John Urschel speaks about graduate studies in mathematics, professional football, and career aspirations

Urschel: ‘In going from football to math, I think football really helped me have perspective.’

Professor John Urschel of the Mathematics Department was appointed as an assistant professor in the fall of 2023. Urschel completed his PhD at MIT in 2021 and was a former NFL player for the Baltimore Ravens for three years. 

The Tech spoke with Urschel as he reflected on his time in the NFL and as a PhD student. This interview has been edited for length and clarity. 

TT: Who or what inspired you to play football professionally/pursue math at a high level?

Urschel: My dad inspired me to play football. When I was a kid, I would visit my dad in Canada and he had this office and his office had a portrait of himself next to the door, and it was him in his football uniform. I always looked at that when I was a little kid. My dad played linebacker at the University of Alberta.

As far as math goes, as long as I can remember when I was a little kid, I loved puzzles and quantitative games. I can’t actually ever really pinpoint a moment where it's not like there was a moment where I really started to love math. I think that math is loosely defined. I've loved it ever since I can remember.

TT: How did you balance Division 1 football and academics at Penn State?

Urschel: When I first got to college, it was quite overwhelming. But eventually you get into a groove into a routine. You sort of learn. You learn when to do what. I really had a good habit in college of making sure I do the most important things first. I always made sure that I scheduled my classes as early in the day as possible to the extent that I could. I scheduled my personal football training  as early as possible when there were choices about which time slot to do lifting or do conditioning.

TT: What was your journey to entering graduate school at MIT? 

Urschel: Before I got to the league, I finished my undergrad in three years. I got a Master’s because I really wanted to keep playing football. At the same time, I didn't want to do my PhD at Penn State because I did my undergrad there.

I'm listed on, you know, [NFL] draft rankings, and I decided to put the PhD on hold. I'm gonna play the league for a couple years, retire and go for my PhD. I play my first year in the league. Things went quite well and I started a bunch of games, but I felt unsatisfied like in my personal life I realized that I really missed the academic environment and being around other people who want to learn.

After my first year [in the NFL] I decided I needed to apply to a PhD program and I got into MIT. And I thought it was a really good fit for me because the sort of math I do is a little bit more on the applied side. I felt like I belonged here, so I accepted the offer and the rest is history. 

TT: Was balancing graduate studies and professional football different from doing both in your undergrad? How did you strike the balance during your PhD?

Urschel: Very poorly. When I was a math major at Penn State, PhD classes there felt manageable. MIT’s PhD program doesn't include all part-time students. I can tell you being a professional football player simultaneously was just too much. I was constantly stressed at work. There are only so many hours in the day. I can say in hindsight it makes for a funny story, but it was not the most pleasant thing to be doing both of these things at the same time. 

TT: How do you spend your typical day?

Urschel: The role of a math professor is a pretty nice one. There's no lab, so there's no physical thing I'm responsible for. It's just math problems that I'm trying to solve and people I am trying to solve them with. I'm also trying to teach how to solve math problems.

My typical day starts with me and my son, and we get to MIT via the T and by foot. Every morning my day starts with a long two mile walk before I settle down here. Depending on the morning, if it isn't teaching, I hold office hours and meet with collaborators, but my day mostly consists of, or at least my favorite days, consist of thinking about math. 

TT: What did you find to be the most unexpected intersection between your math research  and your career in the NFL?

Urschel: I definitely think as a kid, being quantitatively minded definitely helped me in a lot of the more analytic aspects of football. In particular, understanding how these responsibilities of different people fit together in a larger sort of theory or scheme while playing football was helpful. Being able to take information about what I'm seeing helped me more than maybe other people. 

In going from football to math, I think football really helped me have perspective.  I think a lot of times, math can feel very intense if you let it because you're trying to solve some math problem, and it's a little different than doing an experiment or testing some hypothesis. You can spend a very long time thinking about something and not really make any progress either way, so in that way, it can be a little frustrating.

I always kind of think and pretend to myself that I've already retired. Right now this is just this is my post retirement career. And so, I find that's a good way for me to look at it. My day as an MIT professor is much easier than my day as a professional football player.

TT: How did you respond to challenges in football versus in math (and how these overlap)?

Urschel: You're told these things that really get beat into you that you're constantly chasing this perfection that you're never actually going to achieve consistently in terms of performance. You're constantly trying to do better no matter how well you've done and when things are going wrong or when things are performing poorly. The key thing is to always lean into your training, lean into your preparation, and stay the course. The idea that often shows up in football is the idea of purpose. Perfect practice makes perfect. 

The way you are setting yourself up for success is something that has carried over into math, especially when I feel really stuck and feel like I'm not making progress. It's often helpful for me to take a step back and think about whether I am actually setting myself up in the best way to be successful at this? Do I need to go read some different resources to try to help me, you know, be better prepared to solve this problem? Should I talk to some other people to get some perspective?

TT: Which area do you find to be more competitive: football or academia?

Urschel: I will say football is very much more directly competitive, whereas in math it is much more indirect. As a math community, we really do usually feel like we're all part of the same community, with some exceptions. This is how it should be. In general, one shouldn't think of math as like some zero sum game. We're working together to try to solve problems of course, but how much you share with other people varies because you also need the job. There can be a little bit of competition because multiple people will be applying for the same position. There aren’t many academic jobs compared to how many talented and qualified mutations there are, so it can be quite tough. But the good news for mathematicians, both undergraduates and PhDs, is that there are rewarding jobs in industry whether it be tech, finance or other fields.

TT: How do you visualize or conceptualize the math problems you work on? And what do you love most about the field of math?

Oftentimes, I do think very conceptually about things. I'll be walking home and decompressing from the day and I’m slowly letting the things I've been thinking about all day sort of seep in, and really let them sit. This happens a lot before I go to bed. I find that I've been thinking a lot during the day about different things I've been picking very actively. Oftentimes, I have an insight that I text to myself and I put my phone down and in the morning like often I find that I actually had some good insight. 

Taking a step back and thinking about that work with separation is often a very productive way of sort of understanding how things work at a high level. You can do rough calculations in your head or thinking through steps in your head. But I find that sometimes you just get the answer or you sort of figure out the right technique by thinking about it directly. I find that to be really productive.

The thing I love most about math is learning. There are so many rich and beautiful results in mathematics that connect to each other. There's so much that I don't know. Every time I learn something  new or slightly surprising in math, it's a really great feeling. The act of learning is just a really enjoyable thing. That's one of the great things about being a professor is that you get to just keep doing that the rest of your life.

TT: What are your thoughts regarding the general public perception of math and math education?

Urschel: That's a great question. I think there's often a perception in this country that being bad at math or not liking math is something that is joked about often, even by smart people. And I think that numeracy in the same way that literacy is important is a crucial skill in our society. I think these are skills that are useful for many jobs, but more generally, it's just useful for everyone in your day to day life, some fundamental level of quantitative reasoning. 

I think that this is something that we really need to value as a society and it doesn't always get sort of the level of value that I think it does. And I also think that top careers in STEM also should be glamorized a little bit more than they are. 

I recognize that I'm a former pro football player. I've had a much larger platform than most mathematicians because of what I did outside of math. I don't think that's fair because I know so many amazing mathematicians with a lot to contribute to the world and a lot to share with other people, but that's the way our society is right now. 

TT: What do you believe is your biggest accomplishment in math? And, are there any future problems you’d really like to solve?

Urschel: I’m too young—I’m 32, I just got here. Let’s save the greatest accomplishment five years from now, but I would say that my best results certainly lie in matrix analysis and matrix computations. Whether it’s fundamental results about the nature of Gaussian elimination, with techniques that you learned in school to solve a system of equations or results about graphs and networks through looking at algebraic properties. I think that’s probably the area of biggest contributions.

There are a couple of concrete problems for which I say “this is a problem I would like to see solved in the next however many years” and it's important to set those goals so that you are moving towards something concrete. But the joy of it, at least for me, is not the moment I solve that problem. The joy of it is the progress of getting to solving that problem, the joy of  being at odds with a problem like struggling against the problem. 

When you finally solve this problem, this is like the cherry on top. I feel like I understand everything or at least I understand enough to really say something powerful. I find this process of getting to solving the problem to be the most rewarding.

TT: What would you say your greatest accomplishment in football is, or your greatest accomplishment, in general? 

Urschel: I’m quite proud of my time in Penn State, my alma mater—especially in my later years. This was a really tough time for a lot of people in that community. And in hindsight, when I think about my football career, that’s the time period I really look back on very fondly, and that I’m quite proud of.

TT: How do you define progress in math?

Urschel: Who knows? Oftentimes it can be helpful when you have some problem and you can try to break it up into smaller pieces that you think might be a useful ingredient for the bigger problem. Or you can simplify your problem in a number of ways. You can try to prove some lemma or some complimentary thing that maybe helps you understand the nature of the problem. You can also try approaching the problem with some technique and understand the limits of that technique. 

Progress can be hard to track. For instance, I'm working on a research project with a former undergraduate, and we do not know how to solve the problem. We just don't and that's normal. But I had an idea for an insight that might give us a way in that other people haven't thought about. And so you try this insight. You try to prove some things in the direction that you're trying to go at the end. Maybe all the things we proved aren't useful because this technique doesn't work. It's hard to know that until you get to the end and so the more experience you have doing math often the better you are at roughly guessing what your progress looks like. It's a feeling you have.

TT: What are your future career goals and aspirations?

Urschel: At this point in my career, I'm really happy to be back at MIT. I'm here as an assistant professor, so I'll be here for you know, probably the next six years or so. My big career aspirations are to keep doing math, solve really interesting problems and I am eventually looking forward to being in a tenured position at some point, settling down, buying a permanent house. That's a milestone.