Mathematics Professor Rebecca Torrey received her Bachelors of Science from American Univ. She received her Masters of Science from the Univ. of Vermont and her Doctor’s of Philosophy in Mathematics degree from King’s College in London.
What brought you to study math?
When I was an undergrad, I went to school and I wasn’t going to study math, I was going to be a communications major. I didn’t even really know what that meant. I got to school, and I started looking at the course catalog, and looking at the communications major classes, and — no offense to anyone who studies communications — I looked at this list of classes, and said, I am never, ever, ever, ever setting foot in one of those classes, ever. So I turned around and signed up for the hardest math and physics classes I could instead, a complete about-face. The professor I had in the calculus class I started in was amazing, and he converted all of us at least to math minors, and several of us to majors. He was just fantastic. He brought me on board, and I haven’t left.
What’s your specialty?
Number theory. I think part of what drew me to it is the way that it brings together all sorts of different aspects of mathematics from different fields. I study algebraic number theory. There’s also analytic number theory, where you can definitely get into a much more analytic point of view, so you’re using analysis. But I do algebraic number theory, so it’s very algebraic, but you’re still using tools from analysis. You’re using tools from topology, algebraic geometry, everything; it feels like you have to know everything. Of course I don’t, but it’s one of the things that make number theory difficult, but it also makes it very interesting. For the stuff that I’m studying in particular, to even describe the objects is very complicated, but one of the nice things about number theory more generally is that you have these statements of very simple problems. To prove them, you need all of this incredibly complicated mathematics, and so it goes very, very, very deep from these very natural and easy-to-state questions, that you can certainly state to anyone with high school mathematics, but you can’t solve them with high school mathematics.
What classes are you teaching this semester?
This semester, I’m teaching multivariable calculus, Math 211, and I’m also teaching a class called Representation Theory, which is a 300-level class. One way to look at [representational theory] is [as] the interplay between group theory and linear algebra; another way to look at it is [as] a way to study groups, which are a very abstract concept, by mapping them to groups of matrices, which are much more concrete. The incredible thing is, then you have these sets of matrices that you’re looking at in your result, and then you can take the traces of them, throwing out all this information, and astonishingly, you can regain all this information about the group that you want to study. It’s really fascinating, and it’s a tool that’s used all across the board in all different areas of mathematics, but it also has applications, real honest-to-god research [applications] — chemists and physicists use these tools. So in this class at the end of the semester, we’ll look at an example from chemistry, where you study symmetries of a molecule. So you’ve got, like, methyl chloride, it’s got three hydrogen atoms, and you can rotate this thing. You can flip the hydrogen atoms around, and it still looks the same, so it’s got this natural group structure, via these symmetries. Then using representation theory, you can compute the normal modes of vibration of these molecules, using these mathematical tools. And similarly it has applications in physics as well, so it’s nice that it touches down somewhere. For me, I just appreciate the beauty of the math itself. But it’s nice also, when you can be like, oh by the way, there are applications.
What brought you to Amherst?
I am delighted to be here. It’s so nice to be here, and I’ve had such a wonderful experience here, [with] so many great people. I was working at Cornell, not last year, but the year before, and I got an offer for this one-year position at Mount Holyoke, which I really wanted to go to, but it was a one-year position, and I had this other offer for this post-doc, but I had also interviewed for this job at Amherst. And so in the best of the Five-College fashion, they worked this out where I would start at Mount Holyoke for a year, and then move over here. They worked this whole thing out between them, and it was fantastic, and so I’ve had a great two years here so far.
What do you do in your spare time?
I almost don’t have spare time… I play Go. Yeah, I’m obsessed. Go is an ancient Chinese board game, although it became what it is today in Japan. It’s a 19-by-19 grid; it’s a two-player game [and] like chess: total strategy. The rules are incredibly simple, and then you spend the rest of your life studying how to play, because it becomes so incredibly complicated. And for years and years, even though computer programs had beaten the best chess players, they were nowhere near even basic amateur players [in Go]. In the past few years, there actually have been some advances, using Monte Carlo methods, but they’re still not at the professional level, so they’re not very good, but they have actually made some progress. And the game is so beautiful, and they’re so much to study and learn. [Also,] I have ice skates, and I’ve been over to the rink, I think, a total of one time so far, although I’ve been meaning to get over there more. But I go over there, and I try not to fall down, and there are a couple of girls there who are clearly competitive figure skaters. And there’s me and this other kid, just going clump, clump, clump. But I enjoyed it, though it’s not really something that I’d say I do.