This month, the mathematician Karen Uhlenbeck became the first woman to win one of the field’s most prestigious awards, the Abel Prize, which is awarded by the Norwegian Academy of Science and Letters. Uhlenbeck, who is seventy-six and an emeritus professor at the University of Texas at Austin, has done revolutionary work across several disciplines; indeed, the academy lauded “her pioneering achievements in geometric partial differential equations, gauge theory and integrable systems, and for the fundamental impact of her work on analysis, geometry and mathematical physics.” The specifics of some of her discoveries are hard to understand—let alone summarize (see below)—but her career has awed her peers and upended any lingering stereotypes about women and math.

I recently spoke by phone with Uhlenbeck, who is currently a visiting scholar at the School of Mathematics at the Institute for Advanced Study, in Princeton. During our conversation, which has been edited for length and clarity, we discussed how she got into math, the struggles of women in a male-dominated field, and whether mathematicians really have “aha!” moments of discovery.

I read that when you found out you had won the Abel Prize, you were coming out of church. Is that correct?

That’s right. We go to the Unitarian Universalist Church, and I glanced at my phone and I had an e-mail from a colleague at Princeton saying I should accept the call from Norway. So I did. I was surprised that I could press a button and return the call.

You’re the mathematician, so I don’t know what the odds are that if you’re getting a call from Norway, it’s to accept some sort of prize, but it seems like they should be fairly high, right?

I don’t know. I hadn’t noticed I had a call from Norway at that point, but I went and looked, and I did.

When did you first realize that mathematics fascinated you? How old were you, and what was that discovery?

Well, I was really a freshman in college. I had always been interested in physics, mostly physics and astronomy, and I read everything I could find on physics and astronomy when I was in grade school and high school. I didn’t think too much of mathematics, but I started college in 1960, and in the wake of Sputnik they had put in honors-calculus classes, and I managed to get into the honors-calculus class, and I just took to it.

I still remember when I first saw the rigorous definition of a derivative, which involves taking the limit of difference quotients to give meaning to an expression that looks at first glance to be zero divided by zero. I was so excited I turned to a friend next to me and said, “Are you allowed to do that?” I really loved that course and I did very well in it, and I switched my major from physics to math.

And what was your first mathematics job out of college?

I graduated from college and then I went to graduate school, and I spent a year at N.Y.U, New York Courant Institute, in New York, and then I married my college boyfriend and he was a student at Harvard, so I transferred to Brandeis University. And, actually, my first job after I finished Brandeis was a very exciting one. I was a postdoc at the University of California, Berkeley, during the Vietnam War, and that was a momentous event in my life.

What made it momentous?

The Vietnam War and demonstrations—the tear gas, the speeches, classes were cancelled one semester in the wake of Kent State, and it was . . . oh, and there was a lot of fuss about women, too, at that time.

What specifically do you mean by “fuss about women”?

I can’t really give a synopsis of the history of the doors in academia being open to women, but this was right at the time when women were being accepted into graduate school and given jobs, and a lot of people didn’t think that women were suitable and lots of things were said and lots of improper things done. And the University of California, Berkeley, was a very political place.

You said you were moved by the various political goings on at the time, which is interesting because you’re in a profession that I think most people think of as one of the least political things you could be doing. Did you see it that way? Or did you see mathematics as something different?

Well, the fact is I saw mathematics as something different, and I was kind of startled to find it juxtaposed with the political unrest next to it. I was startled to see the politics appear in the math department. It was eye-opening to me, what the world was like. I think up until that time I had seen mathematics as a very bookish thing and that what went on in the mathematical community had nothing to do with the life out there on the streets, and this is not true.

So how does it connect?

It’s done by humans, and all of what goes on between humans appears in the mathematics community, perhaps toned down quite a bit, but it’s not a world of pure brains, people behaving rationally and unemotionally. There are . . . I don’t know, I haven’t thought this question through. I’m sorry.

No, no, it’s fine.

This is a new question for me.

How did you feel like men were reacting to you, as this intellectually serious person? What was that like for you?

It’s really hard to describe to people who are not somewhere near me in age what it was like for women then. The women who had jobs during World War Two were fired. Men came home from the war, and women sat home. And it was only because of the women’s movement and books like Betty Friedan’s “The Feminine Mystique” that the consciousness came up that women could actually do other things. I figured if I’d been five years older, I could not have become a mathematician, because the disapproval would be so strong.

And I do have to say that, in being a mathematician, I’m lucky. I was a very good student, and I was a good mathematician. It took me a long time to realize it. And when I went one-on-one with people and talked to them, they recognized this and they accepted it and they accepted me. The broader world was not so accepting. That is, I sort of had the feeling that a lot of faculty wives in the early days were really very disapproving of women students, and the world out there was not so encouraging, but I felt that, as a very good student, I was accepted by my mathematical colleagues fairly easily.

Reading about your career, it seems like bringing more women into the field of mathematics and supporting them while they’re there are things that have mattered to you. How do earlier eras compare to this one?

There is no comparison. I don’t want to say the playing field is level. I don’t want to say all the problems are gone. I don’t want to say that there are not difficulties for women. But the landscape is completely different. And I actually was not involved in the beginning. When I started out as a student, it was clear that the way to become a mathematician was not to hang around with other women. So I made my way through my career and, at some point, I achieved a certain amount of fame and I looked around and talked with my other women colleagues and we said, “Where are the women coming behind us?”