Ana Rita Pires

In mid-November I had the opportunity to speak to Ana Rita Pires, a lecturer in the School of Maths. Here is my conversation with her.

SE: It’s really nice to talk with you. I’ll start by asking: where did you go for your undergrad, and did you just study maths?

ARP: I did my undergrad in Portugal, that’s where I’m from. When I started, I actually studied medicine; I did one year of this before deciding I missed maths too much. After that, it was straight-up mathematics, pretty similar to what we have here in Edinburgh, maybe with even fewer electives. I loved it, and [laughs] now I have a lot of friends who are doctors in Portugal.

SE: How do you describe your research to non-mathematicians?

ARP: What I do is called symplectic geometry. How would I describe it? Well, first of all, people who aren’t mathematicians are usually just happy knowing that I teach maths at university and I do some research. If they then want to know what that research is about, I tell them that geometry is where we study shapes. The geometry that people will remember from school is Euclidean, in which you have straight lines, Pythagoras’ theorem, and so on. But there are many other flavours of geometry, where your shapes have some added structure, so whereas Euclidean is all about the plane, the shapes I study are not on the plane. They can be more complicated: they can be curvy, have holes, or be 20-dimensional. We could say that we can measure lengths between points in this geometry, or that we can measure areas of small surfaces. The kind that I do, symplectic geometry – and this is where people’s eyes start glazing over – is where we don’t know how to measure lengths, but we do know how to measure 2D areas. It turns out this has a lot to do with physics and with the motion of bodies in space.

SE: Is there a first branch of mathematics that seriously caught your interest?

ARP: I really liked, and this is going back to my undergrad, theory of computation. Logic, Turing machines, I found that fascinating. I think I liked it so much because it was the first really hard class I had while in university. Linear algebra and calculus are a bit more like what you had in high school, so that felt like a continuation, but computation was totally different. [Laughs] But I still ended up in geometry!

SE: Were you into science fairs or Olympiads? Did you work on a lot of projects, either in high school or in undergrad?

ARP: Well, we didn’t have science fairs in Portugal, I don’t think they were a thing. But I did do the math Olympiad. One benefit of being from a small country is that, if your school participates in the Olympiad, your chances of getting far with it are much higher. I even went to the IMO (International Mathematical Olympiad) one year, which was great. It was really exciting to get to travel to do maths. In Portugal, there are few enough students that the people in the national final could all get together for a weekend. That was a fun gathering, with all the other people who love math. That was quite different from my school, where I was one of the only people who loved it. So, I really enjoyed participating in the Olympiads. I also enjoyed buying Martin Gardner’s books and working through the problems. It was fun.

SE: So, what made you decide to do a PhD and go into academia?

ARP: I think that actually ties into the fact that I went to med school. I thought, at the end of high school, I should find a profession that’s rewarding, challenging, and does good for the world, and being a doctor seemed to fit the bill. Then, when I changed to maths, it was because I missed it, and I wanted to do what I liked. So, I went with that philosophy. When I finished undergrad, I thought “what do I want to do right now?” and I wanted to do more maths, so I went to grad school. So, I did that, and here I am. I’m enjoying it, so I’ll keep doing it!