John Urschel: Pro football player-turned mathematician : Short Wave As kids, some of us dream of multiple careers: being an astronaut AND the next president. Or digging up dinosaurs AND selling out concert stadiums. As we get older, there's pressure to pick one path. But what if we didn't have to?

After all, John Urschel didn't. He's a mathematician and professor at MIT. But before that, he played football for the Baltimore Ravens. Today on the show, Monday night football! Host Regina G. Barber talks to Urschel about linear algebra and following his dream of becoming a mathematician while living the dream as a NFL player.

This mathematician had another career: professional football player

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EMILY KWONG, BYLINE: You're listening to SHORT WAVE...

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KWONG: ...From NPR.

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REGINA BARBER, HOST:

When I was in high school, I wanted to be a singer, and I dreamed of also being an astrophysicist. I didn't think they were compatible. I had to pick one - right? - but maybe I didn't.

JOHN URSCHEL: I've loved math ever since I can remember. Like, even when I was little, when I was, like, 4 or 5, I just always loved doing puzzles, always loved doing, like, little math workbooks. And I could literally just, like, hang out in my room for, like, five, six, seven, eight hours on the weekend and just do that and just completely lose track of time.

BARBER: Dr. John Urschel is a mathematician and a professor at MIT. But before that, he was a football player.

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URSCHEL: I got offered a scholarship to play college football at Penn State University, which is, like, a football powerhouse for those people who know American football. And so I was simultaneously falling in love with, you know, math as a - as an actual career, taking all of these college math classes while also trying to be the best football player I could be.

BARBER: He now works on a type of math called linear algebra, solving equations like Y plus X equals three and X minus Y equals negative one where you can solve with the same Y and X would be for both. Go ahead and pause the episode if you want to solve it yourself. Otherwise, a solution is X equals one and Y equals two. So those two equations can represent lines on a grid. And so you can find the solution by moving one space in the X direction and then moving up two spaces in the Y, which gives you the point where these two lines intersect. But this is just two simple equations. Things get more complicated when there's more equations or if an equation isn't simple.

URSCHEL: A big question that we care about is how do we solve, let's say, a thousand equations and a thousand unknowns or a million equations and a million unknowns on a computer? This is a fundamental computation that occurs in countless areas of science, business and engineering every single day.

BARBER: Much like these examples, John's football and math careers intersected at one point when he started graduate school at MIT to pursue a Ph.D. in mathematics, he would also continue to play professional American football in the NFL for the Baltimore Ravens. This fact about his life was surprising to me, but for John, his focus these days is all math.

URSCHEL: People make fun of me for this. If you go to my webpage, the first sentence is I am a mathematician. And multiple fellow mathematicians have actually made this comment to me. They're like, it sounds like you're trying to convince yourself or convince the world.

BARBER: Today on the show, Monday Night Football.

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BARBER: John Urschel tells us what it means to look at equations in multiple dimensions and how he followed his dream to become a mathematician while living the dream as an NFL player. I'm Regina Barber, and you're listening to SHORT WAVE, the science podcast from NPR.

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BARBER: From a relatively early age, John knew he loved math casually in the sense of questioning things and puzzles. But as a potential career, it just wasn't on his radar.

What major did you declare when you entered undergrad?

URSCHEL: This is a little bit of a strange dynamic because I really, really loved math, and I really, really loved this quantitative reasoning. But at the same time, I had no clue what I'm supposed to do with it.

BARBER: Yeah.

URSCHEL: So when I get to college, I started out majoring in aerospace engineering because my mom told me to. My mom said, you know, John, you're really good at math. You're really good at physics. Like, what's the best thing you can be is a rocket scientist.

BARBER: Right.

URSCHEL: So I say, OK, Mom. Sure. So I just started out in aerospace engineering.

BARBER: Such a good son.

URSCHEL: Yeah. You know, I just, you know, I aim to please. And so my very first year, I'm taking all these physics classes, but I'm also taking these engineering classes 'cause I have to. And all of a sudden, the math classes really start kicking in because now I'm taking math classes from math professors. They're really focusing on the question of why? Like, why is this true? Why does this equation happen to be this? And really trying to understand the fundamentals underpinning it in a way that just doesn't really happen in grade school. And then all of a sudden, I started kicking into gear and saying, oh, I really love what these professors are saying in class, and so I'm just going to be a math major.

BARBER: So did you already know you wanted to get a Ph.D. in mathematics and, like, become a professor and research new math?

URSCHEL: I 100% knew I wanted to be a researcher pretty much after my second year in undergrad. I took this class called real analysis, which is, like, you're doing calculus, but let's do it all over again and make sure that we prove every single thing and we make sure everything is really true. And my professor just sort of took me aside, and he just thought I was good at math, which was really nice of him.

BARBER: It was probably true.

URSCHEL: I mean, yes, but he actually reached out to me and he offered to do a research project with me. And so I was convinced, like, this is what I want to do with the rest of my life. Then I finished my undergrad early. I finished it in three years. And so I did a master's in my fourth year. In the fourth and fifth years, because I had already finished my undergrad, I could teach.

BARBER: Oh.

URSCHEL: And I also really, really liked it. And so then I knew for sure I want to be a math professor.

BARBER: And like we said before, there is another career you're known for - football, right? So what was the most challenging thing about playing football but also doing math?

URSCHEL: I think the toughest thing is just time management, trying to balance what is really a full-time job, like, college football at a major institution is really a full-time job, while also trying to be a student and trying to, you know, be the best mathematician I could be. And that usually took the form of me scheduling my weight training, scheduling the football things I had to do as early as possible. Like, I was the person who was trying to take the 6 a.m. slot. Scheduling my classes as early as possible. I want the 8 a.m., 9 a.m. classes so that I could do all the football things I needed to do, do all the math things I needed to do in a day.

BARBER: There's this urban legend that you had to actually keep secret being a grad student from the NFL, or you had to keep being on the NFL secret from MIT because there's this rule, and it's actually a rule in many universities that if you're a grad student, that's your full-time job. So can you tell me more about this legend?

URSCHEL: So the NFL knew I was getting my Ph.D. I specifically asked, and they said, of course, John, you know, we, you know, strongly support players going back and getting their degree. So it wasn't a secret. But the thing that is true about that is MIT did not allow part-time Ph.D. students.

BARBER: Right.

URSCHEL: And so the part that was a little ambiguous, I think, is that I was actually full-time all the time. So I was a full-time student in the fall while being a full-time professional football player in the NFL.

BARBER: So basically, you were keeping a little bit of a secret.

URSCHEL: It's not a secret if no one asks is the way I see it.

BARBER: OK. So you're getting your Ph.D. from MIT. You're still with the Ravens.

URSCHEL: Yes.

BARBER: But cutting ahead in time, you are now an active math researcher, a professor, you cover a range of topics like matrices and networks, and they're all related to linear algebra. So how would you explain linear algebra to one of your teammates?

URSCHEL: So linear algebra is fundamentally the study of straight lines. So for instance, you know, in school, you study lines like Y equals X plus two. Something like maybe Y equals three minus X. And something that you might have done in school is to try to find the point - X, Y - where those two lines intersect. That's one of the earliest examples of linear algebra that most people encounter in school. And often, what I do, especially when I'm trying to solve equations, is I'm trying to find points where a lot of lines intersect or perhaps where a lot of higher dimensional versions of lines all meet - and trying to find those solutions.

BARBER: Oh, my gosh. I love that answer 'cause it made me think of, like, mystery, you know, yarn, and you have all the yarns, and, like, you're trying to connect all the dots in the mystery. And that's what you're doing.

URSCHEL: Yeah, yeah. That's exactly what it is. I mean, when we tell this story of, you know, we have a million unknowns and a million equations, really, what we're doing is, we're just hanging out in a million-dimensional space. And instead of lines, we have a million things that are pretty much, like, all but one dimension of the space. Like, it's, like, a higher dimensional version of a line, higher dimensional version of a plane, and we have a million of them. And we just want to see, where do all these things intersect? Like, where is the point in million-dimensional space where all these things meet?

BARBER: And when you say million-dimensional space, you mean like, when you only have, like, two unknowns, that's, like, two dimensions. And then if you have, like, three unknowns, that's three dimensions.

URSCHEL: Exactly.

BARBER: And if you have four unknowns, that's four dimensions. And now you're talking about million dimensions 'cause you have so many points of reference, points of data.

URSCHEL: Exactly. If we had three variables, we would have, like, three-dimensional space, and we would have three planes - like, three flat tables just hanging out in three-dimensional space. And we would be trying to find a single point where those three planes all meet.

BARBER: And within this umbrella of linear algebra, you also study matrices, right? How would you explain those?

URSCHEL: Right. So then matrices are not such a far leap because a matrix, really - you can kind of just say it's like an Excel spreadsheet of numbers with rows and columns. And if you take those equations that you are studying, those numbers in front of those variables, well, I could just plop all of those in an Excel spreadsheet, and that's a matrix. And so I tell them, like, what do I do with matrices is, I take that spreadsheet, and I do a mathematical analysis of it in many different ways.

BARBER: Right.

URSCHEL: You could always try to make things seem mysterious. But I do think that is, in many ways, the essence of what I do.

BARBER: And all of this allows you to study things like networks, right? You take data about people, the people they do or do not interact with - right? - and turn those interactions into formulas. So what does that look like?

URSCHEL: I get all that data in a spreadsheet, and now I do what I claim I do for a living. I analyze properties of that spreadsheet to tell me about the ways in which those people relate to each other. So each person in this network gets a number. What sort of functions can I define so that people who are really connected to each other - who have lots of interactions - have numbers that are likely to be close to one another?

BARBER: OK.

URSCHEL: And the useful thing there is, if you can find a function where you associate each person to a number, and if two people are really closely connected, they're likely to have a similar number, then you can use those numbers to break up your network into pieces and to recognize structure hiding in the network.

BARBER: So that function becomes a predictor.

URSCHEL: It becomes a predictor. Exactly. And it becomes a really good predictor for things that we can actually prove and that we know can be very, very difficult to compute exactly.

BARBER: It almost sounds like magic that you can, like, write some sort of mathematical function where people are variables, and those variables are similar if they actually know each other and if they're, like, strongly linked.

URSCHEL: Yeah, but that's the magic of math.

BARBER: John, thank you so much for talking to me. I had a wonderful time.

URSCHEL: Yeah, I had a lot of fun, too. Thanks for reaching out, and thanks for doing this.

BARBER: This episode was produced by running back Rachel Carlson and edited by head coach Rebecca Ramirez. Linebacker Brit Hanson checked the facts, and wide receiver Becky Brown was the audio engineer. Beth Donovan is our general manager, and Anya Grundmann is our team owner. I'm quarterback Regina Barber. Thanks for listening to SHORT WAVE from NPR.

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BARBER: OK, John, I'm going to ask you a question that's on a lot of minds. Who do you want to go to the Super Bowl?

URSCHEL: I can tell you what I really want. What I really want is, let's let the Ravens or the Bills win.

BARBER: (Cheering, laughter).

So that the people we care about are happy.

URSCHEL: Exactly. That's exactly what I want.

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