When my husband and I first began courting, I asked to read a copy of his dissertation because I thought it would be romantic. The blue leather-bound book was fairly thin but the title, “On Bilinear Maps of Order Bounded Variation,” was making my brain hurt before I even opened it. When I did peek into the pages, I discovered symbols I’d never encountered before. This man was bilingual, I realized. He spoke a language called mathematics that I only thought I understood.
About six years later, seven months ago now, I met another mathematician here at Northeastern, assistant professor Ben Webster. At the time he was about six months into receiving a prestigious Career Award from the National Science Foundation. With $400,000 over the course of five years, Webster would be exploring “representation theory of symplectic singularities.” I read the grant summary before our meeting, just as I did again a few minutes ago, before writing this post. But it was written in that other language that I simply cannot speak. No problem, I told myself, I’ll just get Professor Webster to break it down for me when I get to his office.
But when I asked him the main goal of his research he recalled a clip from a Nova documentary about proving Fermat’s last theorem in which some of the most brilliant mathematicians in the world attempt to explain something called modular functions:
Though modular functions have nothing to do with Webster’s research, he said, “I feel like the first three guys in that montage.” It’s hard to put into plain English the abstract work he’s devoted his life to. Instead of laughing at me though, like the second guy in the clip, Webster kindly pulled one bit of his work out of the mix, the part that he said is most amenable to cocktail party conversation, and tried to explain that.
He gave me an hour-long course in knot theory, after which I felt vaguely more educated in this other language. But it was really more like spending an hour learning how to pronounce the word “mañana” in Spanish and walking away still saying “banana.” When I got back to my office I think I sat in front of the computer staring at a blank screen for a while and then decided to do something else on my list. I wrote “Webster” in my planner under “To Write” and moved on. For the next five weeks, I copied Webster’s name to my next “To Write” list. I was having a hard time figuring out how to write about something that I didn’t have the vocabulary for. I took a break from copying the name because I knew it wasn’t happening, but, determined, I started copying it again a few weeks later. It has now been repeated 13 times in my planner: “To Write: Webster.”
And so, here we are.
I’ve decided that in order to write this post I’m just going to have to get over the fact that I don’t speak the language and tell you what Webster told me, because even though I can’t speak the language, I can understand that it is beautiful and, well, cool.
Early in our conversation, he said that “math is really about looking at something and saying, ‘well, what sort of structure here is important and what things can I just forget?’” That is, mathematicians only care about the most fundamental elements of a problem. If you’re looking at the mathematics of something being shot out of a cannon, he said, it really doesn’t matter what that something is. Only its trajectory, and the force with which it is launched, for example. “So when I say knot theory,” Webster continued, “I mean thinking about closed loops of string, or closed loops of anything — that’s one of the things you’d want to forget. The important thing is what shape does it have? How is it tangled up on itself?”
Knots. Yep. That’s what we spent the first hour of our two hour conversation talking about. I never knew there was so much math in the pesky tangles that hurt my finger nails to resolve but it turns out knots have a long and rich history. In the 19th century, Lord William Thomson Kelvin got the idea that the different elements might be tiny strings tied up in knots, and that the properties of the elements were somehow dependent on the properties of knots. While this turned out not to be Lord Kelvin’s most on-the-mark insight, it did get people thinking about knots in a more systematic way. The first question they asked themselves, Webster told me, was how to distinguish between different knots. What does that mean exactly? Let’s say you have a rubber band: