Chapters
Shownotes Transcript
You're listening to How to Be a Better Human. I'm your host, Chris Duffy. On today's episode, we're going to be talking about math. And before you skip this episode because you're saying to yourself, I'm not a math person, listen, that is exactly what I would have said too. I was an English major. Math has always seemed like something that other people do, but surely, surely not me.
Until I read a book by today's guest, Francis Hsu. And that is when I realized that there's a lot more to this subject than I had ever realized. It's kind of like how sometimes when I tell people I'm a comedian, they go, oh, I could never do that. I am not funny. I could never tell a joke. Everyone has some sort of sense of humor, right? And Francis convinced me that we all have some inherent mathematical sense, too.
So how do we break the stereotypes around who math is for? And how do we stop seeing math as a test of whether we're good at adding things up, but instead as an amazing way to understand and enhance our humanity?
Well, here is what today's guest, renowned mathematician and author Francis Hsu, has to say about that. The usual way people think about math is something you do to compute a tip at a restaurant, right? It's mechanical. It's often something that just we do because we don't have a calculator handy. And I think that's a very impoverished view of what it means to do math. I mean, I like to say anything a calculator can do isn't math.
Because math is actually more about thinking. It's more about the virtues that are built by engaging in understanding. Math is more about aspects of character that you build, like persistence and problem solving, that I think will carry with you no matter what profession you go into or whatever you do in life.
That's Francis Hsu, author of Mathematics for Human Flourishing. And he's here to talk to us about how math can help us build the virtues that will make us all better humans. Stay with us. We'll return after this quick break.
How to be a better human is brought to you by Progressive, where customers who save by switching their home and car save nearly $800 on average. Quote at Progressive.com. Progressive Casualty Insurance Company and Affiliates. National average 12-month savings of $793 by new customers surveyed who saved with Progressive between June 2021 and May 2022. Potential savings will vary.
These days, we're surrounded by photo editing programs. Have you ever wondered what something or someone actually looks like under all the manipulation? I'm Elise Hugh, and you might know me as the host of TED Talks Daily. This October, I am giving a TED Talk in Atlanta about finding true beauty in a sea of artificial images.
I'm so excited to share the stage with all the amazing speakers of the TED Next conference, and I hope you'll come and experience it with me. Visit go.ted.com slash TED Next to get your pass today. Okay, we are back. Thanks for sticking with us. Hi, I'm Francis Su, and I am a mathematics professor at Harvey Mudd College and a former president of the Mathematical Association of America.
How did you first discover that you liked math? Because I know from reading your book that at certain points you were actually kind of actively discouraged from pursuing math by teachers who were, I'll say, ungenerously not good teachers. Yeah, I had parents who were very, I think, good at exposing me to interesting ideas and questions and nurtured my interest by giving me puzzles and books to read, things like that.
I come back to an experience I had when one of my parents' friend came over and asked me to add the numbers from one to 100 and asked me if I could figure that out on the spot. And I'm like,
No, you know, of course not. I'm a little kid. I can't, you know, I can't add those things up that quickly. And one of the things that I think blew my mind was when this friend said, actually, let me show you a way of thinking about this. And he said, well, if you think about the numbers as arrayed along a line and you pair up the numbers from the outside in, 101 add up to 101, 99 and 2 add up to 101, and
98 and three add up to the same thing, you realize that they're basically 50 pairs of things that add up to 101. And 50 times 101 is 5050. Like, you could almost do that in your head, right?
And that was, to me, mind-blowing. It was like, whoa, actually, because of a pattern, this thing that seemed very hard suddenly opens up and becomes something very easy, simple. And more than that, there's a beautiful idea behind it. And I think experiences like that one helped me to see that math is actually something about thinking, and it's something where you get this aha moment often. Part of what I try to do in the book is frame what the feeling of doing math is.
well, feels like. It feels like a lot of things that we do in other areas of our lives. And that's part of the excitement that draws people to do math. Tell me more about the beautiful idea behind the ability to make those pairs and come up with the answer there. Yeah. Well, one beautiful idea is that there's symmetry, right? It's kind of like the same symmetry you experience in the human body where you have a left hand and a right hand.
and everything over here on the left pairs up with everything on the right. Now, it's not perfect symmetry, right? Like my face isn't perfectly symmetrical. That's also part of what makes us beautiful and unique. And the same thing happens in math, right? Like you might witness a pattern that has some symmetry. It's not a perfect symmetry, but that symmetry gives you a guide for how to think about whatever it is you're thinking about.
Maybe it helps you do something in a better way or a more efficient way. Maybe it helps you also pay attention to the unique aspects of what breaks the symmetry in the thing that you're looking at. You gave a really beautiful speech about the lesson of grace in teaching. And you also turned that into a blog post. You talked about the kindness of a graduate advisor and how that shaped your career. Can you tell us that story or maybe just a version of that story? Growing up, being labeled as good at math,
sort of made me feel like part of my identity was being good at math. And so getting to grad school, which was, you know, I went to the PhD program at Harvard, you meet some of the most talented people in the world. And that was maybe the first time that I experienced this feeling of not being up to snuff, not being good enough, maybe not having the same background as many of my peers. Hitting a wall was, I think, hard, but also having...
Having other people now mark me as somehow not good enough or not capable, I think that was a new experience for me as well. That was maybe the first time that I experienced that kind of situation where people sort of write you off in some sense. And we do that a lot in math, in math education. And part of the argument I want to make is, no, actually, everybody's a math person because everybody's a human person.
And if we pay attention to what makes us human, it helps us to think a little bit more broadly about what it means to do mathematics and to do it well. Getting back to the story of graduate school, when I thought about quitting and, you know, I wrestled with this question of why am I actually doing math, right? Is it for the prestige or...
Is it because I actually love it? You know, those two things had become conflated. And I wrestled very seriously with the idea of quitting graduate school. And I almost did when another professor actually said to me, you're quitting? Why don't you try working with me? And so that was, for me, a moment of
where I experienced grace. Grace is like a word that I think is often used to describe a situation where people give you something that you didn't deserve, right? But I like to say in this situation, like I didn't earn his favor in the sense that people are already writing me off as maybe not able to finish my PhD program. But here was somebody who said, I don't care. I'm gonna take you, right? You work with me.
You know, I've heard you talk and write about before about how we can get so focused in
education on results and grades, test scores that we forget that there's a human component too to this relationship and that building the relationship between a teacher and a student to have there be real empathy and care and like you said, grace, that that is as important if not more important than the actual results of the exams or the grades at the end of the day. That's right. We're such an achievement-oriented culture, achievement-oriented society. But when we think about it,
The most meaningful experiences that we have actually happen in moments between people where they could care less about your resume, they could care less about what you've done. The people who have the most impact on our lives and who touch us are often grace givers. And that's part of my own journey in thinking about mathematics. What is my purpose of getting mathematics? Is it so that I could show people that I'm actually more elite than other people?
That's an achievement-oriented mindset. Or should I think about math as actually something that serves the greater good? And I can contribute to it by being part of it as a mathematician, by helping others see the wonder and beauty of mathematics, helping open up people to human experiences that they deserve to have. I think all of us deserve to see
The beauty of mathematics, whatever ways, makes sense to us. Let's get deeper into that then. So we've talked a couple of times about how math overlaps with what it means to be human or how math can help us to be more human. How so? How do you convince someone of that? One of the ways I do that is by first thinking about what are the human desires that we have. So for instance, Chris, if I ask you, what are some of the hobbies that you engage in?
Well, I love comedy. I love to make people laugh. So let me dig deeper. What need are you meeting, either in yourself or other people, by making people laugh?
It's probably a combination of connection and joy, right? When I tell a joke and someone laughs, I know that we see that thing in the same way. And then there's just the pure joy of laughter and release. Yeah. And some of that joy comes from a surprise, right? So one aspect, I love jokes because, you know, there's a punchline and it's often some unexpected twist on a way that you were thinking about
whatever it is you're talking about. And then suddenly, boom, there's a funny pun and you're like, oh, actually that was, I wasn't expecting that.
There's a certain type of joke where they're like, oh, I wasn't expecting that. That's like a medium. I'd say that's a six on a joke scale, right? Yes. Okay. Yeah, that's right. Maybe that's not the top of the list. I'll tell you my favorite joke. It is my favorite joke. And it's actually a clean joke, so I can tell it on the air. But it's, where does a king keep his armies? I think I know, but I'm going to let you say it anyway. It is sleevies. Yeah, there you go. That was a six, right?
probably. Yeah, that's a six for me. I love the passion, so I'll give you a six for the passion of delivery. Yeah. Now, okay, so that, believe it or not, is actually a similar experience to the feeling of grasping a beautiful idea in mathematics. It's like the unexpected twist where you're like, oh, I can add up
a string of numbers by pairing them up. Not only do I appreciate the joke, but I can go now tell a very similar joke and get a lot of mileage out of it. So this is what a great math education ought to build in us. It should build in us a hunger for a punchline, right? A hunger for a story well told.
And it's often, sadly, missing from many people's mathematical experiences. Often the experience that people have in math is on like timed math tests or on worksheets and homework where you're supposed to get things done in a certain amount of time. And something I was surprised to hear in the book and in learning more about mathematics is that kind of the things that we evaluate people on and when we're teaching math, especially in elementary school and high school, those are really not the skills that mathematicians have.
praise at all, right? That mathematicians don't care how long it takes you to do something. In fact, most great math theorems have been proven over years or decades or sometimes centuries. And it takes instead creativity and collaboration and kind of a sense of humor in the sense of like being able to see things in a new way and think about them differently than everyone else sees them. Those are the things that mathematicians value. And yet we often think about it as like rote knowledge or memorization.
They're also the things that employers value, right? So if you think a little bit about what happens when you get hired, if you have some kind of mathematical training, people don't hire you because you can factor a quadratic, right? They hire you because...
you have persistence in problem solving. You're willing to sit with a hard problem for a long time and see a project through. They hire you because you have good skills to collaborate over something technical, right? - Yeah. - So why isn't that part of our math experiences or the things we value in math education? It should be, we should do more of helping students interact well over mathematical experiences, being able to share ideas without shooting each other down.
or making each other feel like misfits. So let's imagine now, you know, someone's listening to this and they're convinced they're sold, right? Like, OK, great. I get it. I see math can help me to be a human and help me to build the skills of perseverance and creativity, all those things. What would you recommend that they do? How can how can a person who's not a professional mathematician or not a current student, how can they start to put these things into practice in their daily lives?
And I think one of the things we often forget is that math is sort of mathematical thinking, understanding. This is part of many experiences that we have, and it's not just over numbers. So I guess the first thing I would say is for each person to cultivate their mathematical affections, to start opening their eyes to math.
to seeing patterns everywhere and being enchanted by those patterns, right? Actually taking a breath and stopping and listening to the patterns that you are enjoying when you're listening to a piece of music. But, you know, if you're a parent or a coach of some kind, I think another thing to think about is the fact that you don't have to be an expert to be a good mathematical teacher or a good mathematical coach, right, for your kid.
Like many people think, ah, you know, I can't teach this stuff because I don't know the answers. Well, you know what? Actually, it's more about asking the right questions. It's more about being able to guide your kid to learn to think and to reason, right? We don't have to know the answers to all the questions our kids are going to get on our homework. We just have to be willing to sit and help them reason through it, help them think more effectively. So you have a young child.
I do. So how are you doing this personally? How are you instilling a passion for math? Yeah, well, he's only 20 months now. And so at this age, you know, it's not about counting or numbers or anything like that. It's just about having him appreciate shapes, right? Like Nathaniel is his name. He's making connections, actually, and seeing patterns where I'm not seeing them, right?
His first word was helicopter. Although he doesn't say helicopter, he says, da-da-da. He's pointing up and he's mimicking the sound. Very Los Angeles first word. That's a clear child who was born in Los Angeles. Non-stop. Da-da-da. Well, the other day we were in a store and he saw a ceiling fan. And he pointed to it and he goes, da-da-da. Da-da-da.
And I'm like, oh, okay, that's not a helicopter. He made the connection that a ceiling fan and helicopter were alike, not because of the sound, but because of the way they looked, right? The spinning blades. And I'm like, oh, that's a pattern, right? Like that's abstraction, right? Kids are learning to abstract when they're making associations.
So what about for someone who has a kid that's slightly older? So say someone who's actually, you know, starting to be in school, how would you recommend that they instill a passion for mathematics? What can they do? What's a practical thing? Just encourage math talk.
In everything that you're doing, if you're having your kid go to the store and you're having them think through consequences of what things that they were going to buy today and how many we're going to get, I would say beyond counting, I think patterns are more important. So for instance, if you're asking your kid to take five things and add two more things to it,
Often a kid will start from there and they'll have to count one, two, three, four, fives, and then six, seven, right? They'll have to start over. But pretty early, you can have them see that five plus two is actually the same as two by five just by swapping the positions of your two hands, right? Yeah.
And that's a very early picture of what we often call the commutative property of addition. The fact that the order of addition doesn't matter, right? That's an idea. That's probably a more important thing for kids to begin to see than just memorizing how to add numbers. Okay, we are going to take a quick break, but when we come back, we will go beyond the numbers to see how understanding math can actually open us up to new ways of looking at truth, identity, and even justice. Stick with us.
Warmer, sunnier days are calling. Fuel up for them with Factor's no prep, no mess meals. You can meet your wellness goals thanks to this menu of chef-crafted meals with options like Calorie Smart, Protein Plus, Veggie Vegan, or Keto. And Factor has fresh, never frozen meals, which are dietician approved and ready to eat in just two minutes.
That sounds like a dream come true. I cannot wait. So no matter how busy you are, you will always have time to enjoy nutritious, great tasting meals. Make today the day that you kickstart a new healthy routine. What are you waiting for? Head to factormeals.com slash betterhuman50 and use code betterhuman50 to get 50% off your first box plus 20% off your next month. That's code betterhuman50 at 50%.
factormeals.com slash betterhuman50 to get 50% off your first box, plus 20% off your next month while your subscription is active.
Support for this show comes from Brooks. My friends at Brooks sent me amazing new Go 16s that I have been running with. The Go 16 has made me feel lighter and more energetic when I run out the door in the morning. They have soft cushioning through a technology called the Nitrogen Infused DNA Loft V3. It offers just the right softness.
There's also engineered air mesh on the upper side of the shoe that provides the right amount of stretch and structure. It'll turn everyday miles into everyday endorphins. That sounds good, right? Let's run there. Visit brook'srunning.com to learn more.
We're back with author and professor Francis Hsu. So recently there have been news reports of math textbooks being banned from schools in certain places. You know, I think some people like me hear that and it almost seems laughable because like it's math, it's not political. But I think that after reading your book, I came away with the idea, a very compelling idea that in fact, like math is political, that math is about human interactions and it's not just this cold,
sterile world of logic. And that, for example, the types of questions we ask in a math textbook, they have real world implications. And you've been very vocal about thinking that we need to change those and make those more inclusive. How has your personal identity changed
played into your experience with math? Certainly one identity that I have is as an Asian, Asian American. And one of the unearned benefits of being Asian is that people often give you the benefit of the doubt. They believe you can do math because maybe they believe you have some magic ability or gene that you were born with. And I don't subscribe to that idea at all, but certainly benefited from it.
Another identity that I have is as an Asian embedded in an often very white context in mathematics departments. And there's some evidence that shows that people think of Asians not as, you know, having leadership potential. We often call that in the Asian community, the bamboo ceiling, that you aren't viewed as a leader if you're Asian.
And you talk about how in the book you were the president of the Mathematical Association of America and you were the first person
mathematician of color to be the president of that association. That's right. That's right. Yeah. And in fact, a blogger, Angry Asian Man, I think after that happened, tweeted out like, finally, an Asian who's good at math, right? Like he was making the very sarcastic remark that this has sort of been a long time coming, even for a group of people that you think has relative advantages in mathematics. Both take away the credit for the actual humanity of what you've done and your accomplishments and personality.
So this actually gets back to, I think, a point that is very important to make, which is that mathematics, what you think mathematics for is going to strongly determine how you relate to it, how other people relate to it. So if you think mathematics is about achievement,
then you're going to think about math as being something that is competitive. You're going to think about a good job going to one person means a good job is not going to another, right? That's going to lead to a certain kind of attitude around who should have access to mathematics and who shouldn't. Now, if you think that mathematics is actually more of a public good, something that everybody can appreciate, something that everybody can grow in, and good for one doesn't necessarily mean bad for another,
then I think we're going to have a completely different view of mathematics, that it's something that should be more like a human right to be able to experience beauty and joy and wonder. We should all be able to do that, just like we should all be able to experience good music or fine art or the thrill of a football game. You have a chapter in your book about justice.
How is math connected to the pursuit of justice? Because obviously there's a piece of justice that we were just talking about, which is around who is encouraged to do math and who's allowed to do math. But then math itself can also play a role in a broader kind of social justice and also just the concept of justice. So can you talk about that a little bit? You know, when we talk about how math and justice relate, I mean, one way, as you mentioned, is some of the human aspects around who has access to math and who doesn't.
But another is using math to actually model situations that are unjust and maybe prescribe ways of changing the system. So for instance, a good example is some of the conversations around gerrymandering. How do you build a partition, a state into districts that are somehow allow for fair representation? Well, what does that mean? You have to define what you mean by fair.
And so math actually gives us a way of quantifying what it means for a set of districts to be overtly partisan or not. And mathematicians, as well as other people, political scientists, need to be better about communicating the value of what math can offer in those situations and how it can help us maybe get beyond some of the typical opinions that people throw around related to gerrymandering.
Throughout your book, one of the threads is your correspondence with your friend, Christopher Jackson, who's a fellow mathematician who has started studying math while he's been incarcerated.
And he started writing to you for advice on math. And then you two developed this correspondence and his letters are part of your book. So I wonder how does math and your relationship with Christopher, how does that change how you think about justice? A lot of times people hear about my relationship with Christopher and they think, oh, OK, you know, this is a story about how much math I taught Chris. But in many ways, it's a story about how much Chris has caused me to think differently about my own
views on mathematics. You know, after seeing how Chris, who basically didn't finish high school, landed in prison at a, you know, as a teenager, now is incarcerated for some small crimes for 32 years and discovered a love for math in prison. Here is somebody who is likely not going to be able to use math in a career, studying calculus.
What does he see in this stuff? And of course I know what he sees in it. I see beauty. He sees possibility of having a freeing mathematical experience, right? Being able to explore things with his mind, even though his body is incarcerated. Somebody who is entered with very different experiences than I do. The same unifying feeling about mathematics.
It shouldn't be a surprise, but certainly it caused me to think more deeply. How does math contribute to human flourishing? Here's a picture of somebody who's flourishing, even though he's in a very difficult position. He's now reading some advanced math textbooks and even beyond what you read in the book. He's tutoring other inmates to get their GEDs.
This is a picture of somebody who I think I could rightfully say was unjustly given a very long sentence. And he's still flourishing, even though his situation isn't great. He talks about making a legal argument for appealing his sentence, right? And how mathematics gave him a way of
being able to think and reason and to make an argument for his appeal. These are some of the intangible benefits, I like to call them virtues, that are built by having a great experience in mathematics. You also talk in the book about how in 1984, in the book with the fascist authoritarian government, right, one of the ultimate things that they say is that they're going to tell you that two plus two does not equal four, it equals five.
And that that is the kind of ultimate of the controlling of the mind is that they were able to force you to believe something that is verifiably false. Obviously, when I first read 1984, that felt very distant and hypothetical. And now I think for many of us, we live in a world where it feels like it's there. There is a disturbing closeness to the idea of being told that things are not real, which are real. And I think that it's compelling to think about how math is.
is a force against disinformation and authoritarianism because it doesn't allow for that kind of distortion to be true, that you can't make two plus two five.
Ten years ago, if we had had a conversation around truth, I think it would be very easy for people to say, to dismiss the notion of a universal truth, right? Like the idea that there is truth. Often in academic circles, people would talk about the many complexities of truth. And truth is complex. That's part of what makes it hard to talk about, right? Like people have many different perspectives on truth. But that doesn't mean that there isn't some underlying truth that's there, right?
And we're seeing now today a situation where some of the same people who 10 years ago would have denied the existence of objective truth are now saying, wait a minute, like you can't just blatantly lie like that. Like, you know, like they're hearing lots of disinformation, things that are blatantly, clearly not true. And now they find themselves having to defend the idea that there is actually truth. You know, these things are complicated because truth is messy and complicated.
And sometimes people might argue that math sometimes unnecessarily strips away a lot of things that are important in order to get at something essential. But one of the things that I think math does help you see is that you can have some confidence in knowing things. And that confidence carries over to other areas of your life and enables you to say, okay, yes, there are some things we can know.
We need to be able to stand up and defend the truth, even if it's messy and complicated. What are three things—
that a person who's listening right now can do to get more of the benefits of math into their lives? The first thing I would say is that people need to stop talking down about their own mathematical abilities and start talking up ways in which they are thinking creatively. You know, one writer said that literature is equipment for living. And if that's the case, I
would like to say, often like to say, math is equipment for thinking, right? In much the same way that when you read great literature, you understand different ways of living, different ways of being. You're being asked to think about situations that maybe you've never put yourself in. Mathematics often helps you to envision different ways of approaching a problem.
Thinking creatively, strategically, being persistent in how you solve the problem, engaging your ability to quantify, to define, to strategize. You know, these are all mathematical ways of being. And so maybe the first thing I would say is to begin to broaden our conception of what it means to do math as a set of virtues that we are already engaging in.
A second thing that I would suggest is each person find a way to visit a museum, metaphorically speaking, of mathematics. Actually, there is a museum of mathematics in New York City, if you happen to be in New York City. But one of the ways you can do that is to begin to appreciate math by reading popular books.
about mathematics and its value. These don't have to be highly technical books. They could be books that just encourage an appreciation of mathematical ideas. Eugenia Chang is one who has written many books about the value of mathematical thinking, how to bake pie. She compares that to cooking very effectively. Steven Sturgatz is another example of a writer who's done a lot to popularize mathematical thinking. Jordan Ellenberg
And a third way that each person can be a better human through mathematics is, I guess this maybe comes down to the kinds of conversations that people have around math. You can be an agent for changing people's impressions of mathematics. And this will benefit you as well as benefit the people around you because I think the more you start to vocalize that math is a set of
of ways of being, a set of virtues that we're all engaging in every day, I think the more that you'll begin to see math differently as well and see it everywhere in your life. And what is something that has, whether it's a book, a movie, a piece of music, an idea, what's something that has made you a better human?
Well, one thing that's made me a better human is being in relationships and friendships with people who are willing to have hard conversations with me, to challenge me in various ways, while still being a grace giver and showing me that they love me in spite of all my faults. Well, Francis Su, thank you so much for being on the show. It has been an absolute pleasure to talk to you. I really appreciate you making the time. Thank you. It's been fun. Thank you for having me.
That is it for today's episode. I am your host, Chris Duffy, and this has been How to Be a Better Human. Thank you so much to our guest, Francis Hsu. His book is called Mathematics for Human Flourishing. On the TED side, this show is brought to you by Anna Phelan and Sammy Case, who are flourishing mathematically and otherwise.
From Transmitter Audio, Wilson Sayre, Leila Das, Farah DeGrage, and Dan O'Donnell are mathematically seeking truth. And from PRX Productions, How to Be a Better Human is produced by Jocelyn Gonzalez and Sandra Lopez-Monsalve, who are both working on finding beauty through equations of their own. They're working on that right now. Thank you to you for listening. If you enjoyed this episode, please share it with a friend and leave us a review. Have a great week. PR.