My recent post generated a surprising amount of personal emails defending of Philadelphia. I can happily report that, although I didn’t really get a chance to explore the city in any depth, it has at least one excellent cafe. “Thank You, Thank You” is one of the best cafes I have been to in the US; I wish there were something half as decent near Hyde Park. (Hat tip to Toby Gee for finding this in his research.)
Returning to the conference, Terry Tao made the point in his public talk — as others have made elsewhere — that, more than ever, we should insist on rewarding aspects of mathematics beyond simply proof, in particular good exposition, particularly of the deepest and most difficult ideas.
It was interesting, in this light, to see Dennis Gaitsgory’s plenary talk^*. The fundamental problem with the ICM is that there is a contradiction behind the entire concept of an invited talk, particularly a plenary talk. It is simultaneously supposed to be an honor for great work and an opportunity to communicate those ideas. On the one hand, there is no question that Dennis deserves the first honor. On the other hand, the talk was, shall we say, somewhat challenging for a mainstream mathematical audience. I don’t blame Dennis; he has his style of giving talks^**, and this one went more or less exactly as anticipated. But it seems to me that a very simple solution would have been to have asked David Ben-Zvi to talk about the work of Dennis (and his collaborators). I hope for the next ICM the struture committee will consider more radical changes than what they have done so far. Would inviting someone to talk on the work of X be any less of an honour for X than asking X to talk? If they did that with *every* plenary talk, and at the same time made an effort to choose the right speakers (who could even collaborate with X), I think that would be a great improvement.
As the community moves ever so slightly towards demanding better exposition, it is interesting to look back on the Mochizuki circus. If we are going to be honest now, we should also be honest about the past. “Inter-universal Teichmüller theory” is nonsense, and that was more or less obvious to everyone at the time I wrote that post (which was five years after the announcement). The saving grace of those papers is that they were written in “Mochislop,” an almost comically embarrassing STYLE that screams “I am a crackpot.” Were it not for Mochizuki’s reputation, they would have been immediately dismissed. I am glad that, at the time, there were people (Scholze and Stix) willing to donate their time in a heroic effort to actually engage with the mathematics. In today’s world of AI slop, I think people would feel more comfortable not even bothering, and this is a good thing.
^*: The reason I single Dennis out here is not because his talk was in any way particularly exceptional compared to some other plenary talks, but simply because I know him well enough to be able to criticize his talk and feel confident that he will be OK.
^**: A student onced asked Dennis whether, given two correspondences \(X \leftarrow Z \rightarrow Y\) and \(Y \leftarrow W \rightarrow X\), if the fixed point groupoids of \(W \circ Z\) and \(Z \circ W\) are canonically equivalent. Dennis immediately gave the correct answer and said the proof was simple. The student replies “amazing! Most people end up struggling through the technical aspects of \((2,\infty)\)-categories”. Dennis replied “is there any another way?”. OK, well this might not have happened.