Short Wave - Monday Night Football And Pursuing Two Careers With John Urschel

Episode Date: November 27, 2023

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. See pcm.adswizz.com for information about our collection and use of personal data for sponsorship and to manage your podcast sponsorship preferences.NPR Privacy Policy

You're listening to Shortwave from NPR. 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. I've loved math ever since I can remember. Like even when I was little, when I was like four or five,

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. Dr. John Urchel is a mathematician and a professor at MIT. But before that, he was a football player. 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, you know, as an actual career, taking all of these college math classes while also trying to be the best football player I could be. He now works on a type of math called linear algebra, solving equations like y plus X equals 3 and X minus Y equals negative 1, where you can solve what 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 1 and Y equals 2. 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. 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. Much like these examples, John's football and math careers intersected at one point. When he started graduate school at MIT to pursue a PhD 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.

People make fun of me for this. If you go to my web page, 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. Today on the show, Monday Night Football. John Urshel 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 Shortwave, the science podcast from NPR.

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Thank you. 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? 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.

Yeah. So when I get to college, I start 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 as a rocket scientist? Right. So I say, okay, mom, sure. So I just started out in aerospace engineering.

Such a good son. 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 because I have to. And all of a sudden, the math classes really start kicking it. 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. So did you already know you wanted to get a PhD in mathematics and become a professor and research new math?

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. It was probably true. 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. Oh. And I also really, really liked it. And so then I knew for sure I want to be a math professor. 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?

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 I could do all the football things I needed to do, do all the math things I needed to do in a day.

There's this urban legend that you had to actually keep secret being, a grad student from the NFL or you got 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? So the NFL knew I was getting my PhD. I specifically asked. And they said, of course, John, you know we strongly support players going back and getting their degree. So it wasn't a secret. But the thing that is true about that is, Because MIT did not allow part-time PhD students. Right.

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. So basically, you are keeping a little bit of a secret. It's not a secret if no one asks is the way I see it. Okay. Okay, so you're getting your PhD from MIT. You're still with the Ravens. Yes.

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? 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 xy 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. Oh my gosh. I love that answer because 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 and the mystery. And that's what you're doing.

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? 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. And if you have four unknowns, that's four dimensions. And now you're talking about million dimensions because you have so many points of reference, points of data. 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. And within this umbrella of linear algebra, you also study matrices, right? How would you explain those? 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 were 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. Right. You can always try to make things seem mysterious. But I do think that is, in many ways, the essence of what I do. 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? 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. Okay. 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. So that function becomes a predictor. It becomes a predictor, exactly.

becomes a really good predictor for things that we can actually prove and that we know can be very, very difficult to compute exactly. 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. Yeah, but that's the, that's the magic of math. John, thank you so much for talking to me. I had a wonderful time. Yeah, I had a lot of fun, too. Thanks for reaching out, and thanks for doing this. This episode was produced by running back Rachel Carlson and edited by head coach Rebecca Ramirez. Linebacker, Britt Hansen, check the facts, and wide receiver Becky Brown was the audio engineer. Beth Donovan is our

general manager and Anya Grunman is our team owner. I'm quarterback Regina Barber. Thanks for listening to Shortwave. from NPR. Okay, 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? I can tell you what I really want. What I really want is let's let the Ravens or the Bills win. Yeah.

So that the people we care about are happy. Exactly. That's exactly what I want.