Math conferences don’t usually feature standing ovations, but Francis Su received one last month in Atlanta. Su, a mathematician at Harvey Mudd College in California and the outgoing president of the Mathematical Association of America (MAA), delivered an emotional farewell address at the Joint Mathematics Meetings of the MAA and the American Mathematical Society in which he challenged the mathematical community to be more inclusive.

Su opened his talk with the story of Christopher, an inmate serving a long sentence for armed robbery who had begun to teach himself math from textbooks he had ordered. After seven years in prison, during which he studied algebra, trigonometry, geometry and calculus, he wrote to Su asking for advice on how to continue his work. After Su told this story, he asked the packed ballroom at the Marriott Marquis, his voice breaking: “When you think of who does mathematics, do you think of Christopher?”

Su grew up in Texas, the son of Chinese parents, in a town that was predominantly white and Latino. He spoke of trying hard to “act white” as a kid. He went to college at the University of Texas, Austin, then to graduate school at Harvard University. In 2015 he became the first person of color to lead the MAA. In his talk he framed mathematics as a pursuit uniquely suited to the achievement of human flourishing, a concept the ancient Greeks called *eudaimonia*, or a life composed of all the highest goods. Su talked of five basic human desires that are met through the pursuit of mathematics: play, beauty, truth, justice and love.

If mathematics is a medium for human flourishing, it stands to reason that everyone should have a chance to participate in it. But in his talk Su identified what he views as structural barriers in the mathematical community that dictate who gets the opportunity to succeed in the field — from the requirements attached to graduate school admissions to implicit assumptions about who looks the part of a budding mathematician.

When Su finished his talk, the audience rose to its feet and applauded, and many of his fellow mathematicians came up to him afterward to say he had made them cry. A few hours later *Quanta Magazine* sat down with Su in a quiet room on a lower level of the hotel and asked him why he feels so moved by the experiences of people who find themselves pushed away from math. An edited and condensed version of that conversation and a follow-up conversation follows.

*QUANTA MAGAZINE: The title of your talk was “Mathematics for Human Flourishing.” Flourishing is a big idea — what do you have in mind by it?*

FRANCIS SU: When I think of human flourishing, I’m thinking of something close to Aristotle’s definition, which is activity in accordance with virtue. For instance, each of the basic desires that I mentioned in my talk is a mark of flourishing. If you have a playful mind or a playful spirit, or you’re seeking truth, or pursuing beauty, or fighting for justice, or loving another human being — these are activities that line up with certain virtues. Maybe a more modern way of thinking about it is living up to your potential, in some sense, though I wouldn’t just limit it to that. If I am loving somebody well, that’s living up to a certain potential that I have to be able to love somebody well.

*And how does mathematics promote human flourishing? *

It builds skills that allow people to do things they might otherwise not have been able to do or experience. If I learn mathematics and I become a better thinker, I develop perseverance, because I know what it’s like to wrestle with a hard problem, and I develop hopefulness that I will actually solve these problems. And some people experience a kind of transcendent wonder that they’re seeing something true about the universe. That’s a source of joy and flourishing.

Math helps us do these things. And when we talk about teaching mathematics, sometimes we forget these larger virtues that we are seeking to cultivate in our students. Teaching mathematics shouldn’t be about sending everybody to a Ph.D. program. That’s a very narrow view of what it means to do mathematics. It shouldn’t mean just teaching people a bunch of facts. That’s also a very narrow view of what mathematics is. What we’re really doing is training habits of mind, and those habits of mind allow people to flourish no matter what profession they go into.

*Several times in your talk you quoted Simone Weil, the French philosopher (and sibling of the famed mathematician Andr**é** Weil), who wrote, “Every being cries out silently to be read differently.” Why did you choose that quote?*

I chose it because it says in a very succinct way what the problem is, what causes injustice — we judge, and we don’t judge correctly. So “read” means “judged,” of course. We read people differently than they actually are.

*And how does that apply to the math community?*

We do this in lots of different ways. I think part of it is that we have a picture of who actually can succeed in math. Some of that picture has been developed because the only examples we’ve seen so far are people who come from particular backgrounds. We’re not used to, for instance, seeing African-Americans at a math conference, although it’s become more and more common.

We’re not used to seeing kids from lower socioeconomic backgrounds in college or grad school. So what I was trying to say is: If we’re looking for talent, why are we choosing for background? If we really want to have a more diverse set of people in mathematical sciences, we have to take into account the structural barriers that make it hard for people from disadvantaged backgrounds to succeed in math.

*We’ve been hearing more about how these kinds of educational barriers arise in primary and secondary school. Do you argue that they arise in undergraduate and graduate programs as well?*

That’s right. At every stage we’re losing people. So if you look at some of the studies people are doing now about people who take Calculus 1, and how many of them go on to take Calculus 2, you’ll find basically that we’re losing women and minorities at these critical junctures. This happens for reasons that we can only speculate about. But I’m sure some of it has to do with people in these groups not seeing themselves as belonging in math, possibly because of a negative culture and an unwelcome climate, or because of things that professors or other students are doing to discourage people from continuing.

*The obvious problem with this attrition is that when mathematics draws from a smaller pool, we end up with fewer talented mathematicians. But you emphasized in your speech that denying people math is actually denying them an opportunity to flourish.*

Math can contribute in a broad way to every person’s life whether that person actually becomes a mathematician or not. The goal of broadly getting people to appreciate math is not at odds with bringing more people into deep mathematics. Connect with people in a deep way and you’re going to draw more people into mathematics. Some of them, more of them, are going to go to graduate school, and that will necessarily happen if you address some of these deep desires — for love, truth, beauty, justice, play. If you address some of these deep themes you’re going to get more people and a more diverse set of people in deep mathematics.

*Some of those desires are easier to relate to math than others. I think people have a somewhat intuitive sense of how a desire for truth or beauty might be realized through math. But you spent a lot of your talk on justice. How does that relate to mathematics?*

Justice is a desire that people have, and so it leads to a certain virtue which is to become a just person, somebody who cares about fighting for things that defend basic human dignity. I spent the most time discussing justice in my talk mainly because I feel that our mathematics community can do better; we can become more just. I see a lot of ways in which we can do better and become more virtuous as a community.

Being a mathematician in some ways allows us to see things more for what they are. When people learn not to overgeneralize their arguments, they’re going to be very careful not to think that if you’re poor you’re necessarily uneducated or vice versa. Having a mathematical background certainly helps people to be less governed by their biases.

**You’ve been a successful research mathematician, yet you teach at a small college, Harvey Mudd, that doesn’t have a graduate school. That’s kind of unusual. Was there a point where you decided you’d prefer to work at a liberal arts college rather than a big research university?**

When I was in graduate school at Harvard I realized I loved teaching, and I remember one of my professors from college telling me that the teaching was better at small liberal arts colleges. So when I was on the job market I started looking at those colleges. I was interested in the research track and willing to do that, but I was also very attracted to the liberal arts environment. I chose to go and I love it; I couldn’t see myself being anywhere else.

*And how do you think working at a liberal arts college shapes the way you look at the mathematics community today?*

I think one of the things I didn’t address in the talk, but almost did, is the divide in the community between research universities and liberal arts colleges. There is a cultural divide, and the research universities are in some sense the dominant culture because all of us with Ph.D.s come through research universities. And there’s the whole pattern of the dominant culture being completely unaware of what’s going on at the liberal arts colleges. So people come up to me and say: “So, you’re at Harvey Mudd; are you happy there?” It’s almost like assuming I wouldn’t be. That happens all the time, so I find it a bit frustrating to feel like I have to say: “No, this is actually my dream job.”

*What are the consequences of this cultural imbalance?*

Well, the downsides are, for instance, that many of the people at research universities would never consider taking students from an undergraduate college. That’s the downside; they’re missing a lot of talent. So in many ways the issues are analogous to some of the racial issues that are going on.

I think professors at research universities often don’t realize that there are a lot of bright kids coming through the liberal arts colleges. What I’m addressing is the very common practice right now in certain graduate schools of only admitting people who’ve already had a full slate of graduate courses. In other words, they’re expecting undergraduates to have taken graduate courses before they even get considered. If you have that kind of structural situation, you are necessarily going to exclude a bunch of people who otherwise might be successful.

*One barrier you mentioned in your talk arises when senior professors don’t teach introductory classes. Tell me about that.*

I’m being a little provocative here as well. I think what that communicates is: “This is not an important enough segment of people for me to put my attention to.” I’m certainly not saying everybody who only teaches senior-level courses has this attitude, but I am saying there are a lot of people who think the math major is basically there for the benefit of students who are going to get a Ph.D. That’s a problem.

*At the Joint Mathematics Meetings there were a number of prizes specifically for women, and a number of women gave invited talks. Has the math community made more progress on gender equality than on racial inclusiveness?*

Definitely, racial inclusiveness has not come as far or as fast as gender inclusiveness. Currently about 27 percent of people with Ph.D.s, faculty members, are women, and about 30 percent of the ones who won awards in teaching and service are women. So we’re actually doing pretty well on that front. With our writing awards, which are awards for research and exposition — the fraction of women winning those awards is lower.

*Can you look at the process by which gender equality has improved and draw any lessons from that about how to improve racial equality in math?*

Many of the practices that work to encourage women in math also work for minorities. Part of the issue here is that there just aren’t that many minorities who come into college interested in doing STEM majors. So there’s something that happened at the secondary and primary school level, and it would help a lot if we could figure out what’s going on there.

*You used the metaphor of a “secret menu” in Chinese restaurants. What did you mean by that?*

If you go to an authentic restaurant in a big city in New York or California, if you are not Chinese they will give you a standard menu that has things in English and Chinese. But if you’re Chinese, they’ll give you a different menu. Often it’s a menu that is written completely in Chinese and has some additional options that aren’t on the standard menu. And I think that happens in the math community. If you talk to women and minorities they will often tell you they’ve had experiences where people discouraged them from going on, either because they don’t think a woman should be in math, or for other reasons. So I used the metaphor “secret menu” to mean: Do we have a secret menu? And who gets to look at it?

*You told a story about a student who was counseled by a professor to choose a different major on the grounds that the student wasn’t good enough to stick with math. Is that common?*

I think it’s common. Of course we don’t have any data, but I’ve certainly talked to enough people who’ve had those kinds of experiences to know that it’s very frequent and most of those people are women and minorities.

*It’s been almost a month since you gave your speech, and it’s generated a lot of attention on the internet and among mathematicians. What kinds of responses have you received?*

Most of the comments have come from people who are grateful to me for mentioning things that haven’t necessarily been discussed, but also for identifying some of the deep, underlying things that cause us to do what we do. I think a lot of people, especially women and minorities, have expressed to me how important it was for somebody to say that. We’ve been having discussions like this in smaller conversations, and a lot of time it’s preaching to the choir, and so having somebody say that in a big address at the national meeting I think felt important and helpful to them.

*This article was reprinted on Wired.com.*

I'd love to do more math. Or even do it full time but I have a day job.

OMG, thanks for the PDF download link next to the "Print" button! Super easy, no BS, kept me from printing it. Also, thanks for the important article. I'm a math tutor and student at a community college, and I strongly feel that Math would be much more respected and appreciated by the "general populace" if we had better education in it. Many people hate it because they are never taught it well.

My two cents on the problem of the lack of minorities in STEM, and perhaps even the larger lack of students interested in pursuing such studies at a higher level originates from the contemporary college application environment.

In order to ensure high GPAs and test scores students shy away from subjects that they might be interested in but don't excel at. This cookie cutter approach is further encouraged in the modern high school senior by the fact that he/she is not required to take a Math class beyond Algebra II in most counties.

If a more forgiving and less taxing environment was provided, where a student could focus on actual learning and exploring of different fields instead of trying to game the system was provided I can see students less hesitant to take a potentially "harder" class such as Calc 2 after Calc 1.

Disclosure – recent college freshman who faced similar choices

Francis Su's speech was just wonderful and just reading some parts of it really made me understand where he was driving at about those five qualities the Greeks mentioned(play,love.justice,beauty and truth). He speaks with a passion for Mathematics and a desire to see more people study it.

Every 10—15 years or so during my life I've had to revisit math. (I am 57.) Having got UK A-levels in maths and sciences in the 70s, I was fortunately established on a springboard when in my early 30s I visited electronic system design (complex numbers and calculus), then databases (set theory), some challenging fluid dynamics software (tensors) and, quite recently, elbows-deep into encryption (elliptic curves, oh boy).

The process has always started with an appalled "This is gonna hurt", proceeded through brain-cudgelling—and ended with great satisfaction. I thought it was mostly the pleasure of having finally attained some hard-won understanding, but reading this article has switched on a spotlight in the dusty recesses of my psyche … Su is exactly right: there's much more to this than just the math.

If any subject is a perfect training ground for logical thinking and reinforcement of the concept of correct and incorrect, it is math. It is immensely satisfying, but not merely, as I thought, for the selfish egotism of "I figured it", but also for refreshing the mind with clarity and purpose. At risk of sounding a bit evangelical, I realise it is therapeutic.

I'll never explain it as well as Su, so I shan't try further, but I'm sure I'm not the only one who is immensely grateful to him for articulating something previously only dimly perceived.

I loved this article. Yet, there is the other side. When I was in college I was encouraged by my professors to continue in math. I was in the Math Honor Society at the University of Wisconsin-Eau Claire. I attended meetings with very intelligent math majors and they clapped when I gave a presentation using geoboards. The presentations were from a wide variety of math majors. (I am a middle school math teacher now.) As a woman, I felt welcome in the math community. I now teach in a Catholic middle school.

The English are missing all of this: play, beauty, truth, justice and love.

The Math Department at a major university Web page shows pictures of undergrad and grad students. I think it has been years since I saw a single black student photo. [It could be the engineering school applied math is better].

The university is big on inclusion so I doubt deliberate discrimination is the cause–in adequate recruiting may be a cause–I don't know.

There are many commonly sited 'reasons' for so few blacks in math—bad K-12, no role models, bad high school counseling, not knowing what mathematicians do or jobs available.

But something needs to be done ! Everytime I bring up the question, I can tell no one has good/any ideas.

I hope the book/movie "Hidden Figures" can make some changes—so far discussions are women in math not blacks.

Completely agree we need to encourage a broader range of people to take up mathematics, as it increases the influx of radical new ideas. The backgrounds of some of the most creative mathematicians of the past and present – Gauss, Newton, Lagrange, Ramanujan, Grothendieck, Tao – is as astonishingly varied as their contributions.

One question: according to Prof Su "…[W]e’re losing women and minorities at these critical junctures. This happens for reasons that we can only speculate about".

Really ? Are there no studies of this critical issue – and if not, why not ?

As someone who started with pre-calculus at age 33 and who is now (at 47) in a graduate program in math, I wish my professors had given me some advice, namely: It's OK to not get it. The 1st, 2nd, 3rd or 4th time you look at something, it's OK to not understand. For most people, mathematical thinking is, in a very real sense, unnatural. Being at ease with pure abstraction generally doesn't help one avoid predators on the savannah or procure food for one's progeny. Unfortunately, it seems the way math students are nurtured is not unlike assuming that the winner of the 100 meter dash would make a great marathon runner.

Just start anew with mental arithmetic on schools.

my family obligations has always hindered my love of physics, mathematics, and computer science and so even at this age of 66 i always sneak in its secrets

Nice inspiring article for the understanding and contribution of Mathematics for human flourishing. No doubt, mathematics has contributed a significant development.

Su talked of five basic human desires that are met through the pursuit of mathematics: play, beauty, truth, justice and love. Justice and play are understandable. But beauty, truth and love need more explanation. With the advent of digitization mathematics has become the indispensable part of our development.

Great post and regards

Really nice, thanks for this.

One caveat: mathematics is not a belief system. It's also not the secret language of the universe. It's not nice to anthropomorphize Mother Nature.

"If we really want to have a more diverse set of people in mathematical sciences…"

Why is that the desideratum? As far as policy goes, don't we want to maximize, say, theorems proven per research dollar spent?

We live in times some people question the value of science.

If we compare quality of life in the middle ages and today, practical value of science is obvious, isn't it? Isn't it also obvious how big is value of math to science?

Isn't it obvious whole Universe is a mathematical structure?

Isn't it worth to understand better?

http://fb36blog.blogspot.com/2017/02/value-of-science-and-meaning-of-proof.html

As a non physically awkward athletically accomplished white male, I found all of academia, and especially math, to incessantly send the message I dont fit. Comparable women or minorities were in contrast welcomed. The only people less welcome than me were athletically inclined black males. This article is a joke since it makes it sound like the problem is something besides insecure low-t males in general.

I was once a Math major, but I had to give it up. For various reasons I was attracted to the seeming stability of Math, the idea that acts of pure reason lead to consistent and meaning full results. In short I was very naive. Two conversations still stick in my mind. One came from the results of a test. I had submitted a proof on a test and I thought I understood it but received only partial credit. I compared my answer to a fellow classmates that got full marks. They were basically the same. I ask the Professor about this and his answer was, “yes, but I knew he [my classmate] knew the answer”. Meaning that what I wrote on an exam was meaningless because the grade would be based on what the Professor thought I knew, not what I presented. I ask another Professor to explain a proof he had presented that I didn’t understand. We started going through it step by step. At one point I said “stop, this is where I’m lost, how to you know how to go from this step to the next”. He paused a moment, thought, then told me “you just know”. Later I realized that he probably just didn’t know and had taught this by rote for decades. I realized that this subject that I thought was based on objective reasoning was in fact subjective and based on some form of mystic knowledge that you either possessed or were forever barred from. I have more stories like this but you get the idea. These are the people that teach the teachers. I switch to CS and obtained a BS. CS was taught even more poorly than Math, but I was less naïve.

The American higher education system is deeply and fundamentally broken. I believe this is mostly due to the practice of tenure. In most large schools this puts undue emphasis on publishing and acquiring grants and no (or even negative) emphasis on teaching. And again these are the people we depend on to teach the teachers. When I started college some “dean of stuff” gave us a grave speech (I believe it was referred to as a “Welcome speech”) and told us that only 2/3’s of us would graduate. “Look to your left, look to your right, if you graduate one of those people won’t”. Imagine if our lower level schools systems set the same low bar (accepted the same low level of competence in their teachers). This is why it’s so easy to sow the seeds of public distrust of science. Many people who have been through the “college machine” (whether they graduated or not) distrust the motives of academics due to personal experience. It’s very sad and nothing good will come of it. I believe in the power of good science, but I also understand peoples frustrations and mistrust.

In any case, I applaud you sir. You have taken “the path less traveled” and committed yourself to sharing your knowledge and teaching people. You give me hope for a better future. Mathematics contains such beautiful and I hope more people learn to see it.

It is disheartening to see the distortion of normal human virtues in a man who has intellectual ability. The author relies on Aristotle for his apparent argument that mathematics is a path to virtue. Aristotle, like Plato and others of the ancient Greek civilization did believe that men of excellence should educate themselves and hone their abilities, the exercise of which would benefit the host civilization and themselves.

Both philosophers, however, warned of the cycles of civilizations which inevitably follow those of nature, i.e., "everything which has a beginning has also an end, even a constitution…will not last forever, but will in time be dissolved…the laws which regulate them will not be discovered by an intelligence which is alloyed with sense…and they will bring children into the world when they ought not to." (Plato, Republic).

Aristotle would not have recognized virtue in the complaints of the author about his perception of unnatural exclusion of some classes of people from his own branch of academia. It should be recalled that Aristotle believed monarchy, the rule of a man sufficient unto himself and excelling his subjects in all good things, was far superior to timocracy or popular government by all those who owned property (and he believed democracy to be the further perversion of timocracy). Both Plato and Aristotle believed in the value of excellence and warned that the deterioration of civilizations would be characterized by the loss of the real testing of men for such excellence and the replacement with discord, the focus on complaints about place and status (see Plato's discussion of the timocratic man in Republic).

When Thomas Jefferson wrote in the Declaration of Independence "We hold these truths to be self evident, that all men are created equal…" he did not demanding equal placement of all men. Jefferson knew that men were not created equal, writing, for example, in 1768 to William Preston, "I cannot help hoping that every friend of genius, when the other qualities of the competitor are equal, will give a preference to superior abilities." Jefferson's intent was that America should permit the free competition of all men rather than the assignment to particular classes by hereditary privilege, e.g., nobility, or the like (Jefferson did differ from Aristotle and Plato in believing self-government or democracy to be the best environment for that goal).

I dare to point out the horrible approach of the education system as a whole that directly impacts the hard sciences. Academic education solely rewards the correct answer, and while this is important, true science is a process of failure and learning from those failures. In my experience, I've seen many people steer clear of mathematics not because it was difficult but because the difficult work was only rewarded with a correct answer and the process goes unnoticed.

Wonderful. I am a pretty skilled Technician, and hold a BSIT and ASEE. I tested out of most of the courses for the ASEE, because I had been through the Navy's BEEP, Radar, Communications, Calibration and various C level schools, which covered all the material EXCEPT the calculus and no math farther than Cooks math.

After retiring from the NAVY I worked at Fairchild Camera and Instrument on ATE systems, then a couple of years for Advantest America, and finally 16 years at Teradyne. I did design some instrument extensions, write a lot of software, but I never lost the feeling of missing something. I periodically buy text books on calculus and really want to learn, but something is blocking me, I don't know what. I think if practical applicaitons of the various bits were supported in the texts, something like "use dot products to solve this kind of technical issue" with an illustrated example, then people like myself with an applied background would have a better chance.

You should only be asking Wired to link to your site as a source, not vice versa, which they also promptly did. It is off-topic, but of importance. You are the originator.

Wonderful article; thank you.

One aspect of math education that could be improved would be a better balance between engineering math (leading to calculus) and pure math.

In high school, calculus and differential equations are (or were, in my time) put on a pedestal as "math", but nothing is said about logic, number theory, abstract algebra, etc — all of which are eminently approachable by high school students.

I don't know if this sort of thing still occurs, but in the fall of 1956 John Wheeler taught physics to freshman premeds and engineers at Princeton (not honors physics). He brought in Niels Bohr to speak to us one day and I can still see him sitting in a chair mumbling to us in what appeared to be Danish. Emil Artin taught honors calculus to freshman that year.

Somewhat different view:

"We Do Not Choose Mathematics as Our Profession, It Chooses Us: Interview with Yuri Manin"

www.ams.org/notices/200910/rtx091001268p.pdf

This perhaps more accurately resembles Ancient Greek's perspective.

He ought to go teach in rest of world, and find out, most people don't and cannot do math, and don't care. He is too opinionated by teaching rich kids in Harvey Mudd, thinking everyone can do math and love math.

Once upon a time in my early days(1983ish) tutoring math I got a letter from a guy in jail who was trying to complete a pre-calculus correspondence course. He was woefully confused and after exchanging a few letters to help him work out some problems he stopped writing back. As a last resort I sent him a copy of "Prof. E. McSquared's Calculus Primer" I found at the SDSU book store. Six months later he wrote me back "sorry to be out of touch but the book was so good and helped me so much I didn't have time to write you." He completed the course which helped him get got an early release and had since moved back home and gone back to college.

It's the little things.