The International Congress of Mathematicians (ICM) takes place every four years and is the most important international conference in mathematics. The 2006 ICM will take place next August in Madrid. One thing that happens at each ICM is the announcement of the winners of the Fields Medal. This has traditionally been considered the most prestigious award in mathematics, and the closest analog to a Nobel prize in math, although the recently instituted Abel prize may now compete for this honor. The Fields medal is awarded to between two and four people at each ICM, and recipients must be under the age of 40 on Jan. 1 of the year of the ICM. I have no inside information about who will win this year, but in gossip with mathematicians two names that tend to come up are those of Grigori Perelman (for his work on the Poincare conjecture), and Terence Tao.

The other important thing about the ICM is the list of invited talks. The speakers are carefully chosen and are supposed to be people who have done the most important work in mathematics during the past four years. Looking over the list of speakers gives a good idea of who the most prominent names in the business are, as well as what are the hottest topics. It’s an especially great honor to be chosen as a plenary speaker, and the names of these have been recently announced. The invited speakers in the various sections have also been announced, one section covers mathematical physics.

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I have been reading your blog regard ICM2006.

Now Grigori Perelman is problematic, as I believe he may be 40 next year! This has come up before! Infact, this problem is quite serious for mathematics as frankly, essentially all of the TRUELLY great mathematics in the last decade has been done by the over forties (e.g. Oded Schramm of Brownian Frontier Fame!) So much for math being a young man’s game!

Now, you have really got my interest with Terence Tao. Now as an amateur mathematician I am a sort of a math junkie and have been looking at the work of various mathematicians over various fields

I investigated Terence Tao because of his work on harmonic analysis!

But I must admit he was not on my list of Field Medallists! I am interested in why Terence Tao work crops up! Please explain!

Here is my list of Field Medallists.

1. Warwick Tucker

Warwick Tucker has given a rigorous proof that the Lorenz attractor exists for the parameter values provided by Lorenz. This was a long standing challenge to the dynamical system community, and was included by Smale in his list of problems for the new millennium.

I must add that He is working within a new computational field called interval analysis which allows one to solve simultaneous ODE RIGOUROUSLY. Now if you have tried to solve Nonlinear ODE, you will realise this is one of the holy grails of Applied Mathematics!

2. Elon Lindenstrauss

Already, in joint work with Katok and Einsiedler, he has used some of the ideas in this work to prove the celebrated conjecture of Littlewood on simultaneous diophantine approximation for all pairs of real numbers lying outside a set of Hausdorff dimension zero

What I love about this work is that it continues the pathbreaking work of in my opinion, the greatest female mathematician of the 2nd half of the 20th Century, Maria Ratner and her theorem about unipotent flows.

I believe that the work on unipotent flows will be the next revolution in function theory. In particular, I believe it will lead to solutions to many problems in Quantum Field Theory eventually! Watch out!

3. Mark Groves

Someone who has no chance in reality, but his work is something I fully understand!

Winner Richard Von Mises prize in applied mathematics.

What did he achieve?

Solutions to something called the Water Wave problem. But what is important to me is that they confirm an intuition about Nonlinear Wave I have always held.

Essentially, for a large class of multidimensional nonlinear systems, the behaviour moves from linear to solitons to chaotic along various semigroups!

This very simple statement actually provides a small piece of a puzzle about chaos, which has been mysterious for a long time. Basically how does chaos create order in nature? Well, it appears that certain nonlinear systems generate semigroups spontaneously, which does not align itself with the natural semigroup time! This means that chaotic functions can be thought of as acting like solitons in a highly nonlinear environment.

Unfortunately, I do not have any women for the Field Medal at this time. Do not get me wrong, there are many female mathematicians doing great work, but difficult to discern if it is of Field Medal Caliber.

An Amateur Mathematician

I have had a look at the ICM2006 site, and it appears that there is a new prize called the Gauss Prize.

Sound interesting.

An Amateur Mathematician

An Amateur Mathematician exclaims:

He and Ben Green showed there are arbitrarily long arithmetic progressions of prime numbers.

And, he’s won some prizes already for other things, including his work with Allen Knutson, in which they proved Horn’s conjecture. This says what the eigenvalues of a matrix A+B can be, given the eigenvalues of two hermitian matrices A and B. It’s equivalent to a lot of other nice conjectures.

So, he’s cracked some hard problems that are easy to state.

Just to keep the gossip going, Dennis Gaitsgory (recently tenured at Harvard) and Manjul Bhargava are two other names that have popped up during tea at my department.

The only plenary speaker under 40 (if my google checks are ok) is Terrence Tao, so that’s in the bag IMHO. Besides he’s really a good bet as John said, with lots of prizes and big invited lectures already (next are his Chern lectures at Berkeley.)

In fact, he’s got such a wide array of expertise that there’s already only a few people left who could possibly introduce all his work (Bourgain, Gowers…) so the Fields commitee can’t really wait much longer anyway… ðŸ˜‰

As for Perelman, well if his birthdate is indeed the one given on wikipedia, then he’s definitely *done* his work before being 40…

http://en.wikipedia.org/wiki/Grigori_Perelman

Personally I’d expect Artur Avila to win it one day, barely 26 and already quite impressive…

Hi Everyone!

Thanks for all of the wonderful tips!

Unfortunately from my point of view, it appears that the bias against applied mathematics will continue. I am hoping that the Gauss Prize will correct this obvious problem and they will pick someone really wonderful like Kiyosi Ito of Ito Calculus fame.

I am also hoping that the Abel prize commitee pick a Woman next time as there are in my opinion women who are deserving. Karen Uhlenbeck or Maria Ratner would do fine!

An Amateur Mathematician