Don'tcha know how much a million is, Mr. Math Genius?

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If you're intrigued by Grigory Perelman, the man who proved the Poincaré Conjecture and a new hero to refusiniks everywhere for declining the Fields Prize and the million-dollar Millennium Prize, this profile by Sylvia Nasar and David Gruber sheds some light. There are a lot of indifferently introduced characters in the story, and if you have any idea what it means that "manifolds of the fourth, fifth, and higher dimensions were more tractable than those of the third dimension," you're welcome to try it out in the comments. (I say it's still a sphere, and I say the hell with it.) But it's a pretty good portrait of flaming eggheads. Perelman comes off as less of an eccentric than he has in most of the spot news coverage of his solution. The short answer for why he's saying no to the award (while keeping his options open about the million) is surprisingly sensible:

Perelman repeatedly said that he had retired from the mathematics community and no longer considered himself a professional mathematician. He mentioned a dispute that he had had years earlier with a collaborator over how to credit the author of a particular proof, and said that he was dismayed by the discipline's lax ethics. "It is not people who break ethical standards who are regarded as aliens," he said. "It is people like me who are isolated… 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."

The prospect of being awarded a Fields Medal had forced him to make a complete break with his profession. "As long as I was not conspicuous, I had a choice," Perelman explained. "Either to make some ugly thing"—a fuss about the math community's lack of integrity—"or, if I didn't do this kind of thing, to be treated as a pet. Now, when I become a very conspicuous person, I cannot stay a pet and say nothing. That is why I had to quit."

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  1. They are more or less honest, but they tolerate those who are not honest.

    Whoda thunk mathematicians would be so much like cops?

  2. On the subject of million dollar prizes for solving math problems, several years ago, when the prizes were announced, I got this call from my family: “Hey, you’re good at math, right? You got good grades in your college math classes, right? So, um, how about you solve one of these problems and get a million dollars?”

    I had to explain that this wasn’t just a matter of doing a really hard homework set….

  3. But thoreau, the Fields medal winners only get about $13,000.

  4. Only a million?

    Jeez. My bank keeps “proving” that me and all their other customers owe them more money.

    The bank gets a million bucks every couple of hours for that.

  5. It’s my gut feeling this guy has some axe to grind over politics, not props. The folks in my field are very rigorous when it comes to who gets credit for what. And as rigor goes; math first, then physics, and so on. So maybe he didn’t get the recognition he thinks he deserved, rather than the credit.

  6. the article is rather long, but it and recent related articles in the NYTimes suggest that there is a rather blurry line that certain characters are crossing. This article quotes a number of professionals who question the decisions and motives of a few of their ‘outstanding’ peers. One group of them seems more or less to have tried to lay claim to the credit for Perelman’s solution, simply by virtue of having understood it, and reflecting that understanding with more words than Perelman used.

    And it sounds more like he has an axe that he doesn’t feel it’s worth his time to grind, than anything else. What I don’t quite understand is why this even became a story for the mainstream media. The number of people who understand it’s implications or even what it is saying, beyond this superficial silliness about ‘everything being a sphere’ is soooooo small as to be even sillier – no?

    “On the evening of June 20th, several hundred physicists, including a Nobel laureate, assembled in an auditorium at the Friendship Hotel in Beijing for a lecture by the Chinese mathematician Shing-Tung Yau….The subject of Yau?s talk was something that few in his audience knew much about: the Poincar? conjecture, a century-old conundrum about the characteristics of three-dimensional spheres, which, because it has important implications for mathematics and cosmology and because it has eluded all attempts at solution, is regarded by mathematicians as a holy grail.”

    Of course we all like a spectacle. But speculation on this seems only worthwhile to members of the community which it affects. The reason for the attention is that someone didn’t take a million bucks. But do we really care why?

    It does seem idiotic to me that people at this level in any scientific discipline should be arguing so childishly about credit for their accomplishments.

    whateva

  7. I felt the authors were subtly, or not so subtly, making digs at Yau. The article was contrasting a man trying to be a pure mathemetician in an impure world – Perelman, vs. a man cynically trying to use mathematics to promote his own glory – Yau.

  8. I was fortunate enough to be born in a time when the most prestigious outstanding problems could be explained to your girlfriend. The four-color map problem was awesome, you could explain it to anyone in two minutes. Once that went down, there was still Fermat’s last theorem, which required a little high-school algebra to understand, but still quite accessible.

    Of all the Millennium prize problems, the only one I’ve ever herd of is the Riemann hypothesis, which I only just understand myself and couldn’t hope to explain to someone else.

    I still have fun with the Mobius strip (and Klein’s bottle), Flexagons and so-forth. But it was really fun to be able to have a simple problem that could be grasped in under a minute and be able to say, “many of the finest minds mankind has ever produced have assailed this problem… all have failed”.

  9. It does seem idiotic to me that people at this level in any scientific discipline should be arguing so childishly about credit for their accomplishments.

    I think they need the credit for their future survival. Even if you’re working as a professor, you’re generally expected to bring in grant money, and that requires previous accomplishments. “Fame” is a big part of the game. One of the reasons I’m not a profesor; I’d rather just solve the problems, and don’t particularly care about publishing and getting my name out there.

    That’s my perspective from grad school; how ’bout you, thoreau?

  10. I’m not a professor for other reasons, one being that I’m that minority nobody wants today (WM). It does matter when you go for grant money, and the idea that I’m not competing on a level ball field just grates all over. One of my PhD advisors was incompetent, to the point that undergrads laughed at him openly, yet he brought in loads of grant money and made full professor fast.

    He was also black.

    But in truth, the fame is an issue when you go for government grants (like NSF). When it comes to industry, they’re more interested in whether you can do the work.

    OTOH, when industry looks for profs to work with, they often start by looking in the literature. So getting your name out there and published really is important.

    Besides, it’s a funny little truism — if you publish in refereed journals (and work in industry like I do), then your peers think you’re a “real” PhD and not one of those idiot “fakes”. Don’t ask me….

    Nonetheless, I have been in corners of the universe where people steal each other’s work and ideas, and claim it as their own. For the fame. You do have to watch for that. It can leave you burned for a long time if somebody scoops you on something good.

  11. The quest for grant money can lead to other unpleasant activities, like reanalyzing the data until it says what policy writers want to hear. Scientists are human too, with the typical proportion of biases and compromised values. That’s why I get scared when people who never look at primary literature cite science to defend social engineering.

  12. From:
    http://www.newscientist.com/chan…/ mg19125661.400
    “The underlying issue that emerges when you add together Perelman’s work and attitude, the Chinese claims, and the problems of attributing proper credit, is that mathematicians are finding it increasingly difficult to decide whether or not something has been proved.”
    A lot of mathematicians have been using this loop hole of announcing ideas with sketches and then keep changing preprints over years, sometimes radically. Unfortunately Perelman used the same procedure. For whatever reasons, he did not write down a complete argument like Wiles did and it took top class mathematicians a lot of time to complete the sketch. If he does not want to be a part of the dishonest practices, his refusal seems consistent.

  13. From:
    http://www.newscientist.com/chan…/ mg19125661.400
    “The underlying issue that emerges when you add together Perelman’s work and attitude, the Chinese claims, and the problems of attributing proper credit, is that mathematicians are finding it increasingly difficult to decide whether or not something has been proved.”
    A lot of mathematicians have been using this loop hole of announcing ideas with sketches and then keep changing preprints over years, sometimes radically. Unfortunately Perelman used the same procedure. For whatever reasons, he did not write down a complete argument like Wiles did and it took top class mathematicians a lot of time to complete the sketch. If he does not want to be a part of the dishonest practices, his refusal seems consistent.

  14. From:
    http://www.newscientist.com/chan…/ mg19125661.400
    “The underlying issue that emerges when you add together Perelman’s work and attitude, the Chinese claims, and the problems of attributing proper credit, is that mathematicians are finding it increasingly difficult to decide whether or not something has been proved.”
    A lot of mathematicians have been using this loop hole of announcing ideas with sketches and then keep changing preprints over years, sometimes radically. Unfortunately Perelman used the same procedure. For whatever reasons, he did not write down a complete argument like Wiles did and it took top class mathematicians a lot of time to complete the sketch. If he does not want to be a part of the dishonest practices, his refusal seems consistent.

  15. Perelman’s decision makes sense. He has the finances to retire. He doesn’t want fame or attention. He cared more about the proof than his career. Fighting over the prize would just give others an incentive to attack his proof.

  16. surprised that this happens to be the topic where readers reveal just how cynical they can be.

    JG

  17. Why is the story interesting? Because it’s a window into a world of really smart people who are nonetheless eccentrics (and Perelman is certainly eccentric) and engaged in petty fights over turf.

    D-FENS: Grant money is everything, no matter what they say to the contrary.

    I work in a community where fights over credit go in the opposite direction. I know people who want to put everybody’s name on everything, on the grounds that if we all scratch each other’s backs then we all look good and we’re all safe. Now, I’m not interested in cutting anybody’s throat, but if you didn’t do something on the project then why is your name on the project? To me it just seems like common sense.

    My plan: Publish in some big journals. Get an assistant professorship. Get enough grants and publish enough stuff to get tenure. Get tenure. Then just work on whatever problems I find interesting, have fun teaching my classes, and stop worrying about the Big Game.

  18. I’m a mathematician and I think this article and others I’ve seen on the subject are quite misleading. This idea that mathematicians are fighting over who should get credit is a creation of the press. Possibly except for Yau, I haven’t heard of any mathematician even suggesting that Perleman shouldn’t get credit for proving the Poincare conjecture.

    The experts in the field have been extremely fair to Perleman and even gracious. Morgan said flat out at the ICM “Perleman has proven the Poincare conjecture”. Hamilton (the guy whose work Perleman’s proof was based on) said at his ICM talk that he was incredibly happy and enormously grateful that Perleman finished his work. These guys are two of the experts in the field.

    I also don’t think anyone knows why Perleman quit math, but it seems unlikely that it was because he was worried about getting credit for his work or was mistreated by the community. I don’t think he even cares about such things. I just hope no one gets the wrong idea about the mathematical community from these articles.

  19. Mathematician-

    Yep, while the math community no doubt has its politics (what academic community doesn’t?), everything I’ve heard about Perelman suggests that the man has his own personal issues here.

  20. As a graduate student I made the naive mistake of openly discussing my ideas and preliminary results with my well established (long tenured) competition. My advisor sat on my work for too long and the competition published first. The funny thing was that they made the same claim but didn’t have the evidence or data to support it. He took my conclusion and tried, but failed to construct the supporting data. I addressed this failure and other problems with his work in my manuscript. When it was published the guy freaked. He accused me of misrepresenting his work and threatened a response in the journal, I accused him of lifting my idea. It was all ugly. After a few exchanges it became clear that he wasn’t even familiar with the data he published and that some student or postdoc did all the work. But it doesn’t matter that his data doesn’t support a conclusion he took from some naive kid at a conference. He will always get the credit for publishing the conclusion first. This kind of crap is hard to take. On my first ‘first author’ publication there were two extra authors that didn’t contribute to the work, they were there as a favor from my boss. My name made it on one of theirs as well, with no contribution of course. And that is academia.

  21. I would have posted this earlier, but I forgot the name….

    The story of Valery Fabrikant, former associate professor of Mechanical Engineering, who killed four colleagues in 1992 at Concordia Universtiy. “He also accused the university of tolerating the practice of academics being listed as co-authors on papers to which they have not contributed; in 1992, he had gone to court to try to have the names of several colleagues removed from works he had written in the 1980s.”

    Fabrikant is a smart guy, smarter than me, and you can tell by reading his work that he knows he’s a smart guy. (He is a theorist in mechanics, and he continues to work from a prison in Quebec). I’d say there’s more than a little bit of parallel between Fabrikant and Perelman.

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