Math Isn’t Good for You. It’s Good for Us

Most non-mathletes missed the ovation. But back in 2017, mathematician and professor Francis Su gave the presidential address for a meeting of the Mathematical Association of America, and his speech not only fed into magazine interviews and landed a book deal, but it brought those in attendance to their feet. Not a common occurrence for math association meetings. But what Su said resonated, and it still does well beyond those with an immediate interest in mathematics.

The book came out in 2020 with the same title as the talk: Mathematics for Human Flourishing. It’s an academic book from a university press, but it might as well fit in a classics seminar, along with adjacent discussions of Aristotle and Euclid — math in contact with our big questions of humanity. This idea, at least partly, is what inspired attendees years earlier, even if the idea fits expectedly with Su’s work.

Su is a teacher at Harvey Mudd College in California, where, in addition to teaching, his work includes mixing combinatorics (very basically: counting and arrangement) with geometry and topology and using those to study problems in the social sciences. Think game theory or, more narrowly, voting theory. “You can think of it as the mathematical modeling of decision-making,” Su explained over the phone back in October.

Here’s what else he said.

Can you summarize your argument for math as a liberal art?

What I try to help teachers see is that math is not just a set of skills, but also a set of virtues. Skills are things like knowing your times tables or factoring a quadratic. Virtues are ways in which your character/attitudes/dispositions are shaped by doing math. Yes, skills are important. I’m not saying we shouldn’t know our times tables, but actually, what’s more important is being able to tell me that if you divide 100 by 19, you should get something that’s about 5. The virtue of having number sense is far more important in the real world, because, these days, humans’ role with respect to math is actually making sure that computers aren’t screwing up and spitting out ridiculous stuff.

What I try to help people see is that virtues are actually more important than skills. The virtues you build by a great math education are actually things like persistence, curiosity, an affection for mathematics, visualization, or being able to abstract, being able to quantify, to make a good definition, being able to look at a claim and evaluate if it’s reasonable.

You also talk about teaching math as beautiful.

Yes, one of the things I love about doing math is enjoying the beauty of it and being able to see how math can help you see the unseen, to help you see aspects of the world that you didn’t see before. It’s just like the way you inspire people to play music isn’t by making them learn lots of musical scales; you show them the beauty of a symphony, even if they can’t play an instrument yet. That’s what motivates people to want to play their scales. It’s the same with math. We don’t need better human calculators. In an age of computation and AI, we have things that can do that, right? But what we really need are better thinkers.

Famously, you’ve said mathematics is “uniquely suited for the achievement of human flourishing.” What’s the connection?

One aspect of living life well is actually being able to see and experience beauty in all its forms, one of those being mathematical beauty. I think part of what leads to a well-lived life is actually having reasons to live, and part of that is the appreciation of beauty, even the unique form found in math. Another aspect of a well-lived life is learning to reason well.

Math helps you cut through the fog. In this era of highly polarized disagreement, we really don’t need people who only listen to what their friends say and who aren’t able to think for themselves or even appreciate other people’s points of view. A great math education actually helps people to think for themselves, to be able to say, “Wait a minute, I don’t know if this person is using statistics properly.” Or “That sounds like an outrageous claim.”

At the same time, math also ought to teach you to have a little bit of humility. We teach students when they’re handling statistics to say, “Correlation isn’t the same as causation.” Why? It’s because we’re trying to teach people to be humble about what they know and what they don’t know. We should all be circumspect about the claims we make.

We tend to think of math as fixed, the opposite in a sense of humility.

Math actually teaches you to look at a problem from many perspectives. Yet, what do we do? In our educational systems, we teach students there’s only one way of doing things. That’s completely antithetical to mathematical thinking. Part of the wonder and joy is being able to appreciate that there are multiple ways to solve a problem. Being able to see different ways of solving a problem actually should help us appreciate that there are often many points of view in a real life, non-mathematical problem, as well.

What is math?

Math is learning to think well. The idea of math as something calculators do is extremely limiting; in fact, I like to say anything a calculator can do isn’t really math. If you’re calculating and you’re not thinking, you aren’t doing math.

Similarly, you’ve defined math as a “habit of mind.” How do you see this definition playing out for someone who’s not working in the mathematical fields?

If you’re an entrepreneur, for example, you have to learn to think well, to strategize, to be able to break down a complicated problem into parts. That’s a virtue built by a great math education. With any of these big problems you’re trying to solve, you have to learn to visualize them in different ways, to be able to conceptualize a problem, and math helps you do that as well. Anytime you’re thinking well about some problem that you’re trying to solve, you’re doing mathematical thinking.

What does mathematics say about the world and the universe?

With respect to the big questions, math is a vehicle for seeing the big structures, big patterns in the world. For instance, take the recent discovery of gravity waves. Take Einstein’s idea that matter actually bends the curvature of space; astronomers lean on this all the time to try to understand the structure of space. Gravity waves, which we just confirmed only a few years ago, represent probably the biggest discovery of physics in the last century. It offers us a new way of looking at the universe. Yes, it’s a discovery in astronomy and physics, but all that leans on an intimate understanding of geometry.