that Peter is not deleting more of this stuff.
The (mis)allocation of credit appeared in the Chinese press but is attributed not to Yau but to a Chinese mathematician named Yang Le, who as far as I know has no particular expertise in Ricci flow or the Poincare Conjecture.
Dear TheGraduate,
You raise an interesting point about how Yau would be treated if hypothetically he were born and raised American. I’m honestly not sure, based on my own experience. Perhaps a reasonable thought experiment would be to wonder how likely the Newyorker would run such a piece if it so happened that Yau was an American, born in another country X, and his activities were closely tied to being of X ethnicity, for various values of X. Again, I recommend reading the September notices of the AMS (available online) for another perspective on this and related issues (with regards to more “mortal” mathematicians).
tg:
Do you mean the article “An Invisible Minority: Asian Americans in Mathematics” ? I have read that article.
“Do you mean the article “An Invisible Minority: Asian Americans in Mathematics” ? I have read that article.”
Yep. Although I suppose here is not the place to discuss it — as much as I’d like to.
tg:
according to Nasar’s article Yang was indeed talking about allocation of credit, but Yau was standing next to him and confirmed what Yang said. And in any case, if Yau thought this allocation of credit was entirely unappropriate he could’ve distrubuted a statement (eg post it on the Beijing Math Inst site) to that effect, clarifying his position. He did not do that at the time, and the phrase about “50/25/30 breakdown” went arount the world.
BTW, speaking about “invisible minority”. This article in the Notices hinges on the difference between Asians and Asian Americans. This may be a valid point as far as students/postdocs are concerned but for faculty it makes no sense. The absolute majority of tenured math faculty are citizens or permanent residents, so they are already Asian Americans, no matter where they were raised or educated.
Dear geometer,
You might have wanted to direct your comment about Yang’s remarks to Deane. I’ve only spoken about Cao’s remarks at the IMU; I haven’t thought to raise the issue about Yang, although it sounds interesting. In any case, as I’ve said before, whether Yau said these things or not is not relevant to my argument. My complaint is unfair focus on this man and his relationship to the Chinese. I’m sure that if Nasar wanted to, she could research any one she wanted and make a case that that person is scum of the earth.
You said:
“BTW, speaking about “invisible minority”. This article in the Notices hinges on the difference between Asians and Asian Americans. This may be a valid point as far as students/postdocs are concerned but for faculty it makes no sense. The absolute majority of tenured math faculty are citizens or permanent residents, so they are already Asian Americans, no matter where they were raised or educated.”
I’m not sure I fully understand your remark about the “invisible minority”. There are plenty of non-American asians (e.g., mainland Chinese) who graduate from math PhD programs. They certainly have barriers too — but it’s surprising to me how _few_ Asian Americans (given the advantages of citizenship and language) do so. I think it’s this suprising fact that is what the author wants to focus on. The article is mainly about barriers to a tenure track position, I agree — but I still think it is relevant to faculty.
I didn’t think the article of Nasar and Gruber was necessarily disrespectful to Chinese, but what is clear from reading the comments here is that there are people who are eager to make a connection between the aggressive behavior of certain Chinese mathematicians with their nationality. As an Asian, though not Chinese, I am not happy to see those comments.
The fact is that it is not uncommon for successful scientists and mathematicians to have reputation of being aggressive or even nasty. I guess John Nash, who was the subject of Nasar’s book is an example. But you don’t see anyone who associates John Nash’s personality with his heritage. How about Jim Watson? Carlo Rubia? It seems the connection is only made when the scientists/mathematicians are of certain ethnicities.
tg: Sorry for misplacing my post to Deane. Now you say: “My complaint is unfair focus on this man and his relationship to the Chinese. ”
Okay, I don’t think Yau-Tian fights and Chinese math politics are relevant to Nasar’s story, but surely Yau (not anyone else!!) the one who singlehandedly created the controversity on the “who proved the Poincare Conj” issue and this is what the Nasar’s article is mainly about. According to Yau’s survey at arxiv (see last page) the Perel’man’s argument is not written in complete detail, and Cao-Zhu papers give a first complete and detailed account, and that Cao-Zhu contribute original ideas not present in Perel’man’s proof. This feels very different from what Hamilton, Morgan-Tian, Kleiner-Lott are saying. They do say that Perel’man’s proofs are concise but they never doubt their completeness. In fact, in his ICM talk Hamilton said “the Perel’man proof is correct and complete”, and Morgan-Tian, Kleiner-Lott give all credit to Perel’man, they said that no substantially new ideas were needed. To me it sounds like Cao-Zhu could not follow Perel’man’s argument and found it easier to prove it differently. This is okay and happens all the time in math. However, when this happens people say “this is another, perhaps easier proof”, and they get credit for the new proof, not the new result. (Even though Morgan in his ICM interview said he could not see what was so new and different in Cao-Zhu paper). Now you might say that this is a free country and Yau could express his opinion on any topic including Perel’man’s proof, even though other experts say otherwise. Well, if Yau were nobody, people would not worry what he says. The trouble is that because (as I think) Yau is the most influential person in geometric analysis, what he says matters, and when he does something unethical, it hurts the geometry community. So this story is indeed about Yau. If he did not do what he did, there would be no controversity. And Nasar merely aired the controversity to the general public; most of what she wrote about Perel’man’s story is no news to me, and I did not like Yau’s survey the first day I saw it, and I was upset when I heard the “50/20/35 breakdown”. Both events happened way before I read Nasar’s paper.
Dear HI,
“But you don’t see anyone who associates John Nash’s personality with his heritage.”
Absolutely correct, and that’s my point, don’t you see?
HI:
Who here is eager to make a connection between Chinese mathematicians and their ethnicity?
If one were to crudely split the different comments into two groups, All I see are some people that say that the article is outright anti-Chinese and other people saying they didn’t think it was as negative as all that.
Most people are explicitly or implicitly saying that racism and nationalism are bad for mathematics.
Only outlier is ‘ordinaryamerican’ who had some stupid things to say but PW clearly put him in his place.
tg:
I think Asians are unrepresented at the faculty level in comparison to the number of Asians that are present at the graduate student level. I actually had this opinion before I ever set eyes on the September issue of Notices.
I don’t know why that is but I guess the September notices is the beginning of an explanation.
I think one important point that the article makes is that there is a lot of variety in Asia: South Korea, India, Vietnam, Japan etc
Dear geometer,
Based on what I know, I can see why one could be upset about this priority fight. As I’ve been saying all along, even if I grant every fact that you cite (and I’m mostly inclined to), then I still have an issue with the article (and moreover the caricature that accompanies it).
Nasar and Gruber could have written about the controversy of correctness, saying that even a Fields medallist (Yau) was sufficiently unsure — in contrast to his learned colleagues (Morgan, Lott et al); math is about proofs, and sometimes what is a proof is debatable and in this case has caused heated discussion; Yau although raised in China is an American, having been trained in the US and considered among America’s best mathematicians, etc etc. Even keep most of the quotes that are there, but downplaying the whole China connection.
In that case, it would be clear that Yau-Chinese is not the connection, but rather Yau the scientist is. I’d have no problem with such a (boring) article. Nasar and Gruber cleverly and subtlely went just beyond the line.
Nasar is a crafty and skilled writer. She’s no dummy. I’ll assume the same for Gruber. They know Americans have a fear/distaste for China and their expansion. They know incorporating China into this would play well, and she exploited it. But, in my opinion, all people of Chinese descent are detrimentally affected by this approach — a small cost for her paycheck.
Dear TheGraduate,
You say:
“I think Asians are unrepresented at the faculty level in comparison to the number of Asians that are present at the graduate student level. I actually had this opinion before I ever set eyes on the September issue of Notices.”
…and the number of graduate students are underrepresented in comparison to the number of undergraduates. I also agree with you about the point concerning many different “asian ethnicities”.
tg: okay, I see where you are coming from and mostly agree with what you are saying. I might add that what I disliked about Nasar’s paper is that it portaites Yau as no longer so great a mathematician whose best days are long gone, which is why he is playing politics. I think, Yau is truly great, but I also think some of the things he does hurt our field, and I wish he could stop (or be stopped).
tg:
I guess what I am hearing from you is that you think that Nasar and Gruber should have avoided the China vs America issue. So I ask you, why? You say ‘all people of Chinese descent are detrimentally affected ‘ and so I ask you, how so?
Are you saying, there should be no articles about China? China is a country with 1.3 billion people. It is kind of hard to ignore.
Are you saying there should be no articles about the rise in Chinese power on the global stage. (Again, a billion people and hard to ignore.)
Are you saying there should be no articles in America where people express concern about the rise in power of China? (Given that the US is commited to go to war against China if it invades Taiwan, that might be wishful thinking.)
Anyway, the Chinese government is investing a lot in getting better quality schools and keeping better quality researchers in China … everybody knows this.
Actually while I’m on the subject of under representation … Asians are also under represented in US politics … I think if this situation was corrected the US would have a lot easier time dealing with China.
Dear TheGraduate,
You ask:
“I guess what I am hearing from you is that you think that Nasar and Gruber should have avoided the China vs America issue. So I ask you, why? You say ‘all people of Chinese descent are detrimentally affected ‘ and so I ask you, how so?”
Your questions are very valid. However, I have already said and repeated all that I really have to say multiple times. I guess all I have to say at this point is that reasonable people can come to differing opinions about the same issue!
tg:
Okay. Fair enough. Basically I think that if this kind of stuff affects American-born people of Chinese descent then that has to do with the prejudice of the people that are affecting their lives.
The internment of the Japanese-Americans wasn’t wrong because it was wrong to go to war with Japan or to bring up going to war with Japan or even to bring up the rising power of Japan. It was wrong because they were American citizens just like any other American citizens and deserved to be treated as such.
As a person of Russian decent and a lover of trigonometry with a limited exposure to the world of advanced mathematical studies, I observe with a surprise and discontent the tidal wave of negative reaction of Chinese geometry lovers to the article of Nasar and Gruber.
I do not know what criteria Mr. Woit is using to characterize someone’s writing as racist and homophobic views, but I am amused at shear amount or futile discussion about number of Chinese PhD students and whining about being underrepresented, etc, etc, etc.
Nasar and Gruber, in my opinion, made several good points:
a. Some people can not accept the fact they exhausted their scientific potential and are trying to influence the scientific community thru maneuvers looking legitimate. Is not it the reason that many talented people in science world and academia leave being tired of politics, chase for higher place in hierarchy based not on talent but ability to develop connections, build coalitions?
b. It is Yau who turned the solution of the math problem into the matter of Chinese pride, no more, no less. I read in disgust the announcement of Xinhua News Agency English edition stating that Chinese scientists resolved a century-old Poincare conjecture. If Xinhua lied (not for the first time) it was responsibility of Chinese scientists to establish the truth.
c. I was especially disappointed with Yau taking lower road on a loner like Perelman. Perelman clearly has distaste for everything that is not related to the core value of every science, namely contribution to the favorite research field without consideration for success, monetary compensation, vanity, recognition, etc. Not so for Dr. Yau; not being able to contribute any significant work for the last twenty years, he it trying to reach fame utilizing thirst of the Chinese government for good publicity.
While it would not fair to characterize all Chinese based on dirty politics of Dr. Yau, it won’t be inconsiderate to note that none of the Chinese geometry lovers were dare to criticize Dr. Yau. Is it something about introverted nature of Chinese culture that critique is accepted if only comes from inside and only from people within the community of certain statue or authority?
I have great respect for Chinese history and people, but that does not mean I have to agree with superficial speculations of Chinese
geometry lovers. I will tell them, it is not quantity that matters, it is quality. I will tell them, if you can not be at the front, let it go, let others go ahead with their ideas.
To Russian:
How do you know that “none of the Chinese geometry lovers were dare to criticize Dr. Yau”?
There has certainly been plenty of criticism of him on this forum, many of it from Tian supporters, I am sure. (Just ask Peter, who must be tired of deleting all those personal attack posts.) None of them is a “Chinese geometry lover”?
And please do not stereotype Chinese geometry lovers. The vast majority of them are busy doing mathematics and do not post here.
I guess this issue is raising a lot of nationalism. China and America are geopolitical rivals. There is not much than can be done about that except maybe for Americans to try to understand China better and for Chinese to try to understand America better. I think those people who have connections both to China and America can probably make a big difference in this. Such people are more likely to be able to see what things people from both countries will find honorable and desireable.
Russian,
There have been plenty of comments here from Chinese people critical of Yau, and I deleted many such others that were far more hostile.
Everyone,
Please stop with the discussion of nationalism/racism, etc. It’s not going anywhere, has only a little to do with this story, people are just repeating themselves, and it hasn’t been very enlightening. There’s a reason I try and avoid discussing my opinions about political matters here: I find virtually all political discussion on blogs to be a complete waste of time. Most people love to argue their political opinions, very few pay much attention to what others have to say. You end up after a while with pure noise, and participating in it just wastes time and energy. So, please, if you want to discuss the Poincare story, fine, but try and stick to the facts and the mathematics, avoiding personal attacks on Yau, Tian, or anyone else, and you better have something really new and really interesting to say if it’s on the nationalism/racism issue (and it should be related to Poincare).
I am not a professional mathematician, but it seems to me that a number of people here have an entrenched grudge against Yau and that some of these people also form their opinions based on the New Yorker for their “facts” and mathematics.
The critics of Yau here ascribe him certain vague disposition and views that he apparently holds. But it is not clear that this kind of attribution originates from the critics themselves, including the New Yorker, or Yau really holds them (please see the interview given by Cao for the ICM). What we then tend to have is basically a series of personal attack on his character, often based on hearsays and second-hand gossips. Whatever the nature of Yau’s personal character, surely his critics are not saying that they are saints themselves? Not checking facts or distorting them and then proceed to attack the person’s character is utterly deplorable. The best way to have a go at Yau is to do better maths than him, period.
I have a different take on the Poincare Conjecture.
In the press reports that I have read from China, Yau has often maintained that the Cao-Zhu paper was the finishing step of the works of Hamilton and Perelman. Likewise in the Cao-Zhu paper, they explicitly referred to the paramount importance of Hamilton and Perelman. All these are conveniently ignored by some people.
As an outsider looking at mathematics in history, there is nothing wrong with assigning percentages in the debate on Poincare. We may disagree with the allocation, but it is a reminder that major advances in mathematics are often built on the cumulative endeavor of many others. John Morgan, in his ICM talk, indicated that in the currency of the mathematics community, Perelman should be accorded with the Poincare proof. However, according to him, Perelman would not have done it without Hamilton and “vital” contribution from Yau. History will judge the allocation.
Perelman spoke of honesty in the New Yorker. But why does he not have the honesty of acknowledging the works of Cao, Zhu, Morgan, Tian and others in providing the rigor and details for his program? He provided sketches on some of his proofs and over the last 3 to 4 years has not prepared or able to produce rigorous proofs for his program (why Steklov could not help out?). I hope that I am not wrong in saying that sketches can not be regarded as proofs for the requirements of mathematics as a science. I think the works of those authors have given the ICM the added confidence to award Perelman the Fields medal and the mathematics community to accept Poincare has indeed been proved.
To me, Perel’man’s behavior is due to reasons that have nothing to do with mathematics or with the math community. I think he reflects his feelings towards other issues on the math community, by not completing or publishing his proof, by declining to accept prizes, etc, etc.
the fact that 3 different groups completed the Perelman program in roughly the same time suggests that it is routine work. I do not see any point in assigning more merit to the group that could publish a full proof a bit faster than others.
“To me, Perelman’s behavior is due to reasons that have nothing to do with mathematics or the mathematics community”
It is possible Perelman is having a “mid-life crisis” or has even had a nervous breakdown after years of very intense mental work on this problem. Events or personal/professional issues at the Steklov perhaps pushed him over the edge. Speculation of course but it would not surprise me if that indeed is the case.