Update: The four medallists are Perelman (declined), Tao, Russian Andrei Okounkov, and Wendelin Werner. There is a nice article about Tao’s work at the UCLA website. The Nevanlinna Prize went to John Kleinberg.
Tao’s Medal will cause a lot of of excitement in Australia, as he’s the first Autralian ever awarded the Fields Medal.
I’m particularly pleased, as I greatly admire some work Tao did with Allen Knutson on a problem of some interest in quantum information, known as Horn’s problem: given that A+B=C, where A, B and C are Hermitian, what can be said about the relationship between the eigenvalues of A, B and C? There is now a complete (and deep) solution to this problem, and Tao and Knutson played a central role in obtaining it.
This problem at first might not seem all that related to quantum mechanics. It turns out that there are a lot of connections between the techniques used, a fact you can see in some beautiful work by Hayden and Daftuar and by Klyachko, who made important independent contributions to the solution of Horn’s problem.
Of course, this is just one of many things Tao is known for – he’s probably better known for his proof (with Ben Green) that there exist arbitrarily long sequences of primes in arithmetic progression. His web page lists an amazing array of papers, books, expository notes, and other activities (he’s a vegemite fan); it’s a lot of fun to read through!