"I sound my barbaric yawp over the roofs of the world." That raw emotion, captured by poet Walt Whitman near the end of "Song of Myself," describes the way mathematician Francis Su feels each time he sees a particularly elegant solution. He can't wait to share it—with his students, and with the rest of us.
Poetry and math meld naturally for Su, the Benediktsson-Karwa Professor of Mathematics at Harvey Mudd College in Claremont, California. Su's poetry-tinged classroom efforts at Harvey Mudd, where he has worked since 1996, led to the 2013 Deborah and Franklin Tepper Haimo Award for distinguished teaching from the Mathematical Association of America.
Su earned his bachelor's degree with highest honors at age 19 from the University of Texas at Austin. He then earned his Ph.D. at Harvard University under noted mathematician and former magician Persi Diaconis. The first non-white person to be elected president of the American Mathematical Society, Su is a champion of public outreach among mathematicians.
He also instills a playful sensibility in his students. Exams often instruct them to write poems—even in upper-division classes. Former student Sam Antill, now an analyst for the Federal Reserve Bank of New York, wrote this verse about supremums, a mathematical concept:
As an element I ponder, while I set inside my set
What things exist outside my world, and how big can they get?
For I know that we are bounded, by something bigger than us all
But could I hope to see its face, or is it just too tall?
Su spoke at the February 2014 meeting of the American Association for the Advancement of Science in Chicago about elegant and fair solutions to cutting cake and dividing rent among roommates. Afterward, SciCom’s Cat Ferguson sat down to chat with Su about his unorthodox approach to teaching math.
Why do you love math?
Math is amazing. Math is amazing. You have a knowledge of certainty. If I’ve proved a theorem, that theorem is going to last forever. It’s not like someone in the future is going to suddenly show that it’s not true anymore. Whereas if you think about science, it’s different. You have a certain wisdom now about how neurons work, but who knows? In the future it might be overturned.
Of course, we make assumptions: “If A, then B.” And it’s often the “If A” part that’s questionable. Is that true in the real world? I don’t know.
In your public talks and writings, you quote and reference poetry a lot.
I like to write poetry. It's a way to express things that other modes of expression can't capture. Music is like that too. I've written several songs; there's one on my website.
How does that inform your teaching?
People think of teaching as communicating ideas. When you think about poetry or song writing, you think about communicating from the heart. I think there should be more teaching from the heart. You can pull people along emotionally in your teaching by connecting mathematics to meaningful things, like struggle. People connect over struggle.
Often students are so afraid of struggling; they think failure's a bad thing. Professional mathematicians, that's what we do: We struggle. That's where the fun is. We're doing our students a disservice if we're teaching them that doing math is about getting right answers.
You ask a lot of creative questions on your exams.
Yes. In an upper-division analysis course, there might be an exam problem where I have people write a news article. You give them a playful title, like "Great Ideas in Mathematics." The task is to communicate what they learned in class in a way that would be understandable to someone without an extensive math background.
What kind of responses do you get for your poem question?
Oh, some really great poems. What I like about those is people will try to tie mathematical ideas to tangible, real things that people experience. I think one of them is called Ode to an Open Set. He was using the language of analysis to try to describe love.
"Often students are so afraid of struggling; they think failure's a bad thing. Professional mathematicians, that's what we do: We struggle."
It's very XKCD.
Right, definitely.
How do you grade something like that?
They're probably the most enjoyable questions to grade. I'm just looking for any reasonable attempt at communicating an abstract idea to a wider audience. We need more public ambassadors for mathematics.
What are things you wish more mathematicians did to help the public understand math?
I wish more mathematicians would write about math—popular articles, op-eds. I think there are lots of people doing good work and connecting with the local schools. That's really important to nurture. Professional mathematicians have a lot to learn from educators, especially what kids are excited about.
In astronomy it’s very easy to point to beautiful pictures that capture the public imagination a lot more easily than math. But we can help people see that math is around them everywhere. GPS is math. So are search engines and people designing buildings. Whenever I'm with my non-math friends and I see something that's cool, I say, "Oh, that's math in action." It starts a conversation.
What do you want everyone to know?
I think people need to see that math is really a way of thinking. It's not just numbers, formulas, and functions. It's about looking at patterns in the world and trying to understand them, and the art of engaging meaningfully with those patterns.
You need a certain level of proficiency with the skills to begin to appreciate the art. We learn times tables as kids, and yes that's mathematical, but it's boring. You're memorizing those things so you're not stumbling over them when you're trying to understand the big picture. It's like a musician playing the scales. You want to have that finger memory so your brain can focus on higher-level tasks.
You're the first person of color elected as president of the Mathematical Association of America.
Yes, as far as we know. If you look at all the pictures, they're all white men and women. I think it's fitting that it's happening on our centennial. In the second century of the association, we're starting off with somebody who isn't the traditional white male.
Having leaders that represent the diversity of the population is important because people want to know, “Oh, somebody who looks like me is actually able to do this.” I'm not necessarily an underrepresented minority, but if you look at the fraction of Asian professors and the percentage of Asians in higher leadership, they don't compare at all. Some people refer to that as the bamboo ceiling
Do you also see a disparity in gender with your students and colleagues?
Certainly more women are coming into the mathematics profession, which is great. I think overall in the math societies it's probably somewhere around 30% women, a big change from even a couple of decades ago. And that's reflected in what I see at Harvey Mudd, a science and engineering school. When I entered, the school was about 25% women. Now, it's closer to 42% or 43%. Some recent classes have actually been more than 50% women, which is amazing—and much needed.
What do mathematicians actually do every day?
A lot mathematicians are math professors, so the boring answer to your question would be teaching and research.
What does that research entail?
Taking a mathematical question and trying to answer it. My Ph.D. advisor was famous for proving that it takes seven shuffles to mix a deck of cards. We didn’t have a good answer to that until 20 years ago.
Some mathematicians try to understand networks. Social networks, traffic patterns—even how many friendship pairs it takes to get from me to anybody else in the world.
Like Six Degrees of Kevin Bacon?
Yes. That’s a very natural question to ask. Even math that seems playful or recreational might have some cool applications later that we just haven’t seen.
When you were first learning math, did anything seem counterintuitive that now makes sense?
I remember learning in college this weird result called the Banach-Tarski result. It says you can take a solid ball and cut it into five pieces and rearrange the pieces through rigid motions only—no stretching or anything like that—to form two solid balls, each the same size as the original. I thought, “Wait a minute! That seems impossible!” Now I understand why it’s true.
But it’s not true. Is it?
The math is true. In real life you can’t actually do it because it depends on a ball being infinitely divisible. And we know that matter is not infinitely divisible. Beyond atoms, you can’t really break things up.
Somebody might look at that result and say, “Well, math isn’t really useful after all.” That’s the fear when you say something like that. Mathematics is a good model for the way things work, but it’s a model. We have to have realistic expectations.
How do you work out problems? Paper? A whiteboard?
I work on my iPad a lot. If I’m collaborating with someone, I’ll use a whiteboard or a blackboard. I’m getting a TV screen in my office to project my iPad onto. I’m going electronic with a lot of things, but if I’m collaborating I’ll use a board. Sometimes, if it’s just me, I’ll use paper.
You've been training a new generation of mathematicians for almost two decades now. Where do most of them work?
Outside of academia, the NSA [National Security Agency] is probably the largest employer of mathematicians. Doing cryptography, stuff like that.
You’ll also find many in finance. I just met someone who does statistics for the Boston Red Sox, which is really cool. That’s just not a job you think of applying for. But mostly they’re in academia.
Have you ever been approached by the NSA?
I looked into applying for a summer job when I was a college student. But if I were employed by the NSA now, I couldn’t tell you.
I can’t see someone from the NSA also teaching undergraduates how to write poetry about math.
[Laughs] Well, the NSA does employ college math students. They’re often at the big meetings to interview students.
Big software companies employ mathematicians, too. Facebook, Yelp, Google—they need people who understand the mathematics of networks. And combinatorics, clever ways of counting things. If I want to count the number of connections between the 15,000 people at this conference, that’s a combinatorial question.
How many people are at this conference, anyway? Why aren’t more press people going to the math sessions?
I think it’s easy to talk about math as a concept, but hard to talk about the math itself.
Right. You could walk into a session on DNA and at least get something out of it. You walk into a session on algebraic geometry, and it’s not going to be accessible. We have to fix that.
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© 2014 Cat Ferguson
Examine more of Cat's work here: catferg.com
