Wednesday, December 13, 2006

Three thoughts on Anatoly Vershik's article...

Via Peter Woit and Luca Trevisan comes a pointer to an article by Anatoly Vershik in the new Notices of the AMS, lamenting the role of money prizes in mathematics. Three thoughts:
  • "the newspapers, especially in Russia, are presently “discussing” a completely different question: Is mathematical education, and mathematics itself, really necessary in contemporary society ". At the risk of sounding patronizing, I find it terribly worrisome that the place that spawns such amazing mathematicians, and has such a legendary training program for scientists, should even indulge in such a discussion. Especially now, with all the handwringing in the US about the lack of mathematical training at school level, it seems a particularly bad time to abdicate what is a clearly a competitive advantage.

  • He talks about not understanding "the American way of life" as regards how money is viewed. There's a juxtapositon of images that I've always been struck by, and that tennis lovers will recognize: At Wimbledon, the winner is crowned with a fanfare, royalty, and a trophy (or plate); the prize money is never really discussed. At the US Open on the other hand, along with the fanfare comes the huge check handed out by some corporate sponsor while the PA blares out the amount. The trophy presentation, although making for good photo-ops, seems almost anticlimactic.

    I am a little skeptical though whether offering prizes like the Clay prize convinces people that mathematics is a lucrative profession. After all, this hasn't happened for the Nobel prizes.

  • On the false-duality: I've heard a variation of this argument many times. It goes basically like this: "Either you're interested in subject X and don't need motivation, or you aren't, in which case no amount of motivation is going to help". This is possibly true for identifying students likely to make the transition to being professionals in subject X. In fact, I've heard an anecdote from the world of music, about a maestro who would tell all his students that they would fail professionally at being musicians. His argument was that only the ones who cared enough to prove him wrong had what it took to survive.

    One has to realize though that the teaching of a subject is not about creating Mini-Mes: only a small fraction of the students we come in contact with will become professional computer scientists/mathematicians/whatever. But a large fraction of these students will vote, many of them will go onto position of influence either in industry or government, and they will all contribute to a general awareness of the discipline. So it's a mistake to give up on motivating students; even if they never end up proving theorems for a living, a better appreciation for those who do will help all of us.



  1. On the last point I think Vershik is not making a general
    argument about prizes etc in mathematics to motivate people.
    In fact he advocates using money at a lower level.
    His claim is that the Clay problems are too hard for any one
    to attack them for the sake of money and hence has no bearing
    as a motivation. I think his point is valid. 

    Posted by Anonymous

  2. I disagree: here's the passage from his essay that I was thinking of: "More generally, will the approach of the Clay Institute increase interest in mathematics and increase the influx of young people into the field? I am not sure. One must understand that somebody fascinated by mathematics as a teenager needs no additional stimuli, while those who, in their choice of profession, are primarily interested in ensuring a normal comfortable life do not need a million-dollar prize for solving an inaccessible problem,but need something completely different. "

    As for the Clay prizes not motivating anyone, that's I think the point I made in the second bullet, at the end.  

    Posted by Suresh.

  3. If you are fascinated with mathematics and have the leasure of reading and working you don't need anything more, hardly even teaching in the case of some people.

    However if you are not, you might still have the potential to be good at math. This is the case of most students. They just need help and motivation and if they work they will become good.

    Imagine it as a game: The teacher wants you to work. You want to advance and feel gratified with what you are doing. The minimax of reward vs. challenge is the equilibrium of the game.

    Now there are people who are really good but do not want to go into research because there is more money in the private sector. This is just bad investment by companies. Just compare the teaching systems in France and England and you can see how people with strong academic credentials can boost industry a lot more than extra specialized applied specialists. 

    Posted by Salem SAID

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