Andrew Beveridge is a professor in the mathematics, statistics and computer science department. He teaches upper level courses in graph theory, combinatorics, discrete applied math, abstract algebra, calculus and linear algebra. He talks to The Mac Weekly about failed calculus tests, Silicon Valley, combinatorics and bass guitar.
Where were you born, and how did you grow up?
I was born in New York City. My father was a chemistry professor at Hunter College in New York City, so I grew up in New York City and around there.
Do you think having a professor in the house influenced you at all?
Absolutely. It was clear that my father loved his job, but also that it was a challenging job. But it was sort of worth the sacrifices that you had to make. He loved going to work every day and that made an impression on me.
You went to Williams and Yale. Could you tell me a bit about what your education was like, and if it was different or similar to Mac?
I went to Williams expecting to be a physics major, and then got caught up in the Siren song of mathematics once I was there with the really amazing professors who had a really big impact on my life. They were all just amazing teachers in very different ways. Certainly mathematics in a liberal arts setting, and just how accessible they made it and how vital they made it, really had a big impact on me and it was the kind of place I wanted to end up in as well.
How did the professors impact you?
They were just really great teachers and really nice people and there was a lot of community around the department itself. I saw it go from a very sleepy department of about 10 majors a year to about 50 majors a year by the time I graduated, and it was really interesting to be there as that happened and to see how much difference just a couple of people could make in a department. And I think, in terms of them making an impact on me, they were all so different but just true to themselves; it was very inspiring to see people magnify their own strengths and find a way to put that to good use.
So then you left school and went to Silicon Valley.
I have a very unusual trajectory where I got my Ph.D. and started a post-doc and then left academia; that’s actually not so uncommon. The more uncommon part is coming back. [Silicon Valley] was a lot of fun. I was there in the late ’90s and early 2000s, so I was working for a few start-ups, which was sort of thrilling to be in the middle of a cultural phenomenon, but I will admit that I never took the get-rich-quick side of it very seriously. I was there to work on things that I thought were interesting, and if other things happened, that was fine, but there were a lot of people that I worked with in that this was pretty much their life plan. They were going to work hard for a year or two, then become millionaires and it was kind of laughable from my perspective because I had gone through six years of graduate school and post-doc, so I knew what it really meant to work hard and I knew that just because you work hard doesn’t mean that you deserve to be a millionaire for the rest of your life, so it was a very weird anthropological experience for me because I wasn’t like everybody else on that front.
What influenced your decision to go back to academia?
This one’s a complicated story so I have to start it in the right way. In the end, what I realized about myself was that I wasn’t as interested in the business side of things and that’s where a lot of the challenges lay in the Silicon Valley work. And it just wasn’t personally satisfying to me. There were big problems to solve, and it was going to take really smart people to do it, but it just wasn’t calling to me. And I actually really missed the mentoring side of being in academia. There are all these positive interactions that fill your day in academia, whether you are in the classroom talking about something you love or trying to help someone through difficult material in your office or mentoring someone for their honors project. These are all really positive interactions between people and it was something I really missed. In the business world, I really found it was designed for people to be selfish, in that there were certain tasks you needed to perform, and in fact helping other people kept you from doing the thing your boss wanted you to do, so there was not a lot of incentive to be generous. And I realized about myself that that was something that needed to be part of my daily life again.
Trying to crack back into academia was a big decision. It was like jumping off a cliff without a parachute, and you don’t know where you’re going to end up. It’s a very unusual thing to get back into academia after five years out, and people potentially would have all sorts of questions about whether you have what it takes to get your research running again.
How did you end up at Mac?
I knew I wanted to end up at a liberal arts school, and Macalester was hiring the year I was on the job market, and it was very clear to me very early on in the job process that this was the one place where I wanted to end up, that the personality of this particular department really shone through and just cut through everybody else. The dear applicant email that came back from this department was so different than anything else.
Every other email would say something like, ‘Oh, you’ve made our short list, are you going to come to this meeting where you can interview?’ Basically, they were two lines long. The email from Macalester from the current chair Tom Halverson was about three or four paragraphs long and it described Macalester itself, the department itself, the process and it was very personal and very intentional and very warm and this was immediately the only place where I wanted to get a job.
What subject do you teach now?
So this semester’s really fun. I’m teaching combinatorics and discrete math, and these are sort of like a sequence: part one is discrete math, part two is combinatorics. It’s sort of the math that’s everywhere. You’re counting discrete objects as opposed to dealing with continuous phenomena. It’s the mathematics that’s the foundation of computer science. It’s a younger field, compared with calculus, and it’s really coming into its own right now because this is the math of the 21st century. We’re dealing with big data problems, and this is the kind of math you need to tackle them.
What does a combinatorics problem look like?
So here’s a combinatorics problem. A senior and I did this for his capstone project. We implemented an algorithm to match incoming first-year students to first-year seminars. You’ll remember, you rank your top four choices and you get one of them, so this is a big matching problem. It’s a constrained matching optimization problem. You want to make each student as happy as you can, but there are constraints on course sizes and then there are some other things that Macalester would like; for example, you wouldn’t want to have a class of all men or all women. That’s not really in the spirit of the first year seminar. It turns out there are some nice mathematics you can use to solve this matching problem. This has gone through various iterations, so whatever first year course you are in now, I’m partly responsible for that. My algorithm tries to find the best solution as an overall happiness optimization.
What do you like about teaching a first-year course?
One of the funnest parts about it is seeing how much people change over that first semester that they are here. Again it comes down to that mentoring side—I remember there was one week where I mentioned to my student that it was time to start not just completing their work but turning in work they are proud of. And that was kind of an eye-opener. There is this sense as you go through your years at Macalester, you start to have agency over your studies. It’s not what you do because people tell you to do it, it’s you pursuing your interests and wanting to do them well. It’s really fun to see the beginning of that process and when the lights start to turn on for students.
I ended up choosing [to teach a first year course] on combinatorial games like tic-tac-toe. Basically, I trick people into learning how to make mathematical arguments by making optimal strategies. Those are really one in the same thing. That’s the mathematics of it. Mathematics is not just calculation, it’s patterns and explaining patterns.
Why do you like combinatorics?
You know, I’ve always been drawn to it. Ever since I was a kid, I knew that some part of me connected with even just doing calculations. I’m going to try not to say anything hackneyed, but mathematics is ultimately about beauty. It’s about pattern and symmetry, and certainly the kind of mathematics I’m drawn to has a certain degree of playfulness to it. Those are probably words people don’t normally ascribe to mathematics.
Do you have a first mathematical memory?
My parents have a first mathematical memory of me. I would actually ask them to make little addition and subtraction sheets for me to do for fun. There was one time my mother miswrote a question so that she was subtracting five from three, and I didn’t know what negative numbers were, but she decided to give it to me anyway. She said, “Well what is this one?” and I said, “That’s a hole that you have to put two into.” She tells that to me all the time.
Do you have any other memories from your early years in mathematics?
I failed my first calculus test in high school. There’s something about this field that I have the gumption to try to move past and that’s ultimately what I learned about myself as I went through school, that there was something about this subject that kept me coming back. That’s really why I’m a mathematician. I don’t really have a choice but to be this.
Why does what you study matter?
One of my specialties in particular is the study of random graphs, and these have been studied for over 60 years now. They started off as mathematical objects without any applications, but now these are the tools what people now use to study real-world networks like social networks, like Facebook, and so that’s one of the other amazing things about mathematics: when life catches up to the theory.
What are some of the things you research when you aren’t teaching?
I do these pursuit-evasion games both on graphs and in other environments that have applications in robotics.
What’s it like teaching math at a liberal arts school?
One of the answers is that mathematics is a really, really distilled form of critical thinking. It’s about taking the information you have, taking it apart, and putting it back together and creating an explanation. One of the hallmarks of mathematics is that it’s very brief, and that can be very daunting as well. These are the skills you need to make any sort of argument.
What do you do outside of teaching?
I play bass guitar, so I have just started playing again with some people that I was in a band with here in the Twin Cities. I grew up in the ’90s, so it’s sort of like alternative rock. We sort of just get together and make up our own songs and it’s been a really fun creative outlet. I’ve played in rock bands almost all of my adult life. My most recent one was called Math Emergency, but that has a longer story behind it.
What’s the story?
The name came from one day I sent an email to the band saying I might not make it to practice that weekend because I was having a math emergency. And they just thought this was hilarious, like what’s a math emergency? It was because this paper we had been working on for six months was about to be scooped by a very quick and sharp mathematician. He had started working on the problem so basically we needed to finish everything we could as fast as we could to sort of plant our flag.
Did you finish the problem in time?
We did. Yes, we did.