What Can Math Teach Us? | Francis Su

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What Can Math Teach Us? | Francis Su

December 9, 2021

PART OF A SPECIAL 6-WEEK SERIES | Math can often lead to frustration, confusion, and irritation — but might it also lead us to virtue? Join us as we talk with Harvey Mudd professor and author of “Mathematics for Human Flourishing,” Dr. Francis Su. In our interviews with Francis and his friend (and fellow math-explorer) Christopher Jackson, learn how doing math makes us more human and allows us to grow in the virtues of discernment, persistence, and hope. Like what you heard? Rate and review us on Apple Podcasts to help more people discover our episodes. And, get updates on more ideas that shape our lives by signing up for our email newsletter at veritas.org. Thanks for listening!

Transcript

"I've done problems where you know I sat in two hours. My parents took it out and felt great. You know so it's all my patients' persistence.

Just doing what math is teaching us, taught me how to struggle, and the way that's productive, and what to look for to end up with struggle." That's Christopher Jackson. He's a math explorer, someone who loves math and who enjoys doing math problems in his free time. Unlike most of our guests, though, he's not a professor.

My name is Christopher Jackson. I've been learning about mathematics for the last 11 years in prison. I've been a prison 19 years old.

I've been a prison 15 years now." Christopher is incarcerated at a low-security federal prison in Florida. He committed a series of crimes as a teenager and is currently serving a 32-year sentence. He was introduced to us through a common friend, Francis Su, a math professor at Harvey Mudd College.

In 2013, Christopher wrote a letter to Francis asking if he could earn a math degree from Harvey Mudd by correspondence. The answer was no, but that didn't in their conversation. Over the years, they've been exchanging letters, and their friendship has changed how Francis views math.

Chris has really changed the way that I think about the purposes of mathematics for somebody who's in a very different set of circumstances than I am. He was writing me for help with his math education. Why is he learning calculus? He might not ever use, right, professionally, right? That's a question.

He challenged me to think deeply about that as well. What is it about math that is so compelling to Christopher? The surprising answer that Francis gives is that doing math is tightly bound to being human. And being human is important for all of us to experience, especially perhaps those of us in dehumanizing situations.

This is Beyond the Forum, a podcast from the Veritas Forum and PRX that explores the ideas that shape our lives. This season we're talking about the intersection of science and God. I'm your host, Bethany Jenkins, and I run the media and content work at the Veritas Forum, a Christian nonprofit that hosts conversations that matter across different worldviews.

The precise area of math that Francis researches is called geometric combinatorics, which is essentially a mix of counting and geometry, and it has real-life applications. If I am at a cocktail party, I might say that I study problems involving how people interact, so that's called game theory. And often the problems are motivated from questions of fairness.

So, for instance, how do you divide an object fairly among several people? That's a question that economists care about, but mathematicians have gotten involved. Another set of problems I work on is the study of voting and the theory of voting. And what's interesting there is that a lot of the preferences that people have are geometric or topological shapes.

We often think of your political preferences being a raid along the line. A line is a geometric shape. You see you have conservatives on the right and liberals on the left, but you could also study political spectra that are other shapes.

And I often do in my work. Francis became curious about math as a kid when a friend of his parents came over to the house one night for dinner and asked Francis if he could add up all the numbers from one to a hundred without a calculator. Francis had no idea how to answer this puzzle.

I remember this friend of my parents saying, "Well, here's how you can do it pretty simply. If you want to add up all the numbers from one to a hundred, you can pair up one with a hundred, two with ninety-nine, three with ninety-eight, and you get fifty pairs of things that add up to one-on-one. So fifty times a hundred and one is five thousand fifty.

So you can do that in your head. And I remember thinking, "Oh, that's really beautiful." Like, that's amazing. It seemed like a hard problem, but this pairing process where you pair things up was very easy.

And so I remember being captivated by the beauty in that, even as a little kid. And so I got interested through questions like that. As a kid, Francis was already curious about math and his imagination was growing about what kinds of problems math could solve and how it could solve them.

By the time he was studying math in college, though, Francis started to think like a mathematician. What it means to do math is to prove things or is to establish the truth of things. Up until that point, usually what people think of as math is just computational.

And now I like to say that anything a calculator can do isn't really math. The math is really the understanding of why things work the way they work, not calculating a tip. And this idea that math isn't just about adding things up, but about understanding how things work is what makes math about being human.

Francis expanded on this idea at the Veritas Forum event at Cornell last year. People often think of math as just a bunch of computations or skills that you learn, algorithms that you learn to do certain things. And I want to say that math is a lot bigger than that.

I want people to think of math as actually building in us virtues, things like curiosity and persistence and imagination. And these are all things that stick with us no matter what profession we go into. In his book, Mathematics for Human Flourishing, Francis talks about 13 virtues that you can cultivate if you do math.

Today in our conversation we talk about three, discernment, persistence and hope. And we talk about these three because this season is about science and God, and discernment, persistence and hope are three virtues in the Christian life too. First, discernment.

Francis says that learning math can help you make better decisions because you can be someone who isn't easily manipulated. I think it's important for people to see what's at stake when you don't learn math well. And one of the biggest issues, and we're seeing it today, is being able to evaluate information and make decisions based on that information.

Being able to look at evidence and decide whether it's actually reasonable. Christopher talked about math's value in teaching logic and reason too. I started reading like propositional logic, things like personal order logic, and I started reading the law, and I started seeing it with certain clauses, certain symptoms, and certain situations.

And it reminded me of a propositional logic problem. In our conversation, Francis offered some everyday examples. First, he talked about how to evaluate information about the effectiveness of the COVID vaccine.

Take a look at the rate of COVID cases in states compared to the rate of vaccination in those states. You see a strong correlation between high vaccination rates and low COVID cases currently. Now someone might look at that and say that's not evidence of anything.

It could have happened by accident. Well, actually, if you have some mathematical training, you would be able to evaluate how likely it was that that could have happened just by random chance. Another example is social media and how algorithms can be used to sort, track, and even divide us.

People are using math to do things behind the scenes under the hood, so to speak, in ways that you might not even realize if you're not mathematically trained. Like Facebook. I'm being manipulated in some way.

It's better to be aware of that so that you maybe don't get as outraged as you might have because you know that everything you've seen in your Facebook feed, has been designed to get a reaction out of you. And learning mathematics helps you not only to be discerning about what math is doing in your life, but also what math can't do. Math is, you know, often used to quantify things, and that can be good, but it can also be not so good, right? Like, yes, it's good if we can quantify how much that sofa is worth to you, right? But it's maybe not so good if I ask you to tell me how much that child is worth to you.

If we're negotiating some kind of divorce, you can't place a price on a child, right? And so I think we have to be a sanguine about the limitations of mathematics when we think about how we use it. And there maybe gets into questions of the earlier type that we were talking about where you want to be sure that you're using math well, they're not using it to harm people. Another reason to learn math, Francis says, is to cultivate the virtue of persistence.

Christopher talked about the joy he finds in struggling with hard problems. You can't sit down for two hours and work on one problem unless you do love it. You know, so you sit down the way you sit down for that long, you know, and work on a problem and try to figure out what's wrong with this.

And find out if something small, like a negative sign or something like that. And not be frustrated, but actually happy that you found it's just a negative sign. So you have a love in order to sit down that long getting.

And Francis also spoke about sitting with a problem for a long time and cultivating a kind of persistence. I've wrestled with hard problems. And sometimes for years, work done problems that I haven't found an answer and then suddenly stumble upon an answer.

I'm more willing to be persistent at the next hard problem. And so that is part of the engine of persistence, of having that experience of wrestling with something and pushing through the other side. And this virtue of persistence isn't just on the page doing math problems.

It's also in his life. At the Veritas Forum event, Francis shared about his struggles when he was a grad student at Harvard. When I got to graduate school, I met people who were supremely talented in math, much more talented than I was.

And that was the first place that I really struggled with my identity as a mathematician. It made me question if I was doing math for the right reasons because I was no longer the best at what I thought I was good at. And much of my identity had come from thinking that I was the best and then coming face to face with the fact that I'm not.

And he came pretty close to leaving. My research project wasn't going well and I felt like a failure. In fact, a professor basically said to me I didn't have what it takes to be a successful mathematician.

And my whole sense of myself was shot by that remark and that's when I started thinking about doing something else, seriously thinking about quitting. But it was then that Francis ran into another professor in the math department. A professor who Francis knew and enjoyed very much.

I bumped into him and I said, Percy, I think I'm going to quit. And that's when he said, you know, I'd rather see you work with me than quit. And so for me, that was like, I never thought about working with him because the area wasn't something that I felt I was particularly interested in or necessarily good at.

But I said, okay, well, I guess I will give this a try for six months. I gave myself a time limit. And if I didn't make progress at the end of six months, I would in fact quit.

But I was fortunate things worked out and I made progress after six months and so I just stuck with it. And so I ended up publishing a thesis in an area that I never thought I would be doing research in. And Francis's persistence in problem solving has brought him to a rewarding career in math today.

Hi all, this is Carly Regal, the assistant producer of Beyond the Forum. If you're loving the podcast so far, we want to invite you to continue engaging in these important conversations by signing up for our newsletter. Each month, you'll receive thoughtful content about the ideas that shape our lives, updates from our student and faculty partners, and other Veritas news and events.

You can sign up today by visiting veritas.org. Thanks for tuning in and enjoy the rest of the show. Finally, the virtue of hope. One of the keys to persistence is a belief that there is something good on the other side.

That the struggle will be worth it. When Francis was retiring as the president of the Mathematical Association of America in 2017, he talked about hope and his retiring address. And you can cultivate that hope over time.

Having hope is critical to having a good experience in math. But how do you build hope? You build hope when you have certain small victories in thinking and understanding, and being able to wrestle with a small hard problem and see it work. Of course, depending on your circumstances, what you hope for changes.

When you're doing math, you hope for an answer to the problem you're trying to solve. But what about when you're in prison? Can math offer any hope there? In a letter to Francis in September 2018, Christopher said math gave him a reason to hope for a successful appeal in his sentencing. He wrote, "My study of formal logic and mathematics is what gave me the trust in my reason to seek, recognize, and build a legal argument for my appeal.

And confidence and truth is often an impetus to act. His appeal is still in process." The idea that math can give you the hope that there is an answer on the other side of most problems, even hard ones, isn't something that all of us come out of the womb knowing. If you have grown up in a house with less privilege, maybe poor, maybe in circumstances that are really difficult.

And most of your life, you have encountered hard problems that had no solution. It can be really wonderful to learn that actually hard problems do have solutions. Christopher has told Francis that math has given him hope by freeing his mind, even if he is not free in his body.

Part of it is giving him a goals to focus on and a way to free his mind, even if his body can't be free. And I see that over a progression of years now. He's sort of studying advanced textbooks and he's engaging with ideas.

That's one of the things I think he would say is he now lives in a world of ideas. And that's one of the wonderful, most beautiful things about mathematics that fascinates him, after they face him. And for Francis, this hope on the other side isn't just a solution to a math problem, but also a humility and a trust in God, and his plan for both his life and what is to come.

Math petitions have a whole rich context around what infinite means. It gives me a greater appreciation when somebody who isn't as trained in mathematics as I says God is infinite. Like I have a richer understanding of what that means.

Like I know that that means it's really kind of a complex idea. There's also the idea of having a certain amount of humility, intellectual humility, about what I know and what I don't know. And the more math that you learn, the more you realize there's a lot you don't know.

And that's very similar I think to the way that it helps me maybe appreciate my faith with a little more humility and not make assumptions about what I know and what I don't know. Not be dogmatic, which I strive to exhibit a posture of humility about things. When people ask me a religious question or something like that, I have to first admit that there's a lot I don't know, but here's a partial view of what I see.

I'm sure there are other academic disciplines that can instill the virtues of discernment, persistence and hope. So in this way, I don't think math is unique. But I do think that this conversation challenges any assumption that math is cold, overly logical and impersonal.

It's actually something that can grow virtues in us that all of us desire. So now let's say you bought this argument that math is something worth exploring. Where do you start? If you're a student, do you change your major? If you're out of school, do you need to go back and take a math class again? Francis says that you probably don't have to look too far to realize that you might already enjoy math and not even know it.

If you enjoy working puzzles of any kind, then you are already exercising mathematical affection. Sudoku, playing, you know, Settlers of Catan, playing games of any kind. If you are making choices in the grocery store about what to buy and which ones give the better deal, you're already exercising your mathematical mind.

I wouldn't necessarily call that affection. Like this is something you're doing just to make sure that you're spending your money wisely. But it is certainly something that already indicates that you're thinking mathematically.

If you've learned the importance of struggling and persisting at something until you get it, get good at it or you get it right, whatever that looks like, then you're doing something very akin to struggling mathematically and pushing through to the other side. And there are playful math puzzles you can do if you want to focus specifically on math too. Maybe to start with some interesting puzzles or games that you enjoy and have fun with the process of thinking and strategizing.

Those are mathematical virtues. So the number of popular books out there, some authors like Eugenia Chang, Stephen Strogats, Susan Dagestino. I mean, there's a number of different people out there who are writing interesting math books that are very accessible.

Francis says that he grew up with Martin Gardner books. Martin isn't alive anymore, but he has tons of books. After our conversation, I ordered one called Codes, Ciphers and Secret Writing.

And I wish that my 13 year old self had known about this book when I was passing notes with my classmates and didn't want my teacher to read them. Next week, we talk with another mathematician, Dr. John Lennox, who was over at Oxford in England. We talk less about math though and more about logic and how logic and faith in God are not at odds.

You won't want to miss it.

[Music] Hi again, this is Assistant Producer Carly Regal. To close off the first episode of our second season, we at Beyond the Forum want to take time to say thanks to all the folks who helped us get this show together.

Our first thanks goes to our guests, Dr. Francis Sue and Christopher Jackson. Thank you for your great conversations and for taking the time to geek out about math with us. We also want to thank our production team at PRX.

That's Jocelyn Gonzalez, Genevieve Sponseler, Morgan Flannery and Jason Saldana. And of course, we want to thank the students who host and plan these forum conversations, as well as the John Templeton Foundation and all of our donors for their generous support of our conversations. Alright, that's all for this episode.

Thanks for listening to Beyond the Forum.

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