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The Human Nature of Mathematics

On Thursday, October 6, the Harvard Human Flourishing Program will bring Dr. Francis Su to Sever Hall to talk about mathematics for human flourishing. Su received his A.M and Ph.D. in mathematics from Harvard University in the early- and mid-90s, and is currently the Benediktsson-Karwa Professor of Mathematics at Harvey Mudd College. He is a former president of the Mathematical Association of America and has received several teaching and writing awards. His research in geometric combinatorics includes numerous papers co-authored with undergraduate students, and his work has been featured in Quanta Magazine, Wired, and the New York Times. His 2020 award-winning book “Mathematics for Human Flourishing” offers an inclusive vision of what math is, who it’s for, and why anyone should learn it.

We sat down with Dr. Su to talk about his book, what writing it meant to him, and what he hopes it conveys to its readers.

What is the mathematics for human flourishing, and why did you think there was a need for a book about it? 

There are two pieces to that: there’s mathematics, and there’s human flourishing. I think of human flourishing as grappling with the question of what it means to live life well. One way to think about it is to try living to one’s fullest potential and to help others do the same. “Mathematics for Human Flourishing” lays out a vision of a different purpose for mathematics than that to which people are accustomed.

When people think of math, they often think of it as something they have to do in order to get ahead as an individual. In a similar vein, educators often talk about teaching mathematics for “college and career readiness.” And while that’s important, I think if you talk to people who do math for a living and enjoy it, you’ll find a far richer answer to the question why people do math. Mathematicians often study math because they find it beautiful. And seeking and finding beauty is one of the experiences of human flourishing.

People who practice math regularly also do so in a community, working closely with other people. We enjoy the back-and-forth, the give-and-take, brainstorming, throwing up ridiculous ideas on the board and seeing what sticks. When I collaborate with someone, I get to know them in a different way and there’s no shame when we make a mistake. That’s a very different experience compared to what often goes on in the math classroom. Many kids come out of grade school with a certain trauma and anxiety around math, because they’ve been given the impression that math is all about calculation and speed. Many mathematicians who do research are not good calculators and that’s okay. We have tools for that. The joy of doing math comes from understanding.

The book’s origins lie in a 2017 speech you gave when you retired from your position as president of the Mathematical Association of America. Were you thinking of a book already, or did the idea for a book come from reactions to that speech?

One of the things I knew when I was elected president was that at the end of my term, I would have to give a speech at the national meetings. I had some time to prepare, and I wanted to give something different from a standard math talk. I wanted to cast a larger vision that would call on the math community to, in some ways, do better. What came together was this idea of trying to reframe the purpose of mathematics. The speech touched on five basic human desires of beauty, truth, play, justice, and love that are part of what it means to do math. And as I was writing it, I did imagine that I could say a lot more.

I built upon this when I eventually wrote the book. For instance, I talk about the desires we all have for community, for freedom, for exploration, for struggle, and how math can meet those needs. So in the back of my mind, I certainly thought that speech could grow into a book, but I wasn’t looking to write a book when I wrote the speech.

Many online descriptions and reviews of your book use the phrase “mathematical affection.” What does that mean?

When I think about affection, I think about joy, about the emotional reaction people might or could have to mathematics if they were taught it well. It’s what I find is often missing from discussions about why we do math. For instance, the public has heard about the Common Core math standards, which are an important way of helping teachers think about what needs to be taught. Now, one of the great things about the Common Core math standards is that they have content standards and practice standards. The content standards are things like specific things you have to know, and the practice standards are aspects of the way we do math, like being able to reason abstractly and quantitatively, construct viable arguments, make sense of problems and persevere in them.

While I really like the fact that there are practice standards, I find that often teachers focus more on content, because that’s what everyone thinks of as math and they are easier to assess. As a result, math just becomes a list of topics to cover. And while the practice standards are just as important, they don’t fully convey the affective nature of mathematics. One of the things that’s missing from the practice standards is some of the emotional connection that people might have to math. You don’t see anything about affection, joy, or wonder in the practice standards, and that’s a big part of what I think a great mathematical education should include. So that’s something that I highlighted in the book as one of the virtues that is part of what it means to learn math well—to have affection for it. But there are many other virtues, as well.

If you think about what it is that a graduate from Harvard University needs to know, most of them won’t ever really need to factor a quadratic. That’s not to say that learning how to do so wasn’t valuable. One of the things that you realize, if your algebra was taught well, is that the fact we can even figure out how to derive the quadratic formula is amazing. It’s a triumph of human reasoning! So, what’s actually important from a math education are the reasoning skills. Those are what the math graduate is going to take with them no matter what profession they go into. The best answer to the question that most kids ask: “Why do I need to know this stuff?” is not because “the stuff” will be used later. It’s because a great math education builds virtues—like being able to think clearly, to have a little humility about what they know and what they don’t know, to take complex ideas and break them into workable pieces, and to have a disposition to beauty and a deep affection for it.

You begin the book with a quote by Simone Weil, “Every being cries out silently to be read differently.” In this case, “read” refers to “judged.” Is this a call to judge mathematics itself differently, or the people who can and do practice it?

It’s a call for people to judge themselves and others differently, and to see themselves as mathematical beings by their very humanity. Part of the argument in the book is that we’re all human, we all have basic human desires, and math meets those desires in certain fundamental ways. Therefore, we are all math people in some sense. To say that some people aren’t gifted or talented in math is framing math as something meant solely for achievement.

You’re going to have some people who are going to pick up music, sports, or math more quickly, but that doesn’t mean that people can’t be active, engaged mathematical thinkers and can’t grow into having a productive relationship with math. In fact, some of the best mathematicians didn’t pick up math quickly. I think of Fields medalists Laurent Schwartz and Maryam Mirzakhani, both of whom called themselves “slow” thinkers. Speed of acquisition is not the same as mathematical talent. So, should we be talking of mathematical achievement as the primary reason for doing math? No. Do I believe that every human person can have a meaningful and joyful experience in mathematics? Yes.

An essential part of the book is your correspondence with Christopher Jackson. You even shared the Euler Book Prize you received for the book with him. How did that relationship come about? How did it influence you and, eventually, the book?

Christopher Jackson is an incarcerated man who discovered a love for math in prison. He landed there as a teenager after getting involved in drugs and a series of armed robberies and he wrote to me in 2013 asking for help in furthering his math education. Before I met Chrisopher, I intellectually supported the idea that math is for everybody. But receiving his letter and beginning what became a long correspondence really stretched and challenged what I said I believed.

It’s hard to imagine a man who’s been convicted of armed robberies being somehow fascinated and captivated by mathematics. But when you talk to and meet with Chris, you realize that here is someone who has grown and is flourishing in some very difficult circumstances because of mathematics. He’s not free in his body but math has opened him up to a certain world of wonder and awe, and when he and I correspond and talk, we see each other differently than we might otherwise.

When I first got the letter I wasn’t sure what to make of it. One of my first questions was if everyone else in my department got one. It turns out Chris heard about my school on a television show he watched regularly, and he had his mother do a little web search of the math department at Harvey Mudd College. He was wondering if it was possible to get a correspondence degree in mathematics, since they don’t have classes in his prison, and his mother just picked me out of the list of faculty. I eventually decided to proceed with caution but also with the intent to treat him with the dignity that everybody deserves.

The book has few actual equations in it and many personal details from your own life. Why was it important to you to weave those in?

When you’re talking about difficult topics—and I do tackle some in the book, such as issues of race and who has access to math and who doesn’t—one of the best ways I’ve discovered to have hard conversations is to be vulnerable and personal, and talk about my own experiences. I made a choice in this book to open up in ways that some people have said were surprising to them. But I think that’s the only way this book could have happened. If I’m going to talk about math being human, I think the book had to feel very human. The last thing I wanted was for it to feel like just another math textbook. When people ask me what the book is about, I tell them it’s not really a math book, but more about what it means to be a human being.

How will you frame your book and what you say about it for your Harvard audience?

We think of Harvard students as already very accomplished and confident in their abilities. That’s probably not an accurate picture of a young adult. We all have insecurities and internal struggles. Part of what I’ll do in the talk and that I do in the book is help open up a safe space for other people to reflect on their own experiences.

When I was a grad student in Harvard, I taught many students who felt out of place in a math class, even though in my opinion, they belonged there. But they spent a lot of time comparing themselves to other people or had discouraging experiences, like I did. I’m sure it will be different from other audiences that I’ve spoken to in the sense that I have a certain personal connection to the school and the department, and I’ll look forward to the conversations that result.

For more information on the event, click here.

Photo courtesy of Mark Skorovodko.