This year I've been co-writing "Mathematics, Live," an interview series for the Association for Women in Mathematics newsletter. In my interviews I'm "listening in" on conversations between pairs of female mathematicians. The first interview appeared in the May/June issue of the newsletter (password required). In it, I talked with mathematicians Laura DeMarco of the University of Illinois at Chicago and Amie Wilkinson of the University of Chicago.
Both do research in the field of dynamical systems, the study of how abstract mathematical spaces evolve over time. I got the idea to talk with them when I was at DeMarco's invited address at the Joint Math Meetings in January. (If you're interested, Jordan Ellenberg wrote nice post about her talk.) Wilkinson asked a question at the end of the talk, and I realized they would make a great pair for this interview series.
I met with DeMarco and Wilkinson in March, and we talked about how they got interested in math, the importance of female role models for young women in math, and their advice for aspiring mathematicians. This is a slightly abridged version of the interview that appeared in the AWM newsletter. Thank you to DeMarco and Wilkinson for their generosity with their time and advice.
Evelyn Lamb: Would you like to start by talking about how you got into math?
Amie Wilkinson: I got into math in early infancy. I always liked math.
Laura DeMarco: Early infancy?
AW: I'm exaggerating, but I always liked math.
LD: Did you do stuff outside of school, or was it just in class?
AW: I went to a Montessori kindergarten. I think that's the first time I actually saw math. What was great about Montessori was that everything was free-form, so you could just spend all your time at one station, all day long. I spent all my time at the math stations, basically. I would just do them all day. Counting base 5 and stuff like that. I think that's when it was clear that I was passionate about math. You were a physicist, right?
LD: Yes, but not "for real." In my case, I would say that I definitely always liked math. I always liked class, I always liked learning it and doing it. But my brother, who's older than me, was always better than me at puzzles and things like that. He was the one who would go into the contests. He was doing MathCounts and whatever the other contests were, and he was really into them. I wasn't interested in doing the competitions. I sort of found my own path and practiced my flute and did my own thing, but I probably came back to it later than you did.
The first time I thought to myself, "I like math enough to want to do it forever," was some point in high school, when I thought, "I want to be a math teacher." The funny thing is, I remember very vividly sitting on the school bus to go home from high school that day and thinking, "I could be a math teacher. I could just do math forever," thinking that that's what math means, right, to be a math teacher. I had no idea that there was anything beyond being a teacher.
It was in my second year in college when I learned that professors do research. I had no idea what it meant to do research. I was taking a seminar in social sciences. Each week we went through a different kind of theory with various examples. One day, the professor, who was from the law school, said to us, this group of second-year students, "are you aware that all of your professors are doing research?" And I don't even know what that means. What does it mean for my math professors to be doing research?
The next day, I went and asked all of my math professors, "What do you do?" I was taking probability at the time, and I went to my probability professor. "I heard you do research. What do you do?" Imagine what it's like when a student comes and asks you this question. I remember that it was this very awkward conversation. And he said something, and of course I don't remember what he said, and I'm sure I didn't understand it anyway. But the moment was very memorable.
At the same time, I was a physics major. I had loved physics classes in high school, and I thought, maybe I'll just do physics. I knew that scientists do research. That's obvious, somehow. So learning that mathematicians do research too was eye-opening.
AW: That's a great story. I have this picture of you walking into the first professor's office, like: "I've heard that you guys do this research thing. That's not for real, is it?"
EL: Were there any pivotal moments where you knew that you wanted to be a mathematician, beyond learning that math research exists?
AW: My pivotal moment was pretty clear. I went to college, and I was feeling very insecure about my abilities in mathematics, and I hadn't gotten a lot of encouragement, and I wasn't really sure this was what I wanted to do, so I didn't apply to grad school. I came back home to Chicago, and I got a job as an actuary. I enjoyed my work, but I started to feel like there was a hole in my existence. There was something missing. I realized that suddenly my universe had become finite. Anything I had to learn for this job, I could learn eventually. I could easily see the limits of this job, and I realized that with math there were so many things I could imagine that I would never know. That's why I wanted to go back and do math. I love that feeling of this infinite horizon.
To me, that was a pivotal moment, actually just being away from it. In general, being away from math from time to time has definitely been rejuvenating. Like when I had my kids, and just wasn't able to do math for a while. Then I would miss it. Then I'd understand why I'm doing it.
LD: You'd get extra excited about it, and really passionate about it.
AW: Yes. And grateful.
LD: I have these moments where I'm kind of overwhelmed by, "Wow, I really like what I'm doing, and isn't it amazing that I have this job and can live like this!" Of course, I have teaching and other duties, but just the idea that we can be supported, that there is an environment for this. I think that way when it's going well. When it's not going well, I think, "What have I gotten myself into?!"
I didn't know your story, that you had a job the first year after college. I did have some sort of moment that convinced me to go to graduate school. In my last year of undergraduate, my physics professors were very encouraging. There was something about the culture in the physics department that was simply encouraging. Any of their undergraduate students who were doing well were automatically involved in research projects. So I knew most of the faculty members, and it was somehow a natural thing to apply to graduate schools.
The math department didn't feel like that. But finally in my very last year, we got our first woman professor in the department. She arrived in my very last year, and that semester I had decided to ask her to be my advisor for my undergraduate thesis project. Just having her around made a big difference to me.
Then it was that fall semester of my last year of undergraduate that the TA of one of my classes said, "Oh, where are you applying for graduate school, Laura?" I said, "I'm not applying to graduate school. I actually have an interview tomorrow for a job." He said, "What? You're not applying to graduate school?" He was super encouraging. All of a sudden there was this one graduate student who seemed to care and said, "This is crazy! Why aren't you applying to graduate school?"
AW: It was serendipity.
LD: It was sort of just by chance that one person had thought through the idea of actually asking me.
AW: Or not thought through it.
LD: That's right, who had simply asked! My physics advisor had certainly talked about this idea. But I just wasn't passionate about physics by the end.
EL: Are there any math topics that are particularly appealing or beautiful for you?
AW: I like calculus a lot, probably because I learned it when I was young, and I learned it well. To me, it's always comforting to use calculus to do something. The invention of calculus was certainly revolutionary.
LD: A conceptual breakthrough.
AW: It's funny, because it's like we just toss it out there to high school students, and I think a lot of them have no idea of the beauty.
LD: What the ideas really were.
AW: Certainly some of the most beautiful mathematics I've learned is just calculus.
LD: It's funny you mention calculus. I don't think I really appreciated it until I taught it as a graduate student. I was lecturing to these first-year students. I was just wowed by this subject. I had this moment of, holy cow, this is really beautiful! I remember my grandmother asking me what I was thinking about these days. I said, "Well, I'm teaching calculus right now, and you know what, calculus is really beautiful." She said, "OK, Laura, what is calculus? Can you just tell me in 20 minutes, what is calculus?" And it was just the greatest thing to have this opportunity to just sit down with my grandmother, of all people, and tell her.
AW: The proverbial grandmother.
LD: That's right. It's funny because she says that she liked math when she was young, but it wasn't something in that era that she could have pursued. She certainly never pursued anything beyond some basic courses. But she sat through and listened to my explanation.
AW: Do you think she got it?
LD: I don't know. I was speaking more about the philosophy. I wasn't doing any computations. But the idea of differentiation and then integration, and the fundamental theorem of calculus, how it's connected. I don't know if she got it or not. But it was a good conversation.
Women in mathematics
EL: Have you faced any challenges as women in math?
LD: Now I would say it's an advantage. Once we're at the stage that we're at, it's probably more of an advantage than a disadvantage. People want women speakers and women getting involved at different levels, and a certain amount of women at the top levels. Earlier on, it's a different story.
AW: I would agree. As long as you're able to say no, it's an advantage. I think you're asked to do more. It's hard to say no to things that involve young people or women. As you get older, you feel a real responsibility to help the younger people. That's the only disadvantage. I feel like I get asked to do a lot more.
LW: Yes, definitely.
AW: It's hard for me to say no to a lot of it because it's worthwhile. But when I was younger, Laura's story about having the woman math professor really resonates with me because when I was in college there were no women at all at Harvard. No research faculty, zero.
LD: Not even postdocs?
AW: Not even postdocs. And so I think I craved a role model at that point. I think that if one had shown up it would have made a huge difference.
And having kids for me was difficult. It was scary. Partially because I didn't really have that many people to look up to, to say it's doable. Even when Beatrice was born, which was only 13 years ago, it wasn't quite the norm, it wasn't quite supported. That is another thing that I think is much harder for women. Hugely harder for some women. I was just lucky, for a lot of reasons, that it worked out OK.
In general, the stereotype threat business kind of held true for me. I think there was a little nagging voice that said, well, do you really think you belong here, when I was younger. When your confidence level is low.
LD: Yes, when you're not so confident. I wasn't so confident.
AW: No one's really confident at that point.
LD: That's right, nobody is. And people react very differently. But I wasn't the kind of person to react by speaking louder, or by making myself seen. In fact, what I tended to do was try to play down my femininity in many different ways. I dressed like the boys, and I really went out of my way to be less feminine. Now I feel totally comfortable just being who I am. Certainly then I would make an effort not to stand out in some way. I wasn't so confident, and being the only girl in my classes didn't help.
AW: I got certainly some inappropriate off-color comments from people. Those kinds of comments, they were a bit alienating, but I don't think I found any of those kinds of comments particularly discouraging. It was more the general level of apathy that was hard.
LD: Yes, that is something that probably played a role. Personality-wise, I probably needed encouragement. I would have liked to have gotten some explicit encouragement. If I'm doing well, I want to know!
I remember when I finally decided to apply to graduate schools, I had a very close girlfriend who said, "Well, you should certainly apply to Harvard and Princeton, and all the top schools." I said, "Oh no, I'll never get in." So I didn't even bother applying. But I did apply to Berkeley, and I got into Berkeley, and I went to Berkeley. And of course in the end I ended up transferring to Harvard, and I ended up with a degree from Harvard, so somehow it ended up happening anyways. And this friend, she's not a mathematician, so I thought she had no idea what she was talking about, but in the end she was right.
AW: It's so funny that it seemed obvious to her. An ordinary person would think, "Well, of course. You're a top student. You should apply to the top schools." In the math world there's this huge mystique around these top places, and someone who lacks even just a little bit of confidence, it's like "no, of course I'm not going to apply to a place like that." I wonder how many women are kept out of the top places by that kind of attitude.
LD: And not realizing that you should actually go for something.
So you want to be a mathematician...
EL: Do you have advice for young people who might be thinking about doing math?
LD: If you love it, go for it. It is helpful to have some people to talk to. It helps to have an advisor of some sort or a research project to connect you, to learn how to communicate with people.
AW: I'm glad I did math team in high school.
LD: So you did math team?
AW: I did do math team. In junior high school, I was really good at math. I was clearly kind of a math kid, but a bunch of other kids were doing all these gifted programs and taking all these tests, and I was too scared to do that kind of thing, and I probably wouldn't have done very well. When I got to high school, I don't know what pushed me to go check it out, but I did. Doing the math team at my high school was really formative. It gave me a community of other math geeks.
LD: Kids that really enjoyed it. At least now these math circles are starting to pop up around various places.
AW: Yes, the math circles are even cooler because it's not competition. Although, these math competitions get a bad rap. It wasn't just sitting in a room and filling out these tests. There were oral contests. I remember I presented something on curves of constant width. You'd be given a topic, and you'd read up ahead of time. They'd ask you questions, and you could prepare an answer. Then you'd stand up at the board and present the answer. Girls, even then, happened to do very well. There was this girl named Nadia in our school, this extremely tall Russian volleyball player. She didn't do anything else in math team, but she was tops at the oral part of this contest.
Then there was this two-person event, and my high school rival and I were the two-person team. There were all sorts of different things. Different talents could take part, and I'm sure there are things like this now.
That's a piece of advice, to explore. You don't have to be the very best to get something out of it. And another piece of advice, for young people, is that there really are second chances, and things can change. As an undergraduate, I kind of had a very mixed academic record. I did lots of things I loved that weren't necessarily math. I did well in a few math classes, and I did badly in a few math classes. So I was lucky to get into Berkeley. But I found graduate school to be an utterly different experience from college. Suddenly there were no distractions, it was all I was doing.
LD: And you were enjoying it.
AW: I was enjoying it, and I felt at the top of my game. It's worth a shot. That's not the time to be scared to give it a try. If it doesn't work out, it's a year of your life. Big deal, whatever. I just think more people should try.