When people think of mathematicians, they often think of the stereotype: the awkward, hunched-over guy doing groundbreaking research at a bar. Russell Crowe’s John Nash in A Beautiful Mind.
John Urschel isn’t that kind of mathematician. He’s a 6-foot-3, 313-pound man who lines up across from defenders and hits them, hard. Urschel was a first-team All–Big Ten offensive lineman the last two seasons at Penn State, and he projects as a fourth- or fifth-round pick in this week’s NFL draft. He works hard at football, and when he’s finished, he goes home and does math.
Recently, Urschel sent me two of his published papers, one on celestial mechanics, the other on subgraphs, both of which could have earned him a doctorate in math. As the draft looms and his reputation as a mathematician grows, I spoke with Urschel about football, numbers, and the future.
This interview has been edited for length and clarity.
I met you at the Sloan Sports Analytics Conference, so you’re paying attention to the field. In your mind, what’s the biggest advancement in football analytics at the moment?
I’d say the best thing going so far is expected points added. In football, expected points added is how many points a team can expect to score based on down and field position.
I think that’s really a great foundation, because when you don’t take these things into account, every result you come up with, you can just throw out the window now.
In what sense?
A yard is worth different amounts at different points on the field and in different positions and situations. The value of a yard changes. Then we can look at how players perform in certain situations.
Like how well Penn State rushed the ball on third-and-2, for example?
Exactly. Honestly, Penn State’s ability to get two yards at third-and-2 is a lot more important than its ability to get two yards on first-and-10.
But also, in my humble opinion, the thing that’s really missing from football right now is video recognition. That’s the number one thing that should be on everyone’s mind. Let’s get that done.
It’s a lot tougher than basketball. I understand the struggle. You’ve got 22 bodies. It’s very chaotic, especially in the middle when you’re dealing with offensive line, defensive line. But I think that’s the next big step we need because with that data, let me tell you, the sky’s the limit.
Can you talk a bit about the importance of intelligence when it comes to playing offensive line?
Yeah, I’d say it’s crucial to offensive line play, being able to see what the defense is doing, see what they’re showing you, see pre-snap reads, to be able to adjust what your assignments are on the fly, depending on what the defense shows you. So yeah, you have to be very intelligent. You have to be very quick.
Quicker in body, or quicker in mind?
Quick in mind, especially.
With intelligence being such an important part of an offensive lineman and with your mathematical ability in particular, how much do you worry about the head trauma that can stem from playing football?
I’m not really too worried about it. I really enjoy playing football. It’s one of my great loves. You just love hitting people, and I’m a grown man. I deal with the possible risks.
Not all football players are involved in academic pursuits, though. Does the thought of what you’re risking ever creep into your mind?
I just love the game, and honestly, people say yeah, maybe some of the other guys on the field don’t have as much to lose. But I say that all those other mathematicians, they don’t have what I have in terms of physical talents, you know?
That might be the understatement of the century. What football player do you look up to?
He just really gets after guys, has a real mean streak, especially in the running game.
Tell me more about your math research. First, you wrote a paper on celestial mechanics, or how planets and asteroids move. But you didn’t do it with anyone at Penn State. Can you share the backstory?
I actually was doing it through Penn State, in a sense. My professor who taught my analysis course [a class devoted to proving the results of calculus], he actually went back and forth between Maryland and Penn State. The guy I did the paper with was actually his PhD student.
How did this particular research project start?
I was taking a class and my professor really recognized my talents in math. Then he asked me how I’d feel about doing some research. Had I ever done any before?
I told him I hadn’t, so he just started giving me book after book and telling me: “Read it, go through it.” He started emailing me problems every week, problems to work through, things to try to do, and it just spawned from there. Once I got a taste of it, I just kept going and going.
When did you find time to work on the paper while balancing regular coursework and the rigors of a Big Ten football schedule?
That paper in particular, I did most of it in the spring, some in the summer. You know how publications go. Once you do it, it can take like another year, year and a half before it actually gets published. It’s a long process.
Can you explain, for the average football fan, the three-body problem you researched and the results that you got?
You look at this simplified system where there’s just the sun, Jupiter, and this asteroid. To a football fan, this might seem very simple. This is still an extremely, extremely complex problem.
[But] the idea is that this asteroid circles the Sun near Jupiter. The radius of this orbit changes and eventually, the radius of the asteroid becomes smaller than Mars. It actually crosses the orbit of Mars.
And why should the average football fan, or even the average person, care about this? I know questions like that annoy mathematicians, but is there an application?
Yeah, honestly, that paper wasn’t really a big “let me solve this big world problem” thing. It was more of a “let me do some really cool math,” some really cool mathematical physics. I wanted to really use my mind and prove something new.
So for your first paper, you looked at the three-body problem in classical mechanics, which involved real analysis and continuous functions and that kind of thing. For your second paper, you shifted to graphs and linear algebra. Can you explain that paper?
There’s a famous paper from the ’70s by this guy Fiedler. He proved that under certain conditions, you can use linear algebra to break the graph into two parts. Under certain conditions, these two subgraphs are connected.
My aim was to close the book on this. Instead of assuming certain conditions, I assumed the worst conditions possible. Then I proved that the two subgraphs are still connected.
So you improved upon a 40-year-old result?
Impressive. What are the applications for this research?
Most graphs are good and fall under the original Fiedler conditions. But when you start running into graphs that have some symmetry, have some sort of beauty about them, you might run into problems. Then you apply my results.
How did this graph paper come about?
I just had an interest in it. I read Fiedler’s paper for another paper that I’m working on right now. I’m currently revising it.
So there’s a third paper?
Yeah, I’ve got another paper published right now, too, so the graph paper is my third paper. The paper I’m revising is my fourth paper.
You’re holding out on me, John! I didn’t get those other papers.
Yeah, sorry! But I’m working on my fourth paper, and I had to read Fiedler. Then just completely on the side on my own, I just was hammering it like, I think I can do more, I think I can do more.
The guy I co-authored it with, I was just bothering him beyond all belief, telling him this, that, and the other. I think I have this, I think I have that. He’s like a mentor to me.
OK, so you stayed at home for this one? You didn’t have to go to Maryland?
No, no, I definitely stayed at home. He’s a good, good friend of mine, and yeah, we banged it out. When I finally got it done, I was pleased, cleaned it up, sent it out to honestly what we consider to be the top journal in this area of spectral graph theory. We were very pleased to see it got accepted.
Are you worried that playing in the NFL will keep you from working on your math?
Oh man, listen, that’s just fine. You have no idea how pumped I am at playing in the league. It’s what every kid wants to do. I can go back to math when I’m 30, 35.
You’re an outgoing, personable guy. You’re not at all what people think of when they think of mathematicians. How has being a part of two worlds shaped you?
I’d say football’s been good to me in that it’s forced me to stay social. All my football buddies, hanging out with them, hanging out with guys on the football team, going out with my best buds on the team keeps me social. I’m not in a cubicle for 12 to 14 hours a day.
What will you be doing 10 years from now?
Listen, it’s going to sound crazy. I hope 10 years from now I’m still in the league.
Linemen can have long careers.
Yeah, linemen can have very long careers, especially interior linemen, but when I’m done playing football, when it’s finally done, no team wants me, John’s stopped trying, I’m going to go back to get my PhD in math.
And how about in 30 years?
Honestly, whatever I want. I’m going to be perfectly honest with you. I have zero intentions of ever working a day in my life.
I wake up. I get to work out. I get to play football. I get to do math. I never want to be at a point in my life where I feel like I have a job.
Whether that’s being a professor, or being an analytics guy for a football team, I’m going to be happy with it.