The winner of this year’s Abel prize, a prize of over $1 million set up back in 2001 to provide an equivalent of a Nobel prize in mathematics, is…

Actually, I have no idea. If you know who it is, feel free to break any vows of confidentiality in the comment section here. Otherwise we have to wait until 7am EDT tomorrow morning, when the answer will be revealed here.

**Update**: The prize goes to John Thompson and Jacques Tits, for their work on finite groups. More details here, including the citations for Thompson and Tits.

I nominate A Grothendieck, who will be 80 this year, and lives in the south of France.

MathPhys,

A good nomination, but I don’t think it will be him. The Scandinavians already once tried to give him a prize carrying a lot of money (the Crafoord) back in 1988, and look what he did then…

Incidentally, Grothendieck’s birthday is on this Friday, 03/28.

Hamilton perhaps?

I’m betting on Israel Gelfand.

The announcment page says that Marcus du Sautoy will give a popular talk on the subject. Could that be a clue? Marcus has worked on finite groups and zeta functions so it could be someone in that area, maybe.

I guess it would be John Tate or (and) Robert Langlands since Du Sautois speaks after the annoucement.

Zelmanov and Dusa McDuff are on the committee. Maybe M. Gromov?

My bet is someone who, at least, attached his name to a well-known program: Pr. R. Langland or Pr. R.S. Hamilton ..

Gelfand would be a very, very good choice. Besides, he’s well over 90 years old, so it’s about time.

Abel Prize to Thompson and Jacques Tits!

Surprizes all round

John Griggs ThompsonandJacques Titshave been awarded the prize for their contributions to group theory.Thanks for this link Peter! Normally I visit your site to find links to research articles for me to read. I just sent out an email to my Abstract Algebra class with a link to the Abel Prize site and instructions to read the articles on group theory, the history of groups and the group theory of the Rubik’s cube. That should make for an interesting class next week.

Are there any Norwegians who want to translate the jokes in the citations?

Hi Peter, interesting post.

This is obviously a very prestigious prize – great to see it going to group theory.

By the way, I guess there’s a difference between pure group theory and group theory applied to physics?

I ask because most of the names listed in the posts above are not familiar to me – also, although there is a specialist physics prize for “outstanding contributions to the understanding of physics through Group Theory” (the Wigner medal), it has not been won by any of the names above, or by Thompson or Tits..

I sometimes think it’s a pity these prizes are only awarded to the living. If that sounds daft, there are actually two good reasons for posthumous awards

(i) the work of these good mathematician/scientists lives on long after them…and often the true value of the work becomes even more apparent after their death

(ii) while the scientists themselves won’t benefit from posthmous awards, their students, their institutions, and even their countries might benefit, inspiring others to similar feats

For example, should evidence of supersymmetry be glimpsed at LHC, almost none of the pioneers will be alive to see it – so there wil be no public recognition of their long toil in the sixties and seventies. Here in Ireland, I have huge problems convincing people that Dad’s work was important, and am continually confonted with books about Irish scientists that ignore his contribution – a few prizes would help!

Regards

Cormac O’ Raifeartaigh

For those who don’t know much about the work of Thompson or Tits, I am cautiously optimistic that master expositor John Baez (who has discussed finite simple groups, buildings, and other highly relevant topics in past postings) will rise to the occasion.

Would it be imprudent for me to hazard the guess that the award to Tits in particular reflects a resurgent appreciation of the legacy of Klein?

The joke: 604800 equals the number of seconds in a week

Group theory had many origins: the problem of solving polynomial equations via the work of Lagrange, Viete, Cauchy and Galois relating the original problem to the permutations of the roots of the equation, and giving rise to the group concept requiring that the set of permutations must be closed under the product of any two such transformations. This same idea originated in geometry with Klein’s idea that a geometry is determined by the rigid transformations of space that leave invariant the objects of that geometry. There is a third source of the group concept, that goes back to Gauss, Kronecker and Dedekind, and is related to number theory, where a new idea comes into the field, that is studiying a commutative group via its characters, i.e., functions from the given group to the multiplicative group of nonzero complex numbers. And there is a fourth line if we consider Sophus Lie idea to create a “Galois Theory” of differential equations in analogy to the Galois theory of number theory and algebra that studies the symmetries coming from the permutations of roots of polynomials. Lie’s ideas are the ones any Physicist recognizes immediately, all of them quite familiar with differential equations and Noether’s theorem. At the end of the XIX century, Frobenius in Berlin, his student Schur, and Burnside in England introduced the idea of studying an abstract group by replacing its abstract elements with concrete objects, namely, invertible (complex) matrices. Initially they applied this new tool (called the representation of the abstract group) to study the structure of finite groups, but soon they were also considering representations of infinite groups and also of Lie groups, and later on Weyl enters the picture and representation theory (mainly of Lie groups) becomes part of the toolbox of a theoretical physicist. Gelfand, Naimark, Wigner, Bargmann, and many others are associated to the study of representations an characters of Lie groups that are of interest to physicists.

To end this too long comment, what physists call “group theory” usually means “representation theory of Lie Groups”, and the relevance of the abstract representation theory of finite groups is that sometimes it provide methods that may be useful for representation theory in general.

Thanks Felipe, great post

Something completely off-topic here, but I was just wondering if this paper by Prof Ngô Bao Châu (Université Paris-Sud, Orsay) has come to the attention of those concerned. It is written in French, so I don’t think many will be able to understand it, but the abstract is rather interesting.

theoreticalminimum,

Ngo’s work on the fundamental lemma has attracted a lot of attention from experts in that area. I wrote a little bit about it here:

http://www.math.columbia.edu/~woit/wordpress/?p=18

I’d write more about this and about more recent developments like the paper you mention if I actually understood more about it…