Bill Thurston 1946-2012

This morning I heard the awful news that Bill Thurston died last night. Many of us knew that Bill was very ill, but we all hoped (or imagined?) that he would still be with us for a while yet, and the suddenness of this is very harsh. As Sarah Koch put it in an email to me, “Although this was not unexpected, it is still shocking.” On the other hand, I am glad to hear that he was surrounded by family, and died peacefully.

I counted Bill as my friend, as well as my mentor, and I have many vivid and happy memories of time I spent with him. I hope that writing down a few of these reminiscences will be cathartic for me, and for others who are coping with this loss.

I remember seeing Bill for the first time when I arrived at Berkeley in 1995; at the start of the academic year, all the incoming graduate students were ushered into the colloquium room to meet some of the senior personnel. Bill was there in his capacity as director of MSRI (the Mathematical Sciences Research Institute). He was wearing jeans with big holes at the knees. He made a speech about MSRI, inviting us all to come up the hill and interact with the visitors there. He also encouraged us to pronounce it as “emissary”, rather than “misery”; it didn’t work — we all called it “misery” (and still do).

I remember actually taking the bus up the hill (maybe a few months later?) in the vague hope of running into Bill and asking him to be my advisor (people had warned me against this, saying that Bill “wasn’t taking students”, because he was too busy running MSRI). I don’t think I had a very clear plan about how this was going to work out. I walked in and saw Bill chatting with Richard Kenyon about entropy of dimer tilings, and hyperbolic volume; at this point I basically froze, turned around and walked out again.

I remember Bill giving a few talks at MSRI during the special program on low-dimensional topology and combinatorics which ran during the academic year 1996-7. He gave one talk explaining his idea of a new proof of (some version of) the Robertson-Seymour theorem on the well quasi-ordering of graphs partially ordered by taking graph minors; he explained this as a kind of compactness result (any class of graphs closed under taking minors is characterized by not containing a certain finite list of excluded minors). A simple version of this compactness concerns the relation on strings (in a finite alphabet), where one string U contains another string V if the letters of V appear in U in the same order, but not necessarily consecutively; I remember Bill explaining this with the example that the string “topology” contains the string “poo”.

I remember Bill at a one-day conference at MSRI on mathematics and the media, with both mathematicians and journalists in attendance. Bill explained some of his ideas about communicating mathematics; he started by drawing a picture (on a big sheet of butcher paper hanging on an easel), explaining the “evolution of mathematical thought”. It was basically a horizontal line; at the left hand side he drew some sort of lizard, and on the right hand side, a monkey and then an upright stick figure representing the modern mathematician.

I remember Bill running the “very informal foliations seminar” at MSRI with Dave Gabai, Joe Christy, and a few other people. This seminar was not advertised; I basically wandered in off the street into the middle of a 3-hour lecture by Bill, explaining his new ideas about universal circles, and how they might be used to approach the geometrization conjecture for 3-manifolds with taut foliations. By the time he was done, I had decided I wanted to work on foliations, and I more or less had my thesis problem.

I remember when Bill moved to Davis. This was the only time I ever saw him in his office at Berkeley — when he was cleaning it out. I remember the little photo that used to be on the door, the one that’s on the cover of “More Mathematical People”, of Bill as a child working at a desk. He saw me watching him carrying his boxes out of his office and looking at the photo, and gave a slightly embarrassed smile.

I remember emailing Bill in early 1998, to explain a few of my tentative ideas about foliations, which had been inspired by his slitherings paper. He invited me to come out to visit him at Davis and talk to him in person. Over the next year or so, I drove out there perhaps a couple of times per month, struggling up the freeway in my third-hand lemon, with the wind rushing in through the bad seals in the door frame. We would have conversations that lasted for hours; stopping occasionally for lunch and coffee. Bill basically became my “unofficial advisor” (my real advisor Andrew Casson was meanwhile going through a tough divorce, and moving to Yale), and perhaps because he did not have many “real” students at Davis at the time, I got a lot of his attention. We spent a lot of time working through the theory of universal circles; I learned a huge amount of mathematics, not only stuff obviously connected to foliations (or even low-dimensional topology), but combinatorics, analysis, group theory, and so on. And yet, Bill listened very carefully to my ideas, and always gave them his full attention and consideration. At the time I don’t think I appreciated how rare this attitude is in a senior mathematician towards a graduate student.

I remember running into Bill in Black Oak Books in Berkeley — in the legendary math book section, of course.

I remember arriving one day a bit early to find Bill waggling his tongue through a gap where one of his teeth had fallen out. He kept making slightly funny expressions on his face thereafter, and it was hard to stay focussed on mathematics for the rest of the day.

I remember when we were trying to work out the details of some construction, Bill got very enthusiastic and we went to the campus store to buy some enormous sheets of paper and a few sets of colored pencils, bringing them all back to Bill’s office and laying the paper out on the floor. Bill was really excited by this episode; he remarked that he used to do this sort of thing “all the time” when he was at Princeton. I got the impression he hadn’t done it for a while.

I remember one day Bill was with a crowd of graduate students, and he was talking about how intimidating it is to start out in mathematics. He thought more senior people contributed to the difficulty, by trying to give the impression that they understood everything, and he wished that people would be more forthright in admitting when they didn’t understand something. I admitted that I had never really learned the details of Galois theory, and Bill exclaimed “that’s great; that’s the sort of thing I mean. Everyone should know that Danny Calegari doesn’t understand Galois theory”. He repeated it several times, to quite a few people. I waited for him to add some things that he had found hard to understand, but that seemed to be it. (Years later in an email he confessed that he had “never really come to grips with the Burau representation” . . .)

I remember working to try to get a project finished in the week before Bill’s daughter was born (we didn’t make it in time). My wife and I were thinking about having kids at the time, and I shyly asked him about the experience. He became very emotional and tender, and talked about what it was like to hold a newborn and have them lie in your arms, trusting you completely.

I remember seeing Bill in 2007 at the Cornell topology conference, and noticing that he looked kind of shaggy, with a few days growth of stubble. I remember giving a talk about immersed curves in surfaces, and mentioning that there are examples of such curves which do not bound an immersed surface, but which “virtually” bound such a surface (i.e. they have a finite cover which bounds). I remember being startled when, after a few minutes, Bill exclaimed, “well, don’t leave us in suspense! what are some examples?” I remember giving Bill the advance copy of my “Foliations” book (it had just arrived) as a late 60th birthday present (I hadn’t gone to his birthday conference earlier that year), and he seemed really pleased to get it, and immediately started looking through it, especially at the pictures. Later on someone told me he had been “showing it to everybody”, which cheered me immensely.

I remember visiting Bill in winter of 2008. At the time my family and I were on a vegan kick, and I remember discussing veganism, and Colin Campbell’s book “The China Study” with Bill, while waiting for the cafeteria people to make us our vegan burritos for lunch. Bill’s wife happened to be very sick that week, and in addition they were moving house, so Bill was very distracted. I remember the class Bill taught one morning that week, in which he gave some beautiful constructions of families of projective structures on some surfaces; and the next class, when he explained how to immerse a projective plane in 3-space with a single triple point. When I left at the end of my visit, Bill apologized for being distracted with so many other things, but hoped that I’d visit again soon. Of course I told him not to apologize, that I’d had a great visit (which was true), and that I hoped I would come again soon when we both had more free time. That was the last time I saw him.