## Fruitcake fields

So, this year’s Fields Medals go to Terence Tao and Grisha Perelman (duhhhh), as well as to Andrei Okounkov and Wendelin Werner. The Nevanlinna Prize goes to an already-prize-bedecked Jon Kleinberg, my professor at Cornell way back in ’97. Congratulations to all!

Meanwhile, there’s a long article in yesterday’s New Yorker about Perelman and the Poincaré conjecture, by Sylvia Nasar (the media’s go-to person for reclusive mathematical geniuses) and David Gruber. Unfortunately the article’s not on the web, but fearless detective that I am, I was able to track it down in a so-called “bookstore.”

Nasar and Gruber find Perelman in a St. Petersburg apartment, where he lives with his mom, doesn’t check his mail, and just generally makes Andrew Wiles look like a hard-partying, elliptic-curve-modularizing regular dude. Perelman is nevertheless happy to grant Nasar and Gruber an interview, to confirm that he intends to be the first person in history to turn down the Fields, and to complain about his fellow mathematicians’ lax ethical standards.

What exactly is he talking about? It wasn’t clear to me, but Nasar and Gruber devote much of their article to an indictment of 1982 Fields Medalist Shing-Tung Yau, who they portray as trying to usurp credit from Perelman for the benefit of his students Xi-Ping Zhu and Huai-Dong Cao. (Zhu and Cao wrote a 328-page exposition of Perelman’s ideas, complementing other expositions by Bruce Kleiner and John Lott and by John Morgan and Gang Tian.) I have no idea to what extent, if any, the criticism of Yau is justified. But to my mind, failing to write up your result properly, and then getting upset when those who do write it up properly try to share credit, is a bit like leaving your wallet on the sidewalk and then shaking your head at human depravity when someone tries to steal it.

Nasar and Gruber also don’t comment on the obvious irony of Perelman’s “unworldliness”: that, by being such a fruitcake, he’s guaranteeing he’ll draw vastly more attention to himself than he would by just accepting the goddamned medal. (Feynman, though not exactly publicity-shy, employed similar reasoning to conclude that turning down the Nobel Prize would be a bad idea.) Indeed, supposing Perelman did aspire to celebrity status, my public-relations advice to him would be to do exactly what he’s doing right now.

Update: The New Yorker article is now online.

Comment #1 August 22nd, 2006 at 10:33 am

I hope that as many words could be devoted to the personalities of Terry Tao, Andrei Okounkov, and Wendelin Werner. I don’t really know these people well, but my impression is that they are all very nice guys.

Perelman, for his part, doesn’t particularly deserve his strange personality, but he certainly does deserve the Fields Medal. I think that this talk about Perelman leaving his wallet on the street is a presumptuous metaphor. In my view, there is no real standard for writing up results “properly”. If Perelman had pantomimed the proof without writing down anything, that might have been good enough for all I know.

But what can be said is that it’s a shame that Perelman couldn’t set aside some personal grudges to accept the Fields Medal, if that is what has happened. Surely everyone else should try to set it aside regardless.

Comment #2 August 22nd, 2006 at 10:42 am

I think your post is very harsh on Perelman. If he doesn’t want to accept the Fields Medal that’s no sin. Maybe he is a better man than you are?

Comment #3 August 22nd, 2006 at 10:51 am

Writing results “properly” can be debatable but if you throuw bits and pieces here and there and somebody gathers it to make a well-written paper then you shouldn’t bark at them. I do not know how many peeple think that Yau’s students solve Poincare’s conjecture but the mathematics community give Perelman the credit. Take for example, Wiles proof to Fermat’s Theorem. He proved it using Ribet’s work. Amateurs will remember it as Wiles work but ask someone working in this area. They will include Ribet, Frey and all.

I agree that Perelman declining the Fields medal is a shame because this is something which is above your personal problems and conflicts. At least, the community is acknowledging you for your great work.

All said and done, I am not a good writer and an amateur too.

SKU

Comment #4 August 22nd, 2006 at 10:53 am

It is a shame that they don’t have any awards for good supervisors. The first award will go to Manuel Blum and then Umesh Vazirani.

Comment #5 August 22nd, 2006 at 10:57 am

If he doesn’t want to accept the Fields Medal that’s no sin.I didn’t say it was. I merely pointed out the irony of rejecting the Fields Medal

because one doesn’t want the attention.Maybe he is a better man than you are?Again, I didn’t say he wasn’t.

Look, if Perelman was happy where he was, then I agree it would be presumptuous to discuss how he ought to be behaving. But if you read the article, he doesn’t seem at all happy.

Comment #6 August 22nd, 2006 at 11:00 am

It is a shame that they don’t have any awards for good supervisors. The first award will go to Manuel Blum and then Umesh Vazirani.I’ll second that! (Though it’s possible that Blum’s Turing Award was partly for his spectacular advising record.)

Comment #7 August 22nd, 2006 at 11:50 am

Some of the rumors that I have heard, recently and not so recently, are: (1) Perelman’s accusations against Yao are at least highly plausible; and (2) Perelman’s problem is not so much that he hates publicity, but rather that he takes grudges to extremes. If so, his interview with Nasar may not be inconsistent with his “objectives”.

Comment #8 August 22nd, 2006 at 12:09 pm

Some of the rumors that I have heard, recently and not so recently, are: (1) Perelman’s accusations against [Yau] are at least highly plausible;

The article about the Poincaré conjecture in the most recent Notices of the AMS has a link to the slides that Yau used for a public lecture at the Chinese Academy of Sciences. The article pretty much says “judge for yourself”, which is of course hard to do if one is not an expert.

Comment #9 August 22nd, 2006 at 12:32 pm

The article pretty much says “judge for yourself”, which is of course hard to do if one is not an expert.Okay, I’m convinced that Yau is playing games. These slides are at the very least incredibly biased. John Lott’s talk here in Madrid looked totally different from this. If Yau says that he was misquoted, then he is inviting the tedious chore of chasing down who said what when, if it was on tape, etc. As weird as Perelman is, what is going on in China seems gratuitously political.

Comment #10 August 22nd, 2006 at 1:41 pm

A couple of points:

1/ If Perelman really doesn’t care about the Clay money, I can see why he wouldn’t want to march through a numbing 328 page explication of every little point for the benefit of normal people like you and me.

2/ If Perelman isn’t reading his mail or (presumably) talking with reporters on the phone, then aside from Nasar and Gruber nobody outside of Russia is going to go over there and bother him about it. So his strategy to avoid hassles (if that is what it is) should mostly work.

I haven’t actually seen the article yet, but I’m sure this week’s New Yorker will turn up in my mailbox someday. Love the blog.

– Levi

Comment #11 August 22nd, 2006 at 2:00 pm

Whatever Perelman’s intention was for denying the award, it certainly is giving him more attention.

Here’s videoblogger Ze Frank’s take on it (middle segment)

http://www.zefrank.com/theshow/archives/2006/08/082206.html

Comment #12 August 22nd, 2006 at 2:55 pm

Perelman==Grothendieck?

Also, Zhu and Cao begin their article very fairly:

“In this paper, we shall present the Hamilton-Perelman theory of Ricci flow. Based on it, we shall give the first written account of a complete proof of the Poincare conjecture and the geometrization conjecture of Thurston. While the complete work is an accumulated efforts of many geometric analysts, the major contributors are unquestionably Hamilton and Perelman.”As for Yau, well, anyone who can solo-author a review article like this (having 755 references) has all my respect.

Summary: it seems that everyone involved is doing very good work, and behaving politely, openly, and honorably, and writing beautiful articles for us to read.

Golly, maybe that’s newsworthy!

Comment #13 August 22nd, 2006 at 5:10 pm

I understand that Perelman declined the award more as a statement against the internal-political nature of these sorts of awards and gatherings;

It seems more like an existential stance.

Nevertheless, it would have been better if he made his reasons for declining the award public. But this is his choice.

Comment #14 August 22nd, 2006 at 5:50 pm

If Perelman ever explains himself, it will be interesting to compare Perelman’s thinking with Grothendieck’s well-known reasons for renouncing the Crafoord Prize. The point being, that Perelman’s actions may well be in an honorable tradition.

Comment #15 August 22nd, 2006 at 5:58 pm

“The reasons center around his

feeling of isolation from the mathematical community,” Dr. Ball said of Dr. Perelman’s refusal, “and in consequence his not wanting to be a figurehead for it or wanting to represent it.”Comment #16 August 22nd, 2006 at 6:08 pm

…a link to the slides that Yau used for a public lecture at the Chinese Academy of Sciences. The article pretty much says “judge for yourself”, which is of course hard to do if one is not an expert.

You dont need to be an expert to see that these slides are, as greg kuperberg says, incredibly biased. No wonder Perelman got sick of all that, and that he’d rather be picking mushrooms in a forest than participate in the circus.

As for writing the results properly: Wiles did exactly that, and half a year later people still found a hole (closed later by Wiles-Taylor). With proofs of such complexity, the best you can hope for is to give enough details so that experts in the field can hopefully verify the correctness in finite time. Which is exactly what happened.

Comment #17 August 22nd, 2006 at 6:22 pm

Greg:

I hope that as many words could be devoted to the personalities of Terry Tao, Andrei Okounkov, and Wendelin Werner. I don’t really know these people well, but my impression is that they are all very nice guys.I’d love to meet Terence Tao in particular. It’s not so often that someone wins a Fields medal for results I can understand and appreciate.

Comment #18 August 22nd, 2006 at 6:30 pm

I’m surprised no one has mentioned yet the mirror symmetry episode about ten years ago, where Yau and some students claimed that Givental’s proof was incomplete and that theirs was the first. Does anyone know if the that community ever decided either way?

Comment #19 August 22nd, 2006 at 7:50 pm

‘Take for example, Wiles proof to Fermat’s Theorem. He proved it using Ribet’s work. Amateurs will remember it as Wiles work but ask someone working in this area. They will include Ribet, Frey and all. ‘

thats bunk. even Ribet said he didn’t have a clue nor didn’t think that the taniyama-shimura conjecture could be solved. Andrew spent 7 years working on this. he deserves most or all of the credit.

Frey however did make the critical first discovery. if he hadnt rewritten the equation in elliptical form then nothing may have happened for another couple of centuries but of course even Frey didnt know what to do with the elliptical form of the equation.

thats cool that Perleman won the Fields. he won first place in the math olympiad in 82? Noam Elkies was number 2 I think.

Comment #20 August 22nd, 2006 at 10:46 pm

Anonymous: Writing results properly is more important in these really complex problems. Yes the hole in Wiles’s 1st proof was found more easily because he wrote it up thoroughly – this is a good thing. To suggest otherwise implies that it doesn’t matter if holes are there or not as long as they’re not found.

But I agree “properly” is very difficult to judge.

Comment #21 August 23rd, 2006 at 7:47 am

I feel that Peleman has received much attention that is work is needed. His visionary/intuitionistic proof (visionary in the sense that has not been proved in all the passages) is indeed a great result, but is better to have a great proof linked to a conjecture or as Tao has done publish 80 papers with some foundamentals proof on different areas of math and that in some case are understandable by a non specialized mathematician. In fact,a great mathematician ( who is supposed to be by winning the Medal) is a person that has a great result or have touched all the math areas and gave beautifull results in all of them?.

Personally I’m a normal people, but when months ago the not even wrong rumored about the fact that he would have won the medal, I write to him. He reply me with very kindness that he didn’t know anything about. I belive that a great math person is primaly a person only a genius.

Comment #22 August 23rd, 2006 at 11:10 am

thats bunk. even Ribet said he didn’t have a clue nor didn’t think that the taniyama-shimura conjecture could be solved. Andrew spent 7 years working on this. he deserves most or all of the credit.Who says Wiles didn’t deserve most of the credit? But the work of others also matters.

Comment #23 August 23rd, 2006 at 1:40 pm

Frey, Ribet, etc., deserve credit for Fermat in the sense that they reduced the number of open questions. My impression is that this was much more surprising than Wiles proving Taniyama-Shimura. But Taniyama-Shimura was much more important.

Comment #24 August 23rd, 2006 at 6:40 pm

the new yorker article is now online.

link:

http://www.newyorker.com/fact/content/articles/060828fa_fact2

Comment #25 August 23rd, 2006 at 10:44 pm

Stephen Colbert (THE COLBERT

REPORT, COMEDY CENTRAL) complained

that HE didn’t get the fields

medal last night. He also squished

a doughnut into a sphere to

disprove Poincare. He got the

basic facts right! (more so than

a typical episode of Numb3rs).

GREAT STUFF!

Comment #26 August 24th, 2006 at 5:22 am

Now that I have read the New Yorker article, I marvel ever more at Yau’s control-freak tendencies. Where Perelman goes wrong is in thinking that the community tacitly accepts this conduct. At least 70% of the people here, maybe 99%, are on Perelman’s side. Some of Perelman’s comments can be read as paranoid.

Comment #27 August 24th, 2006 at 7:03 am

The New Yorker article IMHO was short-sighted in focussing on inter-personal “controversy” (least..important..story..ever!) rather than the enormously richer story of the role of mathematics in the (re)emergence of China as a global leader in science and technology.

Even before this whole Fields Medal story broke, our UW quantum system engineering group was already working to become familiar with Yau’s work, because Kahler manifolds turn out to be the building-blocks of quantum MOR.

We were also familiar with Perelman’s work, because we found that many of our particular Kahler manifolds were Kahler-Einstein, i.e, fully smoothed under Ricci flow (and we are still struggling to understand why this is so, but we are pretty sure that these geometric features have deep links to information theory and computing theory, e.g., Scott’s Quantum Learning Theorem).

And most significantly, we were familiar with Yau’s scholarly work on the development of

Science and Technology in China, and with Yau’s hugely productive professional relationship with prominent Hong Kong businessmen Ronnie and Gerald Chan. We ended up with enormous admiration for all of the players in this drama: Perelman, Chern, Yau, and the Chan brothers.We wish that the New Yorker authors Nasher and Gruber had written a more in-depth article, perhaps entitled

Thinking Beyond Boundaries and Acting Across Borders, which summarized the global stakes now coming into play, whose informatic and technological foundation is the new mathematical tools pioneered by Chern, Yau, Perelman, and many others.Instead, Nasher and Gruber wrote an “fun” article that challenged no one’s agnatology.

Here I want to give Charles Nelson Yood credit for introducing the word “agnatology” to the computational literature (AFAIK). Yood’s 2005 PhD thesis contains this passage:

A study that asked penetrating questions about the role of industry and competition in science would be a substantial contribution to the growing literature on agnatology, which is interested in the cultural production of ignorance. Increasingly, what we don’t know in science and why may have much to do with the core agenda and methodological imperatives of computational science.Nasher and Gruber missed a great chance to ask Yood’s “penetrating questions” and thereby reduce humanity’s collective agnatology!

Being an optimist, I hope that others will think and write more deeply on the subject of mathematical agnatology. As humanity comes to a realistic appreciation of the complexity of knowledge, the question of what we chose

notto know, both individually and collectively, becomes very practical, and very important!So I will make this prediction. At present, there are precisely zero articles in the Inspec, PubMed, and MathSciNet databases that contain the word “agnatology”. But by the end of 2007, there will be at least 5. And by the end of 2010, at least 50.

Comment #28 August 24th, 2006 at 9:08 am

Now that I’ve read the New Yorker article…

As one would expect from an article in the popular press, Nasar and Gruber put forward a particular view of the controversy. Yau is clearly the villain of the piece. Their description of Yau’s role seems fairly damning, although I would like to hear more about the other side of the story.

What I don’t understand, though, is Scott’s take on this. Why “Fruitcake Fields”? In the article, Perelman comes off as slightly eccentric but nothing more. Have we really reached the point where someone who lets his fingernails grow is obviously a nut? I hope not.

I looked at Perelman’s arXiv articles. I don’t know much about the Ricci flow, and his proofs seem a bit sketchy, but if experts have found that his statements don’t omit anything important, and that all of his statements are correct, then it seems to me that his articles are rightly accepted as a complete proof.

After reading the New Yorker article I suspect that he will be offered the million dollars from Clay, and that he will eventually accept the money. Hope it doesn’t ruin his life.

– Levi

Comment #29 August 24th, 2006 at 3:34 pm

The most damning thing in the New Yorker Article is perhaps that the Yau-founded and Yau-controlled AJM published a 300-page paper by Yau proteges in 72 hours without proper refereeing. This is not the first time that has happened… look up the dates on “Mirror Principle II.”

Comment #30 August 24th, 2006 at 3:59 pm

I agree — in a case like that, what’s the point of having a journal in addition to the arXiv?

Comment #31 August 25th, 2006 at 1:24 am

john, you totally missed the point – china has at best a minor role in the proof of the poincare conjecture, but there’s massive spin trying to say otherwise. To celebrate china for this is giving in to the bullshit.

(Not that I’m saying that China doesn’t have good mathematicians, just that they can’t lay very much claim to being important to the poincare conjecture.)

This whole business of ‘formality’ and ‘review’ is really kind of dumb. A mathematical theorem is only really proven when a computer can verify the proof. Until then, it’s just hand-waving which has some degree of utility when generating a real proof.

Were it standard to present proofs in computer-checkable form, there would be no review process at all. In fact it would be possible to send a proof to a theorem server which would automatically accept any proof which checked out. Had Perelman submitted to one of those, we wouldn’t have had any review process at all, and had complete confidence from day 1, and there wouldn’t be any of this stupid game of who really proved it by making the arguments sufficiently ‘formal’ or ‘detailed’.

I view the switch to doing mathematics in the style just described as inevitable. The quite painful processes of reviewing both fermat’s last theorem and the poincare conjecture show how frayed around the edges the old system is, not to mention the major oops of realizing that there was a hole in the simple finite group classification theorem.

Partly I say this as a programmer. We programmers have been painstakingly dotting every i and crossing every t since the field began, out of sheer necessity, and we don’t complain about it. Ironically I’ve been lectured a few times by mathematicians about how programming is too informal. Pot, kettle, black.

Comment #32 August 25th, 2006 at 3:08 am

Bram Cohen sez:

John, you totally missed the point … [to] celebrate China for [the Poincare Conjecture] is giving in to the bullshit..Hmmm, for me personally what most deserves celebration is Kähler geometry, more than the Poincare Conjecture. And the geometry is itself more worthy of admiration than any of the individuals who helped conceive it. Kind of like analytic functions!

Comment #33 August 25th, 2006 at 8:20 am

It’s interesting to see the following emails/clarification etc. One thing to clarify, all these stuff have been spreading over Chinese academic websites, and I’m not the one who initially release them.

*********************************************

a Clarification from MIT mathematician Dan Stroock:

I, like several others whom Sylvia Nasar interviewed, am shocked and angered by the article which she and Gruber wrote for the New Yorker. Having seen Yau in action during his June conference on string theory, Nasar led me to believe that she was fascinated by S-T Yau and asked me my opinion about his activities. I told her that I greatly admire Yau’s efforts to support young Chinese mathematicians and to break down the ossified power structure in the Chinese academic establishment. I then told her that I sometimes have doubts about his methodology. In particular, I told her that, at least to my ears, Yau weakens his case and lays himself open to his enemies by sounding too self-promoting.

As it appears in her article, she has purposefully distorted my statement

and made it unforgivably misleading. Like the rest of us, Yau has his

faults, but, unlike most of us, his virtues outweigh his faults. Unfortunately, Nasar used my statement to bolster her case that the opposite is true, and for this I cannot forgive her.

**********************************************

State University of New York at Stony Brook professor Michael Anderson’s email to Yao:

Dear Yau,

I am furious, and completely shocked, at what Sylvia Nasar wrote. Her quote of me is completely wrong and baseless. There are other factual mistakes in the article, in addition to those you pointed out.

I have left her phone and email messages this evening and hope to speak

to her tomorrow at the latest to clear this up. I want her to remove this statement completely from the article. It serves no purpose and contains no factual information; I view it as stupid gossip unworthy of a paper like the New Yorker. At the moment, the print version has not appeared and so it might be possible to fix this still. I spent several hours with S. Nasar on the phone talking about Perelman, Poincare, etc but it seems I was too naive (and I’m now disgusted) in believing this journalist would report factually.

I regret very much this quote falsely attributed to me and will do what

ever I can to have it removed.

I will keep you informed as I know more.

Yours, Michael

*************************************

Michael Anderson’s further announcement:

Many of you have probably seen the New Yorker article by Sylvia Nasar and David Gruber on Perelman and the Poincare conjecture.

In many respects, its very interesting and a pleasure to read. However,

it contains a number of inaccuracies and downright errors.

I spent several hours talking with Sylvia Nasar trying to dissuade her from incorporating the Tian-Yau fights into the article, since it was completely irrelevant and I didn’t see the point of dragging readers through the mud.

Obviously I was not successful.

The quote attributed to me on Yau is completely inaccurate and distorted

from some remarks I made to her in a quite different context; I made it

explicit to her that the remarks I was making in that context were purely speculative and had no basis in fact. I did not give her my permission to quote me on this, even with the qualification of speculation.

There are other inaccuracies about Stony Brook. One for instance is the

implication that Tian at MIT was the first to invite Perelman to the US

to give talks. This is of course false – we at Stony Brook were the firs

t to do so. I stressed in my talks with her the role Stony Brook played,

yet she focusses on the （single） talk Grisha gave at Princeton, listing a collection of eminent mathematicians, none of whom is a geometer/topologist.

I was not given an opportunity to set the record straight with the New Yorker before publication; this was partly because I was travelling in Europe at the time this happened, and there was a rush to publish; the publication date is the same as the announcement date of the Fields Medals

I think. I was not sent an advance copy of the article for checking. I spoke with Sylvia on the phone this morning, to no avail. I’ve also had some email correspondence with Yau on the matter over the last day. I apologized to him and expressed my anger and frustration about what was done, confirming to him the quote attributed to me is false and baseless. The email to Yau is now already posted on a Chinese blog site!）.

I’ve learned my lesson on dealing with the media the hard and sour way and am still considering what path to pursue to try to rectify the situation, to the extent still possible.

Sincerely,

Mike

*****************************************

Princeton Professor Joe Kohn’s email to Yao:

Dear Yau,

I learned from Andreea that you were very hurt by my remarks quoted in the New Yorker. I did not mean to hurt you. You are universally recognizd as one of the foremost mathematicians of our times, which explains my first remark. I know how deeply you care about Chinese mathematics and therefore I assume that you would like to be as effective as possible in your leadership of the Chinese mathematical community – and this explains my second remark.

Best regards,

Joe

Comment #34 August 25th, 2006 at 12:04 pm

Certainly there are some fair points in these angry rebuttals to Nasar. Whatever you think of Yau’s machinations or alleged machinations (it’s nothing that I know about first-hand, really), his own great mathematical career is surely more important in the long run.

(Also, to respond to one side point of Scott’s, I don’t know that Perelman is so unhappy with his situation.)

Comment #35 August 25th, 2006 at 12:16 pm

Thanks so much, anonymous! To me, by far the most surprising aspect of the

New Yorkerpiece was the apparent willingness of other mathematicians to openly attack Yau. I couldn’t believe they’d say such things on the record. These letters suggest the following hypothesis about what happened: theydidsay them (among many other things, including positive ones), and then Nasar and Gruber cherry-picked quotes to support the point they’d wanted to make from the beginning.Comment #36 August 25th, 2006 at 5:32 pm

No, no – I was surprised at these open words as well, but I think it is clear that these – highly embarrassing and completely inappropriate letters by the US mathematicians are basically motivated precisely by a fear of Yau. (To me, their tone is similar to exculpations one reads from totalitarian regimes, and I find them scary. I would not want to work with any of those guys anymore.)

As for Yau, we obviously have the case of a great(ish) mathematician who is apparently a – s.v.v. – bad person. That’s not rare, and many great scholars were more interested in political-professional power than in their scholarly legacy. What is strange is that in this discussion, and also in the blog, so many contributors seem to excuse Yau’s actions just by saying that he is (or better was) a great mathematician. Or worse: That he cannot be a bad person because he is (was) a great mathematician. How should that figure?

What people in the community still don’t realize, by the way, is the immense importance of the New Yorker, and what this will do to the story.

The

Comment #37 August 26th, 2006 at 4:16 am

My initial reaction to Sylvia Nasar’s piece was that I wish I could wave a wand so that it would only be visible to mathematicians. This is not inconsistent with Scott’s last comment, but it is also not exactly the same.

I think that it overstates matters a bit to say that Nasar “cherry-picked” her quotes. I talked to three different people here at the ICM who sounded a lot like Sylvia Nasar, even before her article appeared. Now even consistent gossip may not be quite fair. I personally know nothing first-hand about any of this gossip about Yau. But if it is cherry-picking, it is the genuine sort that always comes with gossip, basically because people take Yau’s positives for granted. Yau won the Fields Medal too and no one says that he didn’t deserve it.

On the other hand, I also think that it’s misleading to say that the only reason that Anderson et al speak against Nasar’s article ony because they are “afraid” of Yau. No one like Anderson or Stroock is really worried about finding a horse’s head in his bed in the morning. All that they would be afraid of is poor relations with respected colleagues.

Also, I don’t think that most people considered this gossip, if true, to really be unforgivable. Jimmy Carter had a much-ridiculed quote that he committed “sin in his heart”. Well, so have many mathematicians. If some of the gossip about Yau is true, then all that he would need to do is back off and apologize. I don’t know how that would play out in China, but in the West it would surely do a lot of good.

Comment #38 August 26th, 2006 at 2:29 pm

Good for you Dr. Perelman in

oh so many ways.

mathematician1_00

Comment #39 August 26th, 2006 at 3:17 pm

I do not see how Anderson/Stroock retractions undermine the main points of Nasar’s article, as it relates to “who proved the Poincare Conjecture”. Clearly Yau thinks Cao-Zhu proved it, not Perelman (just look at Yau’s survey at arxiv on the subject), and he did say that “China contribution” is 35%, while Perelman’s is 25%, and he did push the Cao-Zhu paper through the Asian J. Math in no time.

Of course, being a Ricci flow expert, Yau is entitled to an opinion, yet all this happens while Hamilton, Kleiner-Lott, Morgan-Tian confirm that Perelman’s proof is sound and complete (if sketchy), and none of them claims any crucial contribution of their own. To me this says it clear and simple: Yau is (fairly successfully) trying to steal credit for what is in Terence Tao words “the most important math work in the last 10 years”, and Nasar’s article gives a fairly accurate account of the situation.

Comment #40 August 26th, 2006 at 4:57 pm

To Greg Kuperberg:

your post

“If some of the gossip about Yau is true, then all that he would need to do is back off and apologize”

certainly cannot be considered a counterexample to the following

excerpt from the article by Nasar and Gruber:

… As for Yau, Perelman said, “I can’t say I’m outraged. Other people do worse. Of course, there are many mathematicians who are more or less honest. But almost all of them are conformists.

They are more or less honest, but they tolerate those who are not honest…Comment #41 August 26th, 2006 at 5:28 pm

“To me this says it clear and simple: Yau is (fairly successfully) trying to steal credit for what is in Terence Tao words “the most important math work in the last 10 years”, and Nasar’s article gives a fairly accurate account of the situation.” – I’ll second that, although I disagree with the parenthesis, fortunately. And that I can disagree is, in the end, caused, not by Perelman’s very appropriate act of refusing the Fields, but rather by the Nasher-Gruber piece and precisely the non-mathematical audience it gives to the controversy. (Come on, people, to let mathematics as a science hide behind a veil of mystery as a pure, extra-social exercise…?) This is why the remark by Greg, “I wish I could wave a wand so that it would only be visible to mathematicians”, is in the end undermining any possibility of scholarship and science. In the end, the reasons for Yau’s behavior, even if he believes (which he hardly does) that his minions “solved” the Poincaré, which they didn’t (the concept of “solving” in math, sorry, is constructed among the scholarly community as well), the reasons for his machinations are extra-mathematical; they are about power, influence, national prestige, jealousy etc. The entire issue has in that sense nothing to do with mathematics, and thus cannot be fairly judged by mathematical standards.

Comment #42 August 26th, 2006 at 8:13 pm

Okay, as a journalist, I feel I have to chime in.

I think Nasar and Gruber produced a beautifully written and titillating article, and I confess I very much enjoyed reading it. But the part of me that enjoyed it is not a part of me I’m proud of — the article is gossip, pure and simple.

While Anderson and the others sound a bit naive in their dealings with a journalist, I think it’s a shame that Sylvia Nasar managed to elicit and publish several quotes from them that they all felt were not representative or fair, given that there was no higher purpose involved. Journalists are supposed to play hardball when dealing with sources at big companies or in the goverment who are skilled at manipulating the media and have something to hide. In those situations, the press performs a service by providing a check on sleazy activities by powerful people.

But that was not the situation here. Yau is powerful, and, it seems, rather sleazy, but he had not caused any damage. There is no controversy about who proved Poincare. It’s clear — even to non-topologists — that the credit goes to Perelman. Yau’s students were one of three groups who came up with “complete proofs.” This fact alone indicates that no additional huge leaps were required.

For this reason, I feel that the Nasar-Gruber article violated journalism ethics. They achieved nothing by airing this dispute to the public, except to create more ugliness.

Comment #43 August 27th, 2006 at 12:50 am

Achieved nothing? And you are a journalist? Are you sure? From a journalistic perspective, clearly no ethics violations are involved… and there is some legitimacy to cherry-pick quote from big corporations, but not from officialese scientists with big research empires? Bizarre, bizarre…

Comment #44 August 27th, 2006 at 3:25 pm

“They achieved nothing by airing this dispute to the public, except to create more ugliness.”

I think the public will be fascinated, and there is no harm here; I doubt that the image of science will suffer because of the article.

On the other hand, the article does a great service to mathematicians because it sheds light on (what I think is) Yau’s unethical behavior. And we should care, because while Yau is a truly great geometer, he is also a key figure in math politics. As a math politician, Yau is a fair game, as far as probes of unethical behaviour are concerned, yet I cannot imagine this kind of publication in Notices of AMS; fortunately New Yorker has the duty to say what controvesrial. In addition to amazing gossip, the article lists many true (and verifiable) facts about Yau, and we mathematicians should pay attention, and I think we are mature enough to make informative decisions here.

Comment #45 August 28th, 2006 at 3:37 am

I have to agree that Yau is not really succeeding in what he is trying to do — maybe in China it has a chance but certainly not anywhere else. It is also true that a number of people seem to enjoy this gossip at Yau’s expense. I think that it’s mostly okay, because it does look like Yau brought it onto himself. The only side that I don’t like is a certain tone that it is about Russian versus Chinese mathematicians. I greatly respect both, of course, and it would be regrettable if there were any real conflict between them.

Well, it will probably blow over soon enough.

On the other hand, no one here at the ICM enjoys the fact that Perelman refused the Fields Medal. That is un-fun gossip. I think that the IMU president, John Ball, deserves another sort of medal for his impressive and laborious diplomacy, first when he negotiated with Perelman and then in his remarks in the opening ceremony.

Comment #46 August 28th, 2006 at 3:33 pm

This is hardly the first time Yau has been implicated in these sorts of machinations. After Givental’s proof of (part of) mirror symmetry, Yau made a correction to to this proof. Yau and his minions then spent the next few years rewriting math history in their talks, saying that Yau proved this result. On a smaller level I know of people who have submitted papers to JDG and been forced by Yau to put his name on the paper because “didn’t they have a conversation once about this paper”. Its a consistent pattern of activity and its wrong. Further, because Yau has been such a successful advisor its necessary that the Math community do something about it.

Comment #47 August 29th, 2006 at 4:12 am

Not knowing anything at all about the Yau-Tian “power struggle,” if such a thing exists, let alone most of the major players in this story, it seems like the most important point of this article has been neglected. Here we have a youngish mathematician that has decided to leave mathematics, after resolving an epic problem. This is really sad, and it reflects on us. Entering mathematics requires a degree of idealism in the first place (or naievity, as the case may be) as we certainly aren’t remunerated in proportion to our training. To a new mathematician, the field can appear extremely sycophantic, and one sometimes wonders if the field is populated by cannibalistic evil lawyers trying to pad their CVs by shuffling papers around, or people truely motivated by problems they want to understand. I’m over dramatizing, but hopefully you get my point. Good luck Perelman with whatever you do. You’ll certainly be remembered by me — I just got a copy of the Morgan-Tian book bound for convienient bedtime reading.

Comment #48 August 31st, 2006 at 11:08 am

Regarding John’s quoting of Yood’s definition of “agnatology” as the “[interest] in the cultural production of ignorance”: I think Ryan Budney hit the nail on the head when he observed that “[e]ntering mathematics requires a degree of idealism in the first place”.

Careerism is part and parcel of a mathematician’s life, and this has been true ever since people started making careers out of mathematics, which is at least several decades now. Yet, there is this seemingly cultural production of ignorance of this fact, characterised by a belief that somehow, academia (or mathematics in particular) is magically untainted by politics. Not that politics should be a central tenor of the endeavour (indeed, perhaps, in any endeavour), but politicking does happen everywhere, even if it happens somewhat rarely, or less prominently, in some circles.

Thus, we have cases, like Grothendieck and Perelman, where people have abandoned the community: disillusionment, disenchantment, cognitive dissonance between ideals and reality. Then, there are people like Terry Tao, who’s a child prodigy and nice by all accounts. This “niceness”, dare I say, characterises a certain attitude towards the handling of politics: acknowledge such a thing exists, and finding ways to best conduct oneself accordingly.

The Nasar-Gruber article, in this respect, is then an amazing piece of agnatology, because it challenges the current ignorance and misconceptions of the nature of academic mathematics as an activity in society. It may be biased, it may be flawed, it may have errors, but by golly, will it wake up young people and give their idealism a good shaking! Imagine: there is politics within academic maths! The shock! The horror!

Then, maybe, just maybe, some special young people may just temper their idealism with enough realism, and be really nice and smart mathematicians. People who can really build up the community and take the heat as well. Now that’s something to hope for.

Comment #49 September 12th, 2006 at 12:57 am

I’ve been following this drama closely and I thought what is being said in the New Yorker Forum about Nasar’s article was interesting. Here is the link http://boards.newyorker.com/forum.jspa?forumID=1

Comment #50 September 23rd, 2006 at 2:09 am

Here is the alleged letter that AJM editors got from Yau.

Dear Editors,

The paper

The Hamilton-Perelman Theory of Ricci Flow

—the Poincare and geometrization conjectures

by Huai-Dong Cao and Xi-Ping Zhu

has been read by Prof. S.T. Yau and he has recommended

the paper be published in the Asian Journal of Mathematics.

I would be most grateful if you could send me your

comments within the next three days. If no comments are

received by then, the paper is considered accepted for

publication.

Thank you very much for your help.

Very best regards,

S.T. Yau

Raymond Chan

My note: who are the referees? Apparently Yau himself?

Comment #51 September 24th, 2006 at 1:07 am

new yorker cartoon

Comment #52 September 25th, 2006 at 1:47 am

I largely agree with Scott’s comments, except that I think Perelman himself did not care as much as Nasar portrayed. It was Nasar who cared a lot more than Perelman himself and her enthusiasm to make a controversial story that started all these.

p.s. (to anon) Professor Kuhn is a retired emeritus professor at Princeton, a few dozen years older than Yau. I do not think he has anything to fear about Yau.

Comment #53 September 25th, 2006 at 8:47 am

While scott said..But to my mind, failing to write up your result properly, …is a bit like leaving your wallet on the sidewalk and then shaking your head at human depravity when someone tries to steal it.

I would rather believe that he (scott) is patronizing stealing and only confirms the reason why a pure perelman would protest i.e. thieves in the mathematics community that should have been an emblem of purity

Comment #54 September 25th, 2006 at 9:06 am

What Scott said has actually shown a sublunar world where everything is shitty and knowledge is very scarce, quoting one of the online journals, the beautiful thing is that Perelman doesn’t care, and self promotion is already taking ST Yau to court, which Perelman rightly predicted is not a positive thing…to those who are wise…reason along

Comment #55 September 25th, 2006 at 9:18 am

I rightly agree, self promotion is making Yau to spend money on lawyers against Gruber, has not made him more popular than Perelman (Cao seem to have already backed out praising Perelman as their hero and giant), and has likely tanished his image in the maths community of both US and China, even if many would not prove it has. Yau should learn from the “cleverest man in the world”

Comment #56 September 26th, 2006 at 1:05 am

disgusting ….

mathematicians of all people must

know to go beyond the world

of perceptions.

Poincare’s conjecture remains true

regardless of who discovers it,

and is now laughing at a fool like

Yau

Comment #57 September 29th, 2006 at 11:51 pm

Prof. Richard Hamilton, Columbia Univ., responds to the New Yorker article, September 25, 2006

http://doctoryau.com/hamiltonletter.pdf

Howard M Cooper

Todd & Weld LLP

28 State Street, Boston, MA 02109

Direct Dial (617) 624-4713 / Fax (617) 227-5777

hcooper@toddweld.com

September 25, 2006

Dear Mr. Cooper

I am very disturbed by the unfair manner in which Yau Shing-Tung has

been portrayed in the New Yorker article. I am providing my thoughts below

to set the record straight. I authorize you to share this letter with the New

Yorker and the public if that will be helpful to Yau.

As soon as my first paper on the Ricci Flow on three dimensional manifolds

with positive Ricci curvature was complete in the early ’80’s,Yau immediately

recognized it’s importance;and although I had proved a result on which

he had been working with minimal surfaces,rather than exhibit any jealosy he

became my strongest supporter.He pointed out to me way back then that the

Ricci Flow would form the neck pinch singularities,undoing the connected

sum decomposition,and that this could lead to a proof of the Poincare conjecture.

In 1985 he brought me to UC San Diego together with Rick Schoen and

Gerhard Huisken,and we had a very exciting and productive group in Geometric

Analysis.Huisken was working on the Mean Curvature Flow for

hypersurfaces,which closely parallels the Ricci Flow,being the most natural

flows for intrinsic and extrinsic curvature respectively.Yau repeatedly urged

us to study the blow-up of singularities in these parabolic equations using

techniques parallel to those developed for elliptic equations like the minimal

surface equation,on which Yau and Rick are experts.Without Yau’s guidance

and support at this early stage,there would have been no Ricci Flow program

for Perelman to finish.

Yau also had some outstanding students at San Diego who had come with

him from Princeton, in particular Cao Huai-Dong,Ben Chow and Shi Wan-

Xiong. Yau encouraged them to work on the Ricci Flow,and all made very

important contributions to the field.Cao proved existence for all time for the

normalized Ricci Flow in the canonical Kaehler case ,and convergence for

zero or negative Chern class.Cao’s results form the basis for Perelman’s exciting

work on the Kaehler Ricci Flow,where he shows for positive Chern class

that the diameter and scalar curvature are bounded. Ben Chow,in addition to

excellent work on other flows,extended my work on the Ricci Flow on the

two dimensional sphere to the case of curvature of varying sign.Shi Wan-

Xiong pioneered the study of the Ricci Flow on complete noncompact

manifolds,and in addition to many beautiful arguments he proved the local

derivative estimates for the Ricci Flow.The blow-up of singularities usually

produces noncompact solutions,and the proof of convergence to the blow-up

limit always depends on Shi’s derivative estimates; so Shi’s work is central to

all the limit arguments Perelman and I use.

In ’82 Yau and Peter Li wrote an exceedingly important paper giving a

pointwise differential inequality for linear heat equations which can be integrated

along curves to give classic Harnack inequalities. Yau repeatedly urged

me to study this paper,and based on their approach I was able to prove Harnack

inequalities for the Ricci Flow and for the Mean Curvature Flow. This

Harnack inequality,generalized from Li-Yau,forms the basis for the analysis

of ancient solutions which I started, and which Perelman completed and uses

as the basic tool in his canonical neighborhood theorem. Cao Huai-Dong

proved the Harnack estimate for the Ricci Flow in the Kahler case,and Ben

Chow did the same for the Yamabe Flow and the Gauss Curvature Flow.

But there is more to this story. Perelman’s most important is his noncollapsing

result for Ricci Flow,valid in all dimensions,not just three,and thus

one whose importance for the future extends well beyond the Poincare

conjecture,where it is the tool for ruling out cigars,the one part of the singularity

classification I could not do. This result has two proofs,one using an

entropy for a backward scalar heat equation,and one using a path integral.The

entropy estimate comes from integrating a Li-Yau type differential Harnack

inequality for the adjoint heat equation,and the other is the optimal Li-Yau

path integral for the same Harnack inequality; as Perelman acknowledges in

7.4 of his first paper,where he writes “an even closer reference is [L-Y],where

they use “length” associated to a linear parabolic equation,which is pretty

much the same as in our case”.

Over the years Yau has consistently supported the Ricci Flow and the

whole field of Geometric Flows,which has other important successes as

well,such as the recent proof of the Penrose Conjecture by Huisken and

Ilmanen,a very important result in General Relativity. I cannot think of any

other prominent leader who gave nearly support to our field as Yau has.

Yau has built is an assembly of talent,not an empire of power,people

attracted by his energy,his brilliant ideas,and his unflagging support for first

rate mathematics, people whom Yau has brought together to work on the hardest

problems.Yau and I have spent innumerable hours over many years working

together on the Ricci Flow and other problems,often even late at night. He

has always generously shared his suggestions with me,starting with the observation

of neck pinches,never asking for credit. In fact just last winter when I

finally managed to prove a local version of the Harnack inequality for the

Ricci Flow,a problem we had worked on together for many years,and I said I

ought to add his name to the paper,he modestly declined.It is unfortunate that

his character has been so badly misrepresented.He has never to my knowledge

proposed any percentages of credit,nor that Perelman should share credit for

the Poincare conjecture with anyone but me; which is reasonable,as indeed no

one has been more generous in crediting my work than Perelman himself.Far

from stealing credit for Perelman’s accomplishment,he has praised Perelman’s

work and joined me in supporting him for the Fields Medal.And indeed no

one is more responsible than Yau for creating the program on Ricci Flow

which Perelman used to win this prize.

Sincerely yours,

Richard S Hamilton

Professor of Mathematics,

Columbia University

Comment #58 September 30th, 2006 at 12:00 am

Those who claim Yau is doing self-claiming have nothing but bias. Unless you can prove his claim is totally wrong, otherwise, wait and see but make no judgement …

Comment #59 October 3rd, 2006 at 10:40 am

these letters that yau is posting remind me of statements issued by hostages who are being held against their will.

anyway, maybe terry tao will be the next king of mathematics in china.

Comment #60 November 7th, 2006 at 6:16 pm

Everybody talks about Yau’s contact, how about Hamilton’s? Read his letter to ‘dear Mr. Cooper’ — it is clear that he thinks the Clay Foundation prize must be shared between him and Perelman!

Terry Tao for the next emperor of China? I thought he defines himself as an Australian More to the point, a careful read of his 10/29 Poincare’ preprint shows that he votes in favor of Perelman: case closed?

Comment #61 November 22nd, 2006 at 2:00 pm

This seems to be the latest development in the saga. For a paper of this magnitude, I am amazed something like this got past peer review.

From MathForum:

In response to allegations of plagiarism, Cao-Zhu published an erratum. Is it adequate?

Here is the “evidence” supporting the allegation of plagiarism:

http://www.cds.caltech.edu/%7Enair/pdfs/CaoZhu_plagiarism.pdf

Here is the Cao-Zhu erratum:

http://www.intlpress.com/AJM/p/2006/10_2/AJM-10-2-Erratum.pdf

Comment #62 December 21st, 2006 at 6:56 pm

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Comment #63 December 21st, 2006 at 9:54 pm

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