Whither Polymath?

Over at the Polymath blog, Gil Kalai recently proposed a discussion about possible future Polymath projects. This post is partly to direct you to that discussion in case you haven’t noticed it and might have ideas to contribute, and partly to start a specific Polymathematical conversation. I don’t call it a Polymath project, but rather an idea I’d like to discuss that might or might not become the basis for a nice project. One thing that Gil and others have said is that it would be a good idea to experiment with various different levels of difficulty and importance of problem. Perhaps one way of getting a Polymath project to take off is to tackle a problem that isn’t necessarily all that hard or important, but is nevertheless sufficiently interesting to appeal to a critical mass of people. That is very much the spirit of this post.

Before I go any further, I should say that the topic in question is one about which I am not an expert, so it may well be that the answer to the question I’m about to ask is already known. I could I suppose try to find out on Mathoverflow, but I’m not sure I can formulate the question precisely enough to make a suitable Mathoverflow question, so instead I’m doing it here. This has the added advantage that if the question does seem suitable, then any discussion of it that there might be will take place where I would want any continuation of the discussion to take place.

Ted Odell

I was shocked and saddened to hear about a week ago that Ted Odell, a mathematician to whom I owe a lot, died suddenly on January 9th of a heart attack while he was travelling to this year’s joint AMS/MAA meeting in San Diego. He was 65, but seemed a lot younger.

Ted was a world leader in Banach space theory, and in particular in the infinite-dimensional theory. The wry and slightly enigmatic smile you see in the photo was extremely characteristic: if I imagine Ted, I automatically imagine him with exactly that smile. Less clear from the photo, though perhaps it can be guessed from the camera angle, is that he was extremely tall: he belonged to a handful of mathematicians I know who make me feel short (Tom Sanders and Alex Scott being two others).

I first met Ted when I went to my first ever conference, in Strobl am Wolfgangsee in Austria in 1989. I can’t remember how it came about, but I ended up chatting to him, and he started explaining to me in a wonderfully clear way — the kind of explanation you just can’t get from a textbook — how Tsirelson’s space worked. I read in an obituary by András Zsak (which starts on page 30 of this issue of the LMS newsletter) that Ted had a reputation for being kind and encouraging to young mathematicians. He certainly was to me at this conference, taking the time to give this explanation to a graduate student about whom he knew nothing. Most of the next section describes an argument that he sketched out for me on one of those yellow pads of paper that seem to be standard in US maths departments. (I think I’ve still got the yellow sheets that he let me keep, but I’ve no idea where they are.)