An Interview About Undergraduate Math Research

Photo Credit: Sara Bell

For this blog post, I interviewed Cat R., one of my friends from high school, who is currently studying pure math and has been involved in a long-term research project for the past 6 months. 

Sara: Introduce yourself! What type of research do you do?

Cat: My name’s Cat, I’m studying math at the University of British Columbia in Vancouver, and my research is about representing convex geometries, a branch of the larger field of geometry. It’s through a program called Polymath REU.

Sara: How did you get into that research?

Cat: Well, fun story: my planned research program in Germany for this past summer was canceled. So I had nothing to do, and I got an email from the math department. This program was designed specifically for students whose research got canceled. And it looked interesting. 

Sara: Nice. How did you choose the research project that you focused in on?

Cat: It had maybe 12 different projects, and the first week of the program we looked at all the projects and did some background research to decide which project we wanted to work on. Since so many research opportunities got canceled, they were trying something different to help make it available to as many people as possible. 

Sara: How have you found the experience of working on such a large group project?

Cat: Especially since it’s digital, almost all of the work was individual. It was probably less collaborative than usual, even though there were more people to collaborate with, but we definitely did have some meetings in small groups in addition to our weekly whole-group meeting.

Sara: Do you have any advice for students engaging in virtual research?

Cat: It definitely lends itself to different sorts of projects. So the project that I was working on, we wanted to describe exactly which convex geometries could be represented in a certain way, which is a pretty big unsolved problem. And there were roughly 700 geometries, and because we had so many people, we were able to just split them up and try to represent them. I think we really took advantage of the fact that we were virtual and as a consequence had so many people that we could just split up a lot of work. Plus, we ended up using a few online and computer-based tools that I don’t know that we necessarily would have used otherwise.

Sara: Your program had a lot of people from a lot of different schools. What was that like?

Cat: It was fun because everyone had different backgrounds. You didn’t have common points of reference for everything. Everyone thought about things differently. Especially once we started proving things and coming up with theorems, you could see that people were thinking about things in very different ways and sort of if they tended to think about it more geometrically or more algebraically.

Sara: Are there ways in which you feel like you’ve grown as a mathematician through this project? And do you see it tying into your coursework at all?

Cat: Working on an open problem, you might be in a situation where you don’t know if you have the tools for it, if the tools for it have been developed, or if that development is what you’re trying to do, or where you don’t know if there is one simple answer that will solve everything or not. Right now, we have a bunch of different theorems, that we would love to unify, but we don’t see how they’re related. We don’t know if they are related at all. Also, it’s helped me figure out how to manage my attention and what to be looking at, in a strategic way.

Sara: For students who are considering majoring in math or taking math classes, do you have any advice?

Cat: First of all, definitely do it. Take math classes, they’re super cool. Majoring in math? Depends how much you like math. Mainly, just don’t panic because you will see things that are very different from the math you’ve seen before, in high school. There’s a lot of different types of math. But stay calm and be patient! Professors are great, office hours are helpful, and working with other people is very helpful. It took me a long time to figure that out: I think a lot of math people don’t tend to think of it. Some math people like math because a lot of it can be very solitary, but working together can be very rewarding. 

Sara: What about advice for students who are interested in math research?

Cat: Do it! I wish I had done math research earlier. I was pretty intimidated about doing research, ’cause it’s kind of scary if you don’t know if you’re even looking for something that you’ll be able to find, or maybe you’ll put in all this work and it’ll turn out to be obvious in the end. Keep in mind that a lot of really interesting math, even math that took people hundreds of years, looks obvious with hindsight. You’ve gotta get there somehow.

 

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