IRA FLATOW: This is Science Friday. I’m Ira Flatow. There are some natural words, natural pairings. For example, when you say one, it makes you think of the other, like peanut butter and jelly, physics and black holes, math and football. No, that last one might not be one that pops up in your head. 

But for my next guest, math and football were two of his passions. And he says for him, they both gave him a different view of the world. John Urschel was recruited by the Baltimore Ravens in the fifth round of the NFL draft in 2014. He played as an offensive lineman. 

But he wanted to also follow his other passion– higher-level math. So he quit football. And now, he’s a PhD candidate at MIT. And now, he can add an author to that list. Because his new book is Mind and Matter– A Life in Math and Football. Welcome to Science Friday. 

JOHN URSCHEL: Thanks for having me. 

IRA FLATOW: Yeah, it’s a pleasure to have you. You said in your book that every kid is a mathematician. They find logic and reasoning in questioning their parents. What were your early math interests? 

JOHN URSCHEL: Well, this is even before I can sort of remember having math memories. But my mother says that I was quite interested in shapes, in particular. So the first things I learned with respect to math were the different shapes, squares, rectangles, hexagons, octagon, circles, and trying to recognize those shapes out in the world. 

If we were outside and I saw a square, I would point to it. And I would say square. Or if I saw an octagon, I would point to it. And I would say whatever I was calling an octagon. And so this is probably my earliest planted memory of math, I would say. 

IRA FLATOW: Yeah. And your mom– reading in the book– was really key in motivating you to follow your math interest, was she not? 

JOHN URSCHEL: Yeah, absolutely. First of all, I don’t think– I should say she has a bias towards math in that when she was younger, she loved math, she loved science, she loved physics. But I don’t think she pushed me towards math because she loved math. 

I think she really pushed me towards math, because she saw that I had some talent in it. And really sort of my whole life– she’s always been an enabler, always sort of enabling me to sort of do whatever I’m best at, or whatever I enjoy, or whatever I want to be. And that’s something that I’m really thankful to my mother for. 

IRA FLATOW: When you talk to scientists and mathematicians, they usually have a mentor who tutored them through. Could you consider your mother to be one of those kinds? 

JOHN URSCHEL: Yes, I think– well, I’ve had multiple mentors through multiple parts of my life. But in my early life, yes. I mean, my mother– she would buy me math workbooks when I was a little kid. And I would just love doing them. She would buy me puzzle books. I would love Martin Gardner puzzles, different types of puzzle books. 

Every Friday night we would order pizza. And we would play game night. So we would play games like Monopoly or different sort of quantitative-type games where there is chance involved, but you have to make smart strategic decisions. And she just did a number of things to encourage me in math. And I would say she was definitely my first mentor. 

IRA FLATOW: So you learned how to do critical thinking, smart strategic decisions, which I guess from my life of watching pro football on TV, the people who succeed know how to do that on the ball field, also. 

JOHN URSCHEL: Yes. Although, I would say that it’s a different type of decision-making, I believe, depending on your position. 

IRA FLATOW: 844-724-8255 is our number if you would like to talk to John Urschel, co-author of Mind and Matter– A Life in Math and Football. In the book, there’s a story about your dad who enrolled you in college classes when you were still in eighth grade. 

JOHN URSCHEL: I wouldn’t say college classes. He set me up to audit one college course the summer after eighth grade. Because, well, my mom had enrolled me in a summer program that was sort of geared towards engineering, but it was quite hokey. And I didn’t really enjoy it. And so my father agreed to do this for me. And I loved it so much. It was really a lot of fun. 

IRA FLATOW: So you loved math from the early time on. What made you make the decision, then, to go into it as a career? 

JOHN URSCHEL: Yes. So I’ve always enjoyed quantitative reasoning. I’ve always enjoyed puzzles. I’ve enjoyed critical thinking. I didn’t actually know what a mathematician was until I was in college, I have to say. I didn’t know that the career mathematician existed. 

I didn’t know what mathematicians did. I didn’t know who employed them. I didn’t know what they looked like. And so it wasn’t until I was at Penn State and I was actually even majoring in math at the time, but planning to use it for some other field. 

And I was taking this course. And a math professor really took an interest in me. And he saw I was a strong student. And he told me to come visit his office. And he gave me a book to read. And he introduced me to mathematical research. 

And he actually showed me what a mathematician was. And once I started doing math research and once I started interacting with this person, I knew I wanted to be a mathematician. But prior to meeting this person, I didn’t even really know that this was a career that existed. 

IRA FLATOW: So, what? You gave up your football career at age what? 26? 

JOHN URSCHEL: Yeah, that sounds right. I mean, I’m bad with what age I was when I did certain things. 

IRA FLATOW: Did the threat of concussions and head injury have anything to do with saying, I’m going to go into math and it makes sense now? 

JOHN URSCHEL: Well, it’s something you definitely need to think about when you’re making decisions like that. I mean, there’s a lot that goes into those decisions. But of course, that’s something you should think about. If that’s not something you think about, then you’re not doing a good analysis. Also, there should be other things you consider. 

IRA FLATOW: Yeah, like, do you like the subject? 

JOHN URSCHEL: Yeah. Do you like the subject? How important is football to you? 

IRA FLATOW: Sure. 

JOHN URSCHEL: How important is longevity? Things like this. 

IRA FLATOW: Small details. And you’ll make so much more money as a math professor than you will as a football player too, I’m sure, into your calculus. Oh, I got all of those in there. Let’s go to Diana in Houston, Texas. Hi, there. Welcome to Science Friday. 

DIANA: Hi, thanks for having me. 

IRA FLATOW: Hi, go ahead. 

DIANA: I just wanted to ask, what are your favorite fields in math? I just graduated with my bachelor’s degree in math. And I just wanted to see which fields you particularly enjoy. 

JOHN URSCHEL: Oh, thank you for calling in. So I have to say that when I started doing math, I really, really enjoyed probability theory. And I really loved my first stochastic calculus course. Although I don’t work in that area, I would say that this is an area that really sort of– I was really struck by sort of the beauty of the non-zero quadratic variation. 

And it was just something very enjoyable for me. So that– I quite enjoyed. And now, I have to say, I really do love the field of– the theory of computation and computational complexity. Again, a field I don’t work in. But mainly because when you look at all of the proof techniques, and all of the breakthroughs, and all of the papers, you don’t really see certain general techniques popping up again and again. 

Often, you see these sort of wild, inventive ideas. And so I like the idea of a field where you’re always sort of testing yourself and trying very different and very new techniques. But I work in graph theory, and numerical analysis, and machine learning. 

IRA FLATOW: I remember my 10th grade math teacher, Mr. Cavalero, teaching geometry, which I loved. And he said, you will love math, because it’s elegant, it’s beautiful. He was right. We used to make fun of him, because he would talk like that. And by the end of the semester, we all did love math. 

JOHN URSCHEL: First of all, that’s fantastic to hear. You had a very good geometry teacher. Because I have to say, geometry in high school can go one of two ways. First of all, geometry in high school has so much potential. Because this is the first time you’re introduced to the concept of a proof, the concept of truly knowing something. 

IRA FLATOW: And it is beautiful when you see it played out, isn’t it? 

JOHN URSCHEL: Yes, if it’s presented to you in a very nice way as opposed to like, let’s learn this fact, let’s learn that fact. And now, we need to take our piece of paper. We need to draw a line down the middle. And we need to do this, and do that, and do that. 

If you get too caught up in the trees of 10th grade geometry– I think most people take it in 10th grade. If you get caught up in the trees of that, you miss out on sort of the very beautiful forests of the concept of being able to prove with certainty some very basic geometrical facts. 

IRA FLATOW: Let me go to the phones– Sara in Connecticut who wants to talk more about teachers. Hi, Sara. 

SARA: Hi, I’m also a eighth grade math teacher. And I’m familiar with the guest’s article in The New York Times about teachers needing to be more like coaches with the football analogy. I’m also a coach. So I would love to know, what can I do as a math teacher to really bring that element of fun and coaching to my students? 

JOHN URSCHEL: Yes, that’s a fantastic question. So of course, I always encourage making math class fun. The main thing that I was hoping what people would get out of this Sunday Review piece that she’s referring to is just the power of a little bit of motivation, especially in the classroom. 

So the concept of being a math teacher, and recognizing that you have certain strong students, and really encouraging them to dream big, really sort of telling them about different careers that they could do in mathematics, introducing them to famous mathematicians sort of in our current era and the things that they’ve done. 

Introduce them to resources that they can use to try to reach their goals of, let’s say, being great mathematicians or great physicists, sort of in the same way that high school football coaches really, really push their good players to dream big, and play college football, and try to play professional football. 

And I think it doesn’t take much to sort of plant a seed in a young person to tell them like, listen, you are good at this. You can aspire to be the next left tackle for Michigan. I mean, this is what my football coaches were telling me. Or you can aspire to be the next, let’s say, math professor at Princeton or some such thing. 

IRA FLATOW: So because we spend so little time in all the sciences, including math in grade school and high school of exposing the beauty of the topics– I mean, we roll little trucks down, incline planes in physics. But we don’t talk about, well, who the great physicists were or why they were that way. We don’t bring personalities into any of these. We don’t talk about why these things are important. We just present it. And you don’t get to see the beauty that way or how they see it. 

JOHN URSCHEL: No, it’s certainly true. And I must say– so I don’t know if that’s the case in the way physics is generally taught. I know– so if you read the book, you’ll know that my physics teacher had a profound impact on me when I was in high school. And I thought he was quite an amazing teacher. And he did sort of discuss a little bit about the people who discovered certain things, which I think is important to tie a person to certain things. 

But I would say that I think tying people to a lot of the sort of things we teach or a lot of the sort of results in the sciences actually helps humanize it. And it helps you understand that the way that they’re learning it in their classroom is not the simple, clean way that people just came up with it thousands of years ago. 

IRA FLATOW: I’m Ira Flatow. This is Science Friday from WNYC Studios. You were trying to go down the engineering road, but decided to focus on math. What was the difference for you? 

JOHN URSCHEL: Well, so I have to say that first of all, before I tell my story about how I did not become an engineer, I should say that being an engineer is a great profession. And there’s nothing wrong with this. But for me, all my engineering classes were just really not interesting to me. They were so focused on this concept of “how,” this idea of, here’s a formula. 

Here’s some fact from physics, from mathematics. And now, how are we going to use this to solve some engineering problem? And “how” is a very important problem. I mean, it’s a very important question to answer. But I’m very much a “why” person. I see something and I want to know, why is that true? Why does that work? 

IRA FLATOW: That’s what Richard Feynman talked about his whole life as a physicist. You talk about the state of math, that there is a diversity problem when it comes to math. You don’t see a lot of African Americans in math. What are your thoughts about this? 

JOHN URSCHEL: Yeah. So I don’t know. I wouldn’t go– so I wouldn’t say diversity problem. I don’t know how to put it. But I would say that, first of all, African Americans are extremely, extremely underrepresented in mathematics. American women are also underrepresented as are a number of other minorities. 

And I would say that it’s really– it seems to me to be the result of something that really happens from the moment a young person is born until, let’s say, high school, that these statistics are really starting to be made before a student even steps foot on a college campus. 

And I think it’s really just sort of showing that in this country, it still very, very much matters– the household you’re born into, the socioeconomic circumstances that you’re born into. It really affects the quality of education you get. 

Not only that, but it has a strong effect on the social culture that you’re around and whether or not they value education and/or to what degree. And I find that these sort of factors have led the mathematics community to have a sort of skewed representation. 

IRA FLATOW: Quickly, before we go, are you hopeful it’s getting better– signs that it’s getting better? 

JOHN URSCHEL: That’s a great question. I am sort of a constant optimist in many ways. And I really do hope that, first of all, time will just make this better, that things are better now. Children being born now have it better than children being born 20 years ago. 

And so 20, 30 years from now, we’ll see the benefits of that. But I also believe that there’s not– we need to work towards educational equity in the United States. And I don’t think we’re very close to something that’s acceptable. 

IRA FLATOW: So much more to learn about John and read about him in his new book, Mind and Manner– A Life in Math and Football, co-authored with Louisa Thomas. Thank you, John, for what you’re doing and for taking time to be with us today. 

JOHN URSCHEL: Absolutely. Thanks for having me. 

IRA FLATOW: John Urschel– former offensive lineman for the Baltimore Ravens. And you can read an excerpt of the book on our website at sciencefriday.com/football. Mind and Matter– A Life in Math and Football.