William Thurston passed away yesterday. I’m feeling really torn up about this, and I thought that writing about it might help. William Thurston has been a hero and inspiration of mine for a number of years now. I’ve often daydreamed of getting to study with him, or even just getting to hear him speak. And now that will never happen.
In my head, he’s “Thurston”—I would get excited about “reading some Thurston” or running across some new way that he was involved in mathematics that I’m interested in. And maybe he’ll feel like “Thurston” again to me someday. But right now—even though I don’t have any right to speak of him familiarly—I can’t help but want to call him Bill. I know intellectually that the feeling of closeness is illusory, but I can’t help myself.
I came to know Bill’s work through my ongoing interest in non-Euclidean geometry. It’s an amazing subject, full of beautiful objects, ideas, and theorems. It connects with compelling questions of philosophy and psychology, and its historical arc is an epic human story. And maybe most of all, it feels like a world unto itself, one that I’ve inhabited for a while and feel kind of at home in.
Bill’s ways of thinking about three-dimensional manifolds revolutionized their study. I’m a rank amateur when it comes to this stuff, but I’ve applied myself to it the best that I can. Reading and re-reading parts of his The Geometry and Topology of Three-Manifolds—first the lecture notes, and then in book form—has been an ongoing love affair. Reading papers that referenced Bill’s work made me feel like I was circling around something important, something central. It’s just the most beautiful and compelling and exciting stuff–at once dizzying and serene.
And then one day I saw “Bill Thurston” pop up in a thread on MathOverflow, and I was just floored. Could that be the William Thurston? It was. And there he was, just mingling and sharing, probing and wondering. I quickly came to relish the thoughts he would share on the site. Here’s his profile page, which contains links to his MathOverflow contributions. It includes the following text:
Mathematics is a process of staring hard enough with enough perseverance at the fog of muddle and confusion to eventually break through to improved clarity. I’m happy when I can admit, at least to myself, that my thinking is muddled, and I try to overcome the embarassment that I might reveal ignorance or confusion. Over the years, this has helped me develop clarity in some things, but I remain muddled in many others. I enjoy questions that seem honest, even when they admit or reveal confusion, in preference to questions that appear designed to project sophistication.
That is not the tone that is associated with mathematicians. I remember reading the above and feeling so struck and moved—that here was this utterly brilliant person, a living legend, who was expressing forthrightly feelings of confusion—trying to negotiate his own mind and social dynamics and, simply, living. It felt like a revelation. Here’s another of his wonderful contributions to the site.
So often the world of mathematics—the content, the texts, the institutions, the social dynamics—can seem so daunting. Isolating. An enormous edifice. It’s easy to feel small and insignificant.
Here’s an entirely different feeling: the excitement and energy and most of all integrity of living in a world where your heroes are alive. Integrity in the sense that the world feels whole, like something that fits together and whose parts are in harmony. And that you just might have a place in it.
And now the world feels a little diminished to me.
I remember feeling similarly to this when Kurt Vonnegut died. Reading Vonnegut’s novels has been a thread in my life since high school. There are just these moments when I feel an urge toward his humor and outlandishness and compassion and moral depth. I admire and enjoy his work, and his turn of mind often thrills me. I always thought it would be cool to meet him. And then he passed away.
But I never wanted to be Kurt Vonnegut, or even be like him. There were some ways that I felt kind of like him, and that’s why what he wrote resonated with me. And even: reading what he wrote helped to shape who I am.
But I never wanted to see through Vonnegut’s eyes.
With Bill, though, I always really wanted to see the way that he saw. I wanted and want to be able to see and see into geometric structures the way he did—in a way that feels intimate and intuitive. And I wanted and want to see mathematics as a vibrant, interconnected, human pursuit in a way that I feel he had special insight into.
A few months ago I ran across this video of a lecture Bill gave at the Clay Research Conference in 2010. The introduction Bill is given is a great overview of his contributions to mathematics, and the way that Bill talks is marvelous to listen to. But I bring it up most of all to say—just look at the way he moves. There’s something in it that’s just breathtakingly amazing.
Bill both represented something to me and at the same time was the incarnation of the thing he represented. That’s a little poetic and high-falutin, but it’s the best way that I can say it. Bill shaped my idea of what a mathematician and a person can be, and then also satisfied and realized that idea in the concrete. He was at once the “great man” who I admired and a person who made efforts to share himself with other people—including me, in a very small way, without his knowing—so simply and so humbly.
Bill, I only knew you from afar, but I still feel close to you. Your book sits in a special place on my shelf, and your work holds a special place in my heart. You told me things that blew my mind—on the page, yes, but it was like you were talking to me and only me. That first time I really saw what it would be like to live inside of a 3-sphere, it was electric. And in my eyes, at least, you moved through this world with grace and humility and curiosity and unmixed genuineness. I’ll never be able to tell you so in this life, but I’ll say it here anyway:
Thank you, Bill. You are my hero.
Post-script: If you’re interested in reading some of Bill Thurston’s writings, this blog post at Secret Blogging Seminar has a list that’s a great jumping-off point.
Also, here is the celebration of Bill’s life put together by Cornell’s math department, where Bill taught.
I’m sorry for your loss, Justin. This is a beautiful post and tribute to Bill. I love this “I enjoy questions that seem honest, even when they admit or reveal confusion, in preference to questions that appear designed to project sophistication.”
Thank you for sharing.
Thanks for sharing – and I love your quote about the process of doing maths (“staring hard enough with enough perseverance at the fog of muddle and confusion to eventually break through to improved clarity”). I will be sharing this gem with my students today – they are currently staring through a fog right now, and I’m trying to convince them this is *normal* when you are doing maths :-)
I don’t think I’d ever heard of him before the other day, but I’m touched to know how much he meant to you. This write up is a wonderful tribute to Bill Thurston. The work you do — to live a mathematical life, explore the beauty of mathematics, and share it with young people — is even more special. Whether he knew you or not, you are a living tribute to his work and ideals, and though his localized self is no longer active, he acts through you and those you continue to impact.
Math on, my friend. I’ll do it with you.
A beautiful piece, I feel many of the same things. I have to confess when I first heard the sad news I thought “Now we will never see Volume 2”!
What a great tribute to Bill Thurston, who obviously so influenced you and your journey in the world of mathemetics. I too am sorry for your loss.
Often it is hard to find the words to demonstrate to students and others what a subject means to you, how it influenced you and how vast, beautiful and significant it is. Your tribute to Thurston captured not only your admiration of him, but also your awe of the math he worked in. I am awed at how you emphasized this influence, this process and product that shaped your way of thinking, your world view and choice of career, and your love of mathematics. Sometimes the most personal accounts are the most influential teachings. Thank you.
We all have heroes, legends in our worlds, and some of us who are lucky get to live next to them, and even hear their present thoughts and words. Some of us even get to see the humans they really are.
Twitter is not the right medium for my response about Vonnegut/Thurston. Warning: it is very squishy and not really well thought out, it’s just my mushy feelings. It’s also not being edited, so it might be rambly and have some typos in it.
For some reason the day I heard about Thurston’s death felt very much to me like the day I heard about Vonnegut’s death. (Except I wasn’t trying to write an obituary for Vonnegut.) Vonnegut’s writing hit me right in my heart. I started reading him at a particularly vulnerable age in college, and there was something about him that felt like he was speaking directly to me. Vonnegut’s writing seemed starkly vulnerable to me, like he is peeling back the veils to what people really want. In whatever book it is where people have the middle names that denote their family, the way he talks about the human desire to be in relationship is so honest and frighteningly vulnerable. I felt like Vonnegut understood some of my deep desires and feelings that I couldn’t even have admitted to myself.
I didn’t really know who Thurston was when I started grad school, or even when I started working with my advisor, a Thurston “grandson.” When I learned about him, particularly the way he worked on visualizing these structures, and making them real through paper/cloth/yarn models, I felt like there was one other person who understood me. (I sew, and when I am sewing, I am explicitly thinking about charts that are taking the flat plane of cloth and modeling the curved surface of the body. I also visualize hyperbolic surfaces with the type of singularity I study as pieces of cloth. I haven’t gotten around to making these models yet, but I hope to.)
Of course, since my advisor is part of the Thurston line, it’s no wonder I felt this way; he had used Thurston’s ideas to teach me. Unfortunately, I never met Thurston in person, although I may have attended a conference or two with him. I was very shy and had a bad case of impostor syndrome, so approaching someone like him was not something I did. I regret that and semi-regret skipping his 60th birthday conference for a friend’s wedding in 2006.
I wasn’t fully aware of Thurston’s writings about the mathematical process before I started research for his obituary, although I knew he had influenced the way many of my mathematical role models communicate mathematics. When I read some of those articles, once again, they felt like they were speaking directly to me. Thurston’s was not the raw vulnerability I felt like Vonnegut portrays, and there is some false humility in some of his writing (not that he should have been humble), so it wasn’t the same, but it reminded me of Vonnegut in some ways.
So I think with both Thurston and Vonnegut, they felt like very warm, flawed, human people whom I really wanted to meet and talk to. When they died, I knew that would never happen. Like you, I never wanted to be Vonnegut, whereas I would have loved to be able to see geometry with Thurston’s clarity. But the way I feel in the wake of each loss is similar.
Thanks for giving me a chance to think about that a little more. See you on Twitter!
Thank you all for your kind words and reflections. They mean a great deal to me. May Bill live on in the lives of those whom he inspired and continues to inspire.
@Evelyn “Vulnerable” seems like a very apt word. And you saying that Vonnegut and Thurston were “human people whom I really wanted to meet and talk to”, I feel that. Like they knew themselves well and had no pause in bringing that self to others in a way that seems rare. Thank you for sharing your thoughts!
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