As the date for announcement of the 2010 Fields Medals approaches, gossip about who the winners might be has been circulating. Math Overflow is by far the best internet site for authoritative discussion between knowledgeable mathematicians, but, unlike this site, they have a “no gossip” rule, leading to the closing of discussion threads like this one.

You can bet on who the Fields Medalists might be here. I assume there’s no bet possible for Ngo since he’s a sure thing…

**Update**: It’s Ngo and Villani, also Elon Lindenstrauss and Stanislav Smirnov. For the announcement and information about the work of the prize winners, see here. Accurate rumors about this don’t seem to have started circulating until the ICM announced the winners to the press late Tuesday. This information was embargoed until today, breaking the embargo didn’t seem sporting…

**Update**: Best blog by far for following this is that of Timothy Gowers, who was on the committee that picked the Fields medal winners, and promises to tell us about Cedric Villani’s outfit.

Isn’t it conventional to invite future recipients of the Fields Medal as speakers?

If that is the case, we can probably rule out Cedric Villani. In fact, the only people under 40 on the list of invited plenary speakers are Avila, Ngo, and possibly one or two ladies (Dinur and Plofker) whose ages I can’t readily determine. Plofker does not appear to have done anything worth a Fields, and Dinur is a better match for Nevanlinna.

@Nameless: no, the invitations are made long before the Medals are finalized. Extra plenary slots are held open for Medalists who were not already invited. Among the 2006 laureates, only Tao was scheduled to give a plenary; Okounkov and Werner were both scheduled originally for 45-minute talks, and were moved to other slots after the prizes were announced.

I find it telling that those three names (Ngo plus the two at the betting site) have been circulating loudly for a few months without (to the best of my knowledge) any informed suggestion to the contrary. If someone were in the position of being anointed by incorrect rumors, there might be some attempt to dispel the resulting attention. There might yet be a fourth medal as well. Anyway, we’ll know in less than 24 hours.

Much higher quality rumors are now circulating, although embargoed by the ICM until 2am tonight New York time.

In the righteous cause of stamping out ignorance and error, right now I’ll just say that rumors about Artur Avila seem to have no substance.

Manjul Bhargava was a plenary speaker at ICM 2006, giving a nice account of his ‘Higher Composition Laws’ (the 4th paper in this series came out in the Annals of Mathematics in 2008), and was given the AMS Cole Prize in 2008 for this. There are 5 recent (since May) preprints on the ArXiv with very deep applications of his methods (e.g., 100% of quintic fields have S_5 as Galois closure); that on the boundedness of the average rank of elliptic curves (with Arul Shankar) is particularly amazing and wonderful. (They get a bound of 1.5 for the average algebraic rank; previous results on the average analytic rank pioneered by Armand Brumer 20 years back were a) higher, b) conditional on GRH etc.) So he deserves a Fields medal. However, as noted in the discussion here last year, he will still be eligible in 2014, and these papers probably came out too late for affecting the choices this year.

But I’ll still be disappointed if he’s not on tomorrow’s list!

If the list of speakers’ names and attendees’ names at the ICM web site are accurate, that would filter out some of the candidates. Manjul’s name has not been there for several weeks, so are a bunch of others. It seems that Jacob Lurie’s name just appeared recently, if my memory is correct.

Winners:

Elon Lindenstrauss

Ngô Bảo Châu

Stanislav Smirnov

Cédric Villani

two out of four a year ago. Not bad !!!

Who was on the Fields Medal Committee?

Laszlo Lovasz (chairman), Corrado de Concini, Yakov Eliashberg, Peter Hall, Timothy Gowers, Ngaiming Mok, Stefan Müller, Peter Sarnak, Karen Uhlenbeck.

I don’t know where else to ask, so I will ask this here. Do you think that there is a change of the type of work that is getting the fields? My impression is that the medal was given for work that finds applications to physics. (are these really needed applications from the physics viewpoint ?) Furthermore, the connection is with statistical mechanics, not string theory. Are the powers behind the math scene signaling the new direction they think math will profit to explore? Or is it part of the previous scheme of things?

Michael,

Thanks a lot for finding that and posting it!

Tooth Fairy,

I don’t think you can conclude that much about trends in mathematics from these choices for the Fields. I believe that any Fields medal committee would have chosen Ngo, but that another committee could very easily have chosen different people for the other three. The choice of these three reflects who is on the committee and who they’re getting advice from, as they try and choose 2 or 3 people amongst maybe a dozen or so equally distinguished young mathematicians. There’s a sizable randomness factor here. As far as the connections to physics go, analysis has always drawn inspiration and problems from physics, going all the way back to the beginnings of the subject, there’s nothing new here.

I suppose you could draw one conclusion, that the lack of a Fields medal for any of the more esoteric string theory or qft-related topics many people are working on reflects a judgement that there hasn’t been anything really dramatic coming out of that area in the last few years.

@Tooth Fairy: as an outsider I’d say the spirit of the prize hasn’t changed, it’s just that what current mathematicians do is more varied than 40 or even 20 years ago. It’s still that great math prize which rewards great proofs.

Werner’s medal and now Smirnov’s medal are really awards for the probability side of things, the insight on brownian motion geometry. Given the wide range of math used to model physical phenomena (and, as a result, the number of exciting mathematical problems coming from physics), it’s bound to happen from time to time that some medalists have results of physical significance. Same with Villani: definitely it’s subtle analysis first and foremost, with delicate estimates and innovative new norms.

So I don’t think at all it’s a signal or anything regarding applications to stat phys v strings, it’s all about recent great mathematical results.

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