Fifteen Questions: John C. Urschel on Numerical Linear Algebra, Coffee Shops, and the NFL

John C. Urschel is an assistant professor in the MIT Math Department and a Junior Fellow at the Harvard Society of Fellows. He previously played for the Baltimore Ravens. This interview has been edited for length and clarity.

FM: What drew you to specialize in matrix analysis and numerical analysis?

JCU: I find that the type of area of math I work in has been strongly influenced by who my mentors have been and who the people are who have taken an interest in me and said, “Oh, I think John can do math.”

I ended up taking a Ph.D. class in numerical linear algebra. Again, the professor in that class took some interest in me, offered me a research project, and that’s how I started working on things related to matrices and linear algebra. From there, I’ve grown to really like the field.

FM: In 2015, you had a concussion while at a training camp, and you were unable to work with high-level math for a few months. What made you return to the field after you healed?

JCU: So I was out for — not a couple of months, maybe under a month — but I was definitely out for a bit.

While I was healing, I thought a little bit about how unfortunate it was to get a concussion, but at the time, I was focused on getting back out on the field.

My first practice, things weren’t going so well. I was keeping my head out of things. My position coach worked with me after practice to make sure that I was ready to go. From there, I just got back to it. I was focused on getting back with my teammates and getting ready to play because, at the time, I was a pretty serious contributor to the team.

FM: Why did you ultimately decide to leave the NFL?

JCU: All of a sudden, my priorities became raising my daughter, being around and being healthy to hang out with my daughter when she’s older and I’m older, being able to do math, and doing math at a high level.

Football came third on that list. Football is a great sport, but it’s a pretty violent sport. When it’s third on your list of priorities, it’s probably not a good idea for that to be something that you keep doing when it’s a very serious sport. It is a sport I love.

FM: Have any of your students ever been fans of your football career?

JCU: Not so openly, which I appreciate. It’s nice. I had a class last year on numerical methods. I’m teaching this course, and about halfway through the semester, someone in office hours mentions to me that they had no idea that I used to play football, and, in fact, the class just didn’t know. I guess I was trending on Reddit or some such thing, and so one of them opened up Reddit, and I was on the front page for some — I don't know why. I’m not on Reddit, so it’s not me on Reddit, but something about me. Then they were like, “Wait, I think that's my math professor. That can’t be right.”

FM: How do you feel about football from a health perspective, given what we now know about its connection to CTE and brain damage?

JCU: The way football is often viewed within American culture is not necessarily something that I fully agree with. For instance, I feel like in a lot of places in this country, football is viewed as the default sport for a healthy young boy. I’m not sure I’m on the same page with that. For instance, I think, first of all, there’s not that much benefit to contact football before late middle school, or I would even say until high school.

This is, of course, every parent’s own opinion. If I were talking about my own son — this will be something that will come up eventually — I think not. When it comes to high school football, I think it’s a great sport. It has a lot of really good benefits, but it’s a really violent sport. It’s a sport that I think you should not be playing unless you find that aspect of it is something that is really good for you and you really enjoy it — and the physical contact of it is something that you really get a benefit from.

FM: What advice would you give to student-athletes balancing their academics and their sport?

JCU: Football, especially at a top Division I program — despite the NCAA limits on hours — it’s really a full-time job. Then you also have academics to worry about. I would say the thing that helped me the most is that I always try to structure my schedule so that I take care of the most important things first.

I would sign up for the 6 a.m. lifting session. I would sign up for treatment as early as possible. I would also schedule my classes as early as possible for anything.

Then later on, maybe at night, if I’ve done everything I need to, I’ve done all my P-sets, I’m studied up, I’ve done all I need to do for football, I can relax.

FM: Has your mathematical knowledge ever been useful to you in a football game?

JCU: I’m going to say my mathematical knowledge has never once been useful in a football game, but I do feel that the skills that math teaches you have been really helpful. One thing that has been helpful for me throughout my career is quick quantitative reasoning. It’s not a single math formula.

FM: You play competitive online chess. What draws you to the game?

JCU: Competitive is a very strong word. I’m a very average chess player. I enjoy it. It’s a fun game. It’s nice to have hobbies. I’'s nice to have things to do that are different than work. It’s the sort of thing I like doing at night, again, when my day is done and when I’ve done everything I need to do.

My wife would say, “You’ve had such a long day. You want to relax and turn your brain off by focusing really hard and trying to solve complicated chess puzzles or try to play stressful chess games.”

FM: You’re on the selection committee for the Mathical Book Prize, an annual award for fiction and nonfiction books that inspire children to see math in their world. Of all of the books you’ve reviewed for the prize, which one stands out to you and why?

That is a tough one. We’ve gone through so many great books. I love being one of the chairs of that committee. You get to read so many great math books for young people.

For young ages, I would say the book “Zero Zebras.” It’s an interesting book that goes around the idea of zero.

FM: What is your current favorite NFL team?

JCU: I played for the Ravens, so I always hope the Ravens do well. I’m always happy to see them doing well. But I’m a Bills fan. I grew up in Buffalo. I’ve been a fan since I was a little kid. I suffered through the 90s as a little kid — lots of Super Bowls, no Super Bowl championships. So, I’m a Bills fan for life.

FM: The Urschel-Zikatanov theorem is named after you. In layman’s terms, what does the theorem do?

JCU: The naming of that, I think, was very kind of some of the people working with the American Math Society and the Notices. That was one of my earlier papers with a Bulgarian mathematician, Ludmil Zikatanov, who was one of my mentors. I’m his former student, but he’s also a very good friend. He was a groomsman at my wedding, and this was something we studied when I was a student at Penn State. It, in the simplest terms possible, was related to the connectivity of what are called nodal domains for a graph or a matrix.

FM: Do you prefer Harvard Square or Kendall Square?

JCU: I don’t think that’s much of a debate. I think Harvard Square is at least 10 times better than Kendall Square, especially because Kendall Square just lost its Clover. It had a Clover, and it lost it. It was already a little suspicious, and it just went downhill from there. Whereas Harvard Square just has so much. I love MIT, but if there’s one thing I have to gripe about, it'’s the food options around MIT. When you’re at Harvard, you’re spoiled for choice.

FM: What's your favorite food option in Harvard Square?

JCU: I’m a coffee shop person — I don’t know why. I really have strong coffee shop vibes. I’m happy with a good Tatte, Tatte is nice. I like Mexican food — so, the taquerias. There’s no singular one thing I’ll always get, but I just like having lots of options.

FM: You’re on the board of the National Museum of Mathematics. What’s your favorite exhibit?

JCU: My favorite one — and probably the most famous one from the National Museum of Math you see in newspapers — is the bike with squares for wheels. So, it’s a bike with squares for wheels, but the terrain is such that it still feels like a normal bike.

FM: Your wife, Louisa Thomas, is a sports journalist. Has her writing influenced your perspective on football?

JCU: She knows a lot about a lot of sports, especially tennis, which is her expertise. But I played football for a long time. I really know football. So I would say I’ve learned from her about tennis and some other things. I think when it comes to football, it’s mostly her learning things from me. Oftentimes, when she’s doing something and it’s football-related, she’ll ask me lots of questions because I have an expertise that’s hard to come by. Somehow, even though she is a sports writer, I'm still the football expert in the house.

—Magazine writer Vivian W. Rong can be reached at vivian.rong@thecrimson.com.