ICM2010 — Spielman laudatio

I’ve saved the best till last, which should not be taken as a negative comment about the other laudationes, since Gil Kalai’s was a tour de force. His first distinction was that he was the only one of the five speakers not to be wearing a tie. He was, however, wearing a suit, so the result was to look smart in a trendy way rather than smart in a more standard mathematician-giving-important-talk way. And he opened his talk daringly with the promise that his would be a comprehensible talk, which got a laugh from the audience.

On a more negative note, I was a bit shocked that a significant proportion of the audience got up to leave before he started, as if to say, “The real business is over — this is just the Nevanlinna prize.” All I can say is that it was their loss, not just because of the wonderful talk but also because of the wonderful mathematics described in the talk.

ICM2010 — Villani laudatio

The first thing that stood out when H-T Yau got up on to the stage was his relative youth. (I’ve just looked him up and he was born in 1959.) He began with an amusing quote from von Neumann, who advised Shannon to use the word “entropy” on the grounds that “Nobody knows what entropy really is, so in a debate you will always have the advantage.” Part of the reason von Neumann said that was that there has always been a tension between the irreversible nature of entropy and the reversibility of the Newtonian mechanics that is supposed to underpin it. How can the two be reconciled? My impression is that this quasi-philosophical problem has largely been sorted out (so in particular, I’m not about to say that Villani has “solved the mystery of entropy” or something like that). In fact, let me reproduce Yau’s list of Villani’s three major achievements.

1. He established a rigorous connection between entropy and entropy production. (I don’t actually quite know what he meant by this.)

2. He established entropy as a fundamental tool in optimal transport, and curvature in metric spaces.

3. He rigorously proved a phenomenon known as Landau damping, a very surprising decay of the electric field in a plasma without particle collisions (and therefore without entropy increase).

I’ve just looked at Tao’s post on the Fields medallists and my understanding is such that I’m not even quite certain which of the above three achievements he is describing in detail. (That’s a comment about the headings — Tao writes with his usual clarity.)

ICM2010 — Smirnov laudatio

Next, Kesten shuffled on to the stage. He has an unusual face, in that he has a white beard of the kind that looks as though it is never trimmed — indeed, I think that is probably the case, given the way it grows out sideways as well as down — and looks slightly fake, to the point where one cannot help imagining what he would look like without it, to which the answer is that he would probably look a lot younger as the hair on the top of his head is black. (As I write this, in a large room with dozens of terminals, he has just walked in.)

He began by telling us that Smirnov had got perfect scores in the International Mathematical Olympiads in 1986 and 1987, just in case we were in any doubt about his mathematical talents. His next remark came as a very pleasant surprise: even since the committee had made its decision — in fact, in the last two months — Smirnov had proved a major result. Let me begin by saying what that was.