Professor, I hope we can start at the beginning, relatively the beginning, so

I'm gonna ask you to be 10 years old again. Okay. Tell me where you are, and tell me a little bit about your family life. Well, I live in the country in northern New Jersey, about an hour north of here, and I'm the eldest,

well, my last sibling has just been born. My youngest sister was just born, and we were relatively isolated as a family. There were some kids down the street that we ended up playing with, but just another couple of little kids, and so I

didn't run around with packs of kids, and I had lots of time to myself, so I don't remember exactly how old I was when I started doing jigsaw puzzles and playing very long complicated games of double solitaire and daydreaming. And your own impulse, your own impulse to do this? I think it was disapproved of by my parents. My mother

didn't care for the jigsaw puzzles. Tell me about your parents. My mother was an artist, and my father was an engineer. They both got out of college in 1932, the first generation in their families to go to college, and 1932, as you know, was probably the

depths of depression, and I don't know, my parents never really talked that much about their upbringing, actually, but my mother was one of twelve children in the middle somewhere. Her father was a Methodist minister, and who died when she was about

five or so, and she was, I think, helped by an older sister to go to college, and she was studying art at the Art Students League when she discovered that she needed to make a living and switched to CCNY and

became a high school teacher. And my father was sent to MIT by his mother's sister who funded him at MIT, and I think he would have loved to be an academic, but economics were such, and so they both got out of

college in the middle of the Depression, and my father, the only job he could find was in the gold mines of California. Really? Yeah, so my childhood was overshadowed in some sense by the shadow of the Depression on my parents.

Right. How, this is the first of the questions, we'll see how many there are about the situation of being a woman. In this case, it's just a matter of parents' expectations for you. You are the oldest child. I'm the oldest child. So that can help in terms of ambitions, but are they pushing you in

any direction? Are they recognizing what clearly are your abilities? How are they thinking about you as you remember? Well, as I remember, I mostly, no, they did not push me. They pushed my brother, who was two years younger, and they had expectations

for him. And in fact, in my childhood, I remember playing with the blocks and Lincoln logs and the rector sets that my brother had. Right. And I was actually the tomboy, and he actually had difficulty with sports. And so, in some sense,

we were versed in roles, which was very unfortunate for him. In my case, I benefited from having the opportunities that he had. And I was the one that played football, touched football with the kid down the street.

And nobody is saying to you, that's not what girls do? Well, my mother was an artist, and my mother had some very interesting friends. So I don't think they approved, but they didn't come down on me hard about it. Let's put it that way. So back to the relatively isolated, in the best sense, person who could determine her own interests. So

there you are, not necessarily playing all the time because you have the puzzles to do and so forth. No, and I read. We went to the library every week, and I would come home with a big stack of books and stay up at night reading novels. Novels.

So you're not yet looking at physics textbooks. Well, I did when I got older, but no, when I was young, I was just reading. There was this wonderful little series of books of biographies. I've met some of the MacArthur fellows, I don't remember them. They were orange mostly, but every once in a while there was a turquoise one, and they were almost all men.

But every once in a while there was a woman, and I believe George Washington Carver was represented in them. And those were wonderful little books that I read my way through and wish there were many more. Is it fair to say, I placed you at ten, so maybe that's a little early for

ambition, but would you say that ambition was forming in you to do something worthy of a biography? Yeah, yeah, I think so. Well, it was really a question of having a relatively confined childhood. Certainly my mother took me into New York to museums and things, and I remember being taken to concerts every once in a while.

My parents were intellectuals in relatively un-intellectual surroundings, and we went camping every summer. The camping every summer was something that stands out for everybody in my family.

My father, who had a job in managing a foundry which was not suited to him at all, would sort of loosen up for the two or three weeks we spent camping up in the Adirondacks.

I think I'd better get you into school. And instead of going through all of it, of course, because we don't have the time, is it in elementary school, is it in junior high, high school, where perhaps you're either found as an intelligent young person encouraged by a mentor, or are you pretty much again shaping your own intellectual life?

Is there somebody to remember at this time who saw the talent in you? Actually, I don't remember. I've thought this through my life, and I actually do not remember being encouraged by people.

I was a good student, and I was very energetic and very curious. I do remember that I already had trouble keeping my mouth shut. That is, I'd get an idea and I'd want to talk about it. And it was much later in life I learned not to do that. I think I finally learned not to do that. I can keep quiet.

So I remember from a childhood having difficulty, having normal conversations, because I'd get all interested and excited and want to talk about something, and this was not the sort of thing that one did in suburban New Jersey.

And maybe a lot of other places. Right, I think so too. So, now I'm going to place you in the counselor's office at the end of your high school, determining what's next. How do you decide, if there was no one mentor, you're deciding yourself in a way, for the next stage?

Right. Well, I don't remember any guidance counselor, believe it or not, but it was assumed we would all go to college. My parents went to college. That was given. That was given, and I was interested in math and science, in science. Math doesn't really meet at that level, in high school level.

But I was interested in science, and my father at some point had brought home Fred Hoyle's books on cosmology. And I read them. I still feel guilty for the fact that I didn't work through all the arithmetic. I mean, about how stars form and all that, but I was fascinated by it.

And so, I wanted to study science. I wanted to study physics. You got into a pretty good university. Well, yeah, that's interesting, because for some, I remember distinctly the process, because my father had gone to MIT, his aunt had said him. And so, I applied to MIT. I applied to Cornell, because somehow or other, Cornell seemed like a romantic place.

And I applied to the University of Michigan. We had relatives in Michigan. And I got into all three, and I still remember making the decision not to go to MIT.

And I don't know to what extent it was influenced by my parents, but it was for economic reasons. I knew that it would be hard for my parents to pay the... Would it have been extremely unusual for a woman to be at MIT, or is MIT already... It would have been really unusual, which I can assure you, because I taught at MIT in 1968.

And you did not see... I am very glad I didn't go to MIT. I went to the University of Michigan, I got into the Honors Program, and a whole world opened up to me. I also was more comfortable in the Midwest. Somehow or other, the women there were different, or the girls, but...

Self-reliant, you mean? Well, more, I don't know, much less concerned with clothes and hair and stuff like that. Right, less of a Barbie doll culture. I think so, I think so. Or maybe that was just college, but I...

If I remember correctly, and of course it's your memory that counts, your first opportunity to choose a major was physics. I went there thinking I would major in physics. Okay. Although this may not be a very interesting question, what about physics in particular drew you?

Well, I've been fascinated by cosmology, and I was fascinated by quantum mechanics and particles. I understood the Bohr model of the atom at that point, and I was very interested.

But I have to say that probably the main thing that turned me away from physics was just not having good experience in the lab. And a lot of that had to do with the fact that you had a lab partner who wasn't very interested or didn't have the same attitude you did and stuff like that.

So, I know it's melodramatic to put it this way, but you had a conversion experience to mathematics. Yes, I did have a conversion. By the way, I should also add that I actually dropped my physics major the time when I was going to a lecture in which they took attendance.

And I was absolutely offended by this. Not that I was someone that cut classes all the time, but they took attendance in the physics lecture, and I dropped out of physics at that point. But, yeah, I was converted to mathematics my first semester in calculus. I want to hear about the conversion. What happened? Well, I still remember the first moment when I suddenly realized the power of mathematics.

I had actually not taken calculus in high school. There's a story behind that, but I'll maybe skip that. So, I knew how to compute some derivatives and integrals of polynomials, so I picked that up.

I remember going to a help session. My professor was Maxwell Reed. I went to a help session, and I still remember the name of the TA. It was Birdie Burl.

We'd done limits, and at some point in this help session, he showed us how to take a derivative. I remember that moment of excitement, saying, can you really do this?

Are there rules and ways of thinking that allow one this kind of power over this kind of thought? I still remember, well, at this point, it's remembering, remembering, I'm afraid, but I still remember the excitement. I remember turning to the fellow next to me and saying, are we really allowed to do that?

Okay, you're now a convert. What do you do about it? Do you formally take a mathematics major? Yes, yes, yes, and actually, I also was there since I lived in New Jersey.

I remember being in Michigan over a holiday and bumping into a math professor in an art museum. He had me grading his linear algebra class before I had taken linear algebra.

No. I think as a sophomore, they had me in a graduate algebra class, which I did not understand at the time, but three years later, when I came to take my prelims on the subject, it came back to me. It was kind of an interesting thing that you can actually sit through a class and not understanding it,

but a couple years later, it can actually make sense to you. It was a very interesting experience. Somebody is noticing you. That's right. I don't think I noticed being noticed, meaning I was very uneasy with myself and very awkward and very clumsy and felt out of place most of the time.

I've been escaping into books my whole life, so I basically was escaping into mathematics at this point. I believe that I was helped a great deal more than I was aware of at the time. Of course, I was not one of a group of people. I had a boyfriend who was a graduate student in mathematics,

so I fit into the culture fine. I fit into the community of mathematics, but I wasn't really aware of the fact that there were a lot of people who were pulling for me.

That was really true, especially in my undergraduate years. Is there one name we should put on the record as particularly important, at least as you looked around you? No, no. I had a whole series of completely different professors. They were all different.

They all were encouraging, though. I don't actually remember anybody telling me that I shouldn't do mathematics because I was a woman until I got to graduate school. Really, but if you looked around at other mathematics majors, were you seeing many other women?

There were, I think, two other women in my honors calculus class after two years of calculus, and I think both of them got PhDs. I did lose track of them, but there were, of course, no women, and I don't remember any graduate students being women.

My colleague Martha Smith at the University of Texas was, I think, two years behind me at Michigan, again in the honors program. So there were women students, and I remember the fact there were women students, so we weren't so strange as students.

There were no professors, and I don't remember any graduate students, actually. Were you required as an undergraduate in the honors program to do a thesis? No, no, I didn't, but I was in graduate courses. As I said, I actually sat in a graduate course as a sophomore, and I did my junior year abroad in Munich,

and again I had the benefit of these wonderful lectures in German, polished, gorgeous lectures of the sort that you never got back in the classes.

There was a difference between lectures, you see, and classes, and in Michigan I got classes. There I got these beautiful polished lectures. In German? In German. And your German was up to their... I do not have a good year for languages, but I took two years in German, and I was fairly fluent in German by the time I spent a year in Germany.

Okay, so we're going to graduate you. We're going to assume that you graduated with honors. I was, yes, I was. And now you face... Phi Beta Kappa is what they call it. Now you face the decision of somebody who is quite serious about her future as to where to go for graduate work.

Right, and I don't remember my... I ended up going to NYU. The factors involved were very complex because my boyfriend was going to Harvard in the East Coast.

NYU had a very good reputation for women. There was a man named Lippmann-Bears there, and he turned out a whole generation of women professors, and many of them you can talk to.

He was quite a remarkable man. He actually had left NYU by the time I went there, but NYU had this very good reputation for women. And also my mother had actually gone to school in New York, and I remember she lived on Christopher Street,

and there was some sort of attraction to New York, and it was close to New Jersey where my parents were. And so, but after a year there, I got married, and I moved to Boston where my husband was in graduate school at Harvard.

In that relationship, and now I'm merely speaking of the relationship, marriage now, to mathematicians. No, my husband was a biophysicist. His father was a very well-known physicist, Uhlenbeck, and in fact you will still run across the Ornstein-Uhlenbeck process as very important as statistical mechanics.

Okay, I'm going to revise my question to say two people developing careers, maybe not in the same field. Is there, as now we think about it, a disproportionate expectation that his career would be more important than yours in life planning?

I don't know. I would say taking my viewpoint throughout my life is that I'm pragmatic, and I can't imagine living with somebody who was unhappy. So I don't think I would press at any point in my life to do something that I thought would make the person I was living with unhappy.

And so the idea that he was marrying somebody who was intent on a career, as I assume you were. Well, I don't think it was possible to be intent on a career.

I mean, you know, there was a professor, Kathleen Morawitz at NYU, but she was somehow very protected by the faculty there, and her father had been a well-known mathematician.

And so she seemed somehow special. So I don't really know what I thought at this point. It didn't seem possible. But then, you know, this was post The Feminine Mystique and Betty Friedan, and things were changing.

So we're now 65, 66? Yeah, yeah. About that time. Yeah, 65. I would say that I was just taking one step ahead. I got an NSF fellowship. I had support for my graduate career.

And so I was actually just taking one step at a time, and I was interested in what I was doing. So I would say I was ambitious for the next step in doing mathematics. Very ambitious. Very ambitious. But I did not look down. If you'd asked me if I would ever be a professor, I would say no.

No. No, that's not important. If that had been important, I couldn't have done it. So I'm going to coin a phrase, and you tell me if it's right. You're driven by curiosity. I mean, it's the problems you're facing. Curiosity, also the knowledge that this is an age-old subject, that it's been developed before. There are many great people who studied it.

I mean, that was one of the excitements about it. You understood what the Heine-Borel theorem was. And this was, you know, these are people who came generations before you. So there's more to just plain being curious. It's fitting into some great picture.

Because you said that, I'm going to ask a question, or at least note, as a historian, I'm in a field where the past is the past. And by that, I don't mean what is studied, but even what is written. You know, it's superseded, but it strikes me with many mathematicians, I've had the opportunity to interview, that you live together with your antecedents. I mean, you have an ongoing conversation across the ages.

Yes, I think that's correct. Yes, yes, yes. And to me, that's thrilling to imagine a field that continues. Yes, very much so. Very much so. I think one does. And it changes with time.

And it never, I mean, even in the process of being interviewed for all this, I've made new connections with my past, with the past, which has been very enjoyable. Okay, so you married. Yes. You're moving to Boston now because your husband is at Harvard. What do you decide to do then?

I applied to Brandeis. I just was wary of going to Harvard or MIT. MIT because of your father? No, no, no, because it was, I would have been, I recently sort of lucked out, sort of understanding what it was I was wary of.

I was wary of being the woman. I wanted to be the mathematician who happened to be a woman. And I did not want to put myself in a position at one of these elite places where I was the woman.

The prized woman. I was, I would just be exceptional, I would be the exceptional, not because I was smart, not because I had ideas, but because I was female. Right. And I had some gut instinct to stay away from that. And I think it's what made all the difference in the world to my career.

So Brandeis didn't know that you were a woman? I'm sure they did. And they said something the first week. But yeah, and so I got a little, I got a flack, but it disappeared very rapidly. And you know, I've actually really just had this insight. My professors were 10, 15 years older than I was, if that.

At Harvard, they would have been 40 years older than me and have all this career, would not have many women students. Well, I had young professors who maybe didn't even have that many students. And so a woman shows up, well, you know, it's just a student. That's right. It's exactly that. And so it was, it was really a, I mean, I feel that,

you know, I'm here right now today, partly because I sort of, I made some very lucky choices. Yes, that was. Let me assume you're being noticed at Brandeis. Yes, yes, yes.

Are there particular professors who are influencing you in the direction you're going to take? Well, certainly my thesis advisor was a tremendous influence. I mean, Richard Pallet. And at that time, and it was also the field that he represented to me at that time that excited me.

This was a period of time in which a big change occurred in the way partial differential equations, even ordinary differential equations, partial differential equations, and calculus of variations problems, and all sorts of classical fields, which had been basically described with lots of, lots of indices, lots of functions.

Mostly written in coordinate space. And the field, the field was developing, but at that point,

it took a turn that really, I'm still seeing the effects of some 50 years later. Yeah, and I don't, it was a change in perspective. And the way I can describe it is, is that

functions, instead of being regarded as the one variable dependent upon another, functions themselves became points in an infinite dimensional space. This is a revelation of the time?

Well, it was something that happened slowly. For instance, you see it already in quantum mechanics, where quantum mechanics is described in terms of functions, but they're points in a Hilbert space. And so it had its origins already, but I did nonlinear analysis, and quantum mechanics is based on linear

analysis, but of course the work in linear analysis that was done was actually very foundational at that time. And I mean, the exam, I can give you examples of how you saw this happen. For instance, there's

the Atiyah-Siger index theorem that says you can treat operators which map one set of functions to another, that's one infinite dimensional space to another, we're given a framework where they could be thought of as like matrices.

And that's a very important point. And my thesis advisor had been very involved in the development of this. In fact, he had written a survey, collected a bunch of lectures and written a survey volume on the Atiyah-Siger index theorem.

And he, together with Steve Smale, developed a condition where calculus of variations problems, which are functions on an infinite dimensional space, these calculus of variations problems could be treated like finite dimensional calculus problems.

How did you determine the problem for your dissertation? Well, my problem for my dissertation basically grew out of my thesis advisor's interest in the calculus of variations. He gave lectures on the calculus of variations and wrote notes, and I remember proofreading the notes. I was a terrible proofreader too, so I wasn't good at everything I did.

But anyway, so in the wake of work, there was a lot of technical things that I did in my thesis, like putting metrics on infinite dimensional manifolds and proving certain kinds of functions satisfied certain conditions and so forth.

My thesis was long and fairly complicated, and it gave me a very solid grounding in this viewpoint of really function spaces are really just an elaboration of finite dimensional spaces that you can learn to think of like that. But I don't think my thesis was in itself at all groundbreaking.

Okay. But I had, I had been. And then I actually finished a year earlier than my husband did. And there was some difficulty finding me a position for a year.

Okay, now, obviously, you are now career oriented. I mean, you have a PhD, you have to look for a job. But before we get into that, either dilemma or opportunity, I want to ask a very general question about, and maybe there's no answer to this, about mathematics and collaboration or individual isolated thinking.

As you as you went toward the influence of your professor, your advisor is clear. But are you surrounded by a group of graduate students? And are you thinking together? Are you thinking in isolation?

I there are some other graduate students, and maybe a young postdoc who were trained in the same kind of thinking I was, but I don't remember. I do remember the postdoc gave a

course on dynamical systems, and he still remembers me keeping him honest about the proof of very basic theorem. So we certainly had, I certainly had contact, but I did not talk that about mathematics to other people. I talked about it to my thesis advisor. Right. But I and I also should say at this time, there I certainly had another influence on me, which was my

husband's father, George Uhlenbeck, who is a very well known physicist, and who had a lot of opinions about mathematics and physics. But I also got an insight into academia a little bit through him. And, but I also remember a lot his opinions about math and physics and so forth.

So I would say, certainly at that time, my thesis advisor was also interested in physics, but through my husband's father, I became more and more interested in physics.

I certainly, for instance, I did, I actually, strangely enough, sat through the chemistry quantum mechanics course at Harvard with my husband, who was taking it, because it was not the natural thing for a mathematician to do, but the opportunity was there, and I did that.

So I was already thinking in terms of, I wasn't thinking narrowly. I did not, I really, I chose my thesis advisor and my thesis topic because it seemed a real, really a big opportunity.

I do remember saying, you know, I'd rather do this than prove some special case of some special boundary value problem for some technical thing. Am I allowed to introduce the word ambition now? Well, I've been ambitious for a long time, but I was intellectually ambitious. You're bringing this up to me, and I don't

think I ever recognized this before, but it really wasn't possible to be ambitious to become a professor or become somebody famous. But it was possible to be ambitious intellectually, and I've always been ambitious intellectually, and this, I mean, I've always

read, most of my career, I've always read a lot, and I've always been interested in a lot of things. Don't you want a job now? Well, I haven't, I get, well, I was somebody's wife.

Did I want a job? I don't, I want to, I did the next thing in each step, at every step, at this point I did the next thing. Well, I got my PhD, and I needed a temporary job, and we looked for one in the area, and

I almost got one at Boston College, but then at the very last minute, MIT offered me some sort of instructorship. They, they remember it a lot more glamorous than it was because they have some, they

have some fancy instructorships, and I was a regular instructor, I was a regular plebeian instructor there. But, but As a mere instructor, what were you going to be doing? Well, I went to seminars, and I taught two semesters, I taught, I taught, I taught, I

remember teaching ordinary differential equations, and I went to a lot of seminars, and I sort of felt I was on the fringes of something very exciting, but I never felt in the middle of it. Right. But I do remember I met Nancy Coppell there, Nancy Coppell was a more instructor, and she had been at Berkeley with, and

so I did, there was another, suddenly there was another woman in this surrounding environment of global analysis, is what it was called then. So, since you're a wife as well as an intellectual, is your husband's, are your husband's job prospects good?

Oh yeah, he was, he was biophysics at Harvard, and you know, at the top of, and very ambitious, I should say. As was appropriate for men of the time.

Right. How are you now, get me to a point where you actually can become a member of a faculty, what does it, what does it take, how many years of intellectual wandering, not in terms of your interest, but in terms of your career?

Well, the introduction to the career really came at the University of California Berkeley, which is where my, I went after one year at MIT, I went to the University of California Berkeley, this is 1979, 19, sorry, 69. Yeah, during the Vietnam War, and so my eyes were open to a lot, a lot of demonstrations, a lot of

professors behaving in ways that I hadn't expected professors to behave at all, and a lot of pressure about being female.

I don't know exactly, and I still don't understand, it was an extremely uncomfortable situation to be in, because this is the place where I suddenly became the woman. There were two of us, Lenore Bloom and myself, we were both instructors or whatever, you know, position they gave to new PhDs, and somehow or other there was controversy about everything.

And some of the people were saying, these are brilliant people, make them full proof, I mean, give them all the opportunities, and some of the people would say they should be home keeping house, and having children.

And this would be said in faculty environments? Yes, yes. Well, I don't know, I wasn't in the faculty meetings, I'm sorry, I don't know, but it was all over the place. You felt it? I felt it all, well, and it was said to me. It was said to you? I'm getting the feeling that just because it's said to you doesn't mean you're going to believe it.

So how are you going to get out of this mess? I mean, the mess of a limited prospect at Berkeley? Well, you know, here, the European tradition that my husband's family was in held good stead, I just clung to the fact that, you know, there's an

intellectual tradition out there, and it doesn't matter whether you have a job or not, I'm part of it, and it's, and I'll just do the next thing. And, you know, I don't know whether, it's probably not appropriate to tell this story here, but I'll tell it anyway, because it's typical of what would happen.

See, so I went in at the beginning of my second year, and I said, my husband wanted to stay in Berkeley. And he, you know, he was in a position where he could move up on the ladder, in the lab he was in, and so forth. And I went in and I said, do I have any chances for staying on in Berkeley?

And I remember distinctly told exactly how I was told, I was told epsilon chances. And I'm a mathematician, I know what epsilon means. And so I went home and told my husband, no, we'll look for a job somewhere else. And we looked for jobs elsewhere. Together. Isn't this against nepotism rules at the time?

It was, and we ran into that. And that, there's some unpleasant situation. And by the way, most of those nepotism rules were only hearsay, they were actually not legally on the books. Really? Yes. Anyway, but I don't, I don't know, I, this was a very disturbing time in my life.

And so, and so my husband did not take the best job he could get. We went to, and so I guess by now, but by now we were thinking in terms of both having a career. So we went to University of Illinois in Champaign-Urbana, and there was some fuss about my job there too.

I, I don't, you know, it was, it was, and also there were something like four faculty wives who were mathematicians who were teaching calculus. And had PhDs in mathematics. And here I was, you know, the only one in a regular faculty position.

Which the other women did not particularly... No, it wasn't done. Well, no, I wouldn't want to say it doesn't support. They were mostly older than I was. And I never became very friendly with the other women there, but I don't, I really didn't...

They didn't resent you? They did not resent me. No, no, no, they did not resent me. But I don't know. On the other hand, I was, I was actually quite uncomfortable. Very there. Because there really wasn't any role for me except as a faculty wife.

That was, at least that was, that was sort of what I felt. Now, how is this affecting your intellectual work? Actually, I did great. I don't have any idea how during the Vietnam War and my years at Champaign-Urbana, and the next years, my marriage broke up, I, you know, got a new boyfriend and all that,

and I have no idea, but I was, I was, I remember, I was very interested in some problems about, that came from general relativity and the incompleteness of space-time and singularities and space-time and spending. My husband would work in the lab at night

and I would go to the chemistry library and take the proceedings of the Royal Society down and read Hawking and Penrose on this. So I was, part of it is that I've always, my husband was very serious,

professionally serious, and I was serious. What is the public, publication sequence, I mean, where you're beginning to tackle, well you've been tackling serious problems all along, but you're developing intellectual curiosity in various ways. Do you publish much at this point?

Yeah, I publish quite a few things, but at that time, those papers became actually quite well known. But at that time, I was actually thinking by myself, which is, I mean, it wasn't like I was working with a bunch of people and solving a problem,

it was somehow or other I'd hit a problem and I'd say, oh, I have the tools to handle that, let's see how we can do it, and I would do it, and I remember publishing, writing papers and publishing was kind of nightmarish for me. I felt very isolated when I did it, but I did it. You did it, and somebody read it. Well, somebody read it, there's a paper, yes, people read it, I mean,

and some of those, one of those papers, very early papers, is still quoted when you go to seminars on eigenfunctions of problems. So how can I get you to a happier place in your career?

It's not working at this point in terms of the classic advancement. Well, yeah, I don't know. It isn't working at this point. And so, at this point, my marriage broke up and I picked up a new boyfriend, my present husband, Robert Williams, who was quite a mathematical character,

there's a whole story, he has an interesting story, too, but he was a little bit of a wild card, he was a mountain climber, but also even more, very intellectual, in fact, if anything,

he's more intellectual than I am, so we, and we became drinking buddies and intellectual buddies, and we traveled, and I spent a couple, a semester at Northwestern as a visitor, and then I got a job offer from the University of Illinois at Chicago,

where I had female colleagues, and where I felt quite comfortable, and I started talking mathematics with people, the mathematician next door to me was Howie Mazur, who did Teichmuller theory, and I started learning some mathematics about Teichmuller theory from him,

and so I was, I was uncomfortable when I was at the University of Illinois in Chicago, it was a city university, the faculty wives were unheard of, you're in the middle of the city, I mean, you have one math party a year or something,

and I had female colleagues. How do I get you on a tenure track somewhere? Oh, I'm sorry, I got tenure, I got tenure from Urbana-Champaign. You did? Yeah, yeah, yeah, I was, I don't remember exactly whether I got it before I left or after I left,

but I mean, in the process of, by moving around at that time, I got tenure. So you're a tenure professor now wherever you go? Yeah, yeah. That's an advance. That's an advance. Well, you know, in fact, I'm sorry, but I did not really want tenure because I did not really want to live the life,

I mean, so it was not a big occasion for me. Really? Right. It was not a big occasion for me, I thought, well, you know, tenure, I might be doing this, you know, I might be entertaining, I might be a faculty wife for the rest of my life. Okay, so tenured in spite of herself.

Yes, it was, that was really the way it seemed to me, in fact. Now I need to get you, two things, I need to get you to a breakthrough moment in your mathematical inquiry, and I need to get you to Texas. Okay, well, actually, the first breakthrough moment really came

when I was, at the end of my career at Champaign-Urbana, a postdoc, Jonathan Sacks, from the University of California, Berkeley. He was, I never knew him there, I guess he must, we did not overlap, so I don't really know, came and we started talking

and he talked to me about minimal surfaces and minimal spheres and I had not thought about this problem before and at some point I realized it was very close to the things I've been thinking about in my thesis and I realized that making a small perturbation from the problem

that we were trying to solve, I could solve it from my work very easily with this work in my thesis and all the machinery there and so we sat down and we wrote a couple papers on this, how to do this perturbation and actually come up with solutions to the problem.

So this is really the bubbling process. What happens is you have a slight modification of the problem that you can solve and then you look at the limit and what happens in the limit is you get a solution which might be trivial but you also get some places where the solution doesn't converge

and you look at them, you think of it as being bubbling and you actually look at it under a microscope and lo and behold, you can see a whole solution on the plane. So I certainly feel Jonathan sort of changed my life at this point

and so this was the first breakthrough I had. It feels like a breakthrough at the moment? Or is it only later on when the implications? Oh, I had no idea that 40 years later people would actually cite this paper.

I had no idea about this. It seemed to me it was just, in fact, the subject in mathematics was not as large as it is now. See, I'm talking about a revolution that I was part of and that form of mathematics, that nonlinear analysis applied to geometry and topology and algebraic geometry and so forth

came about through this process when before I was a graduate student, through my graduate student days, and the subject, you know, it was very noticeable that in 19, we're about 1980 or so,

there were no, the major graduate schools didn't have anybody in this subject. Whereas now, if you look around, all the major graduate schools have lots of people in these subjects so you can just sort of track what fields people are studying

to see how it's changed. And so I was really well poised at the beginning of this and really took part into it and it was very exciting intellectually. I mean, I didn't see it going anywhere for me personally, but intellectually it was very exciting. Now I want to get you to Texas.

Okay, okay. Well, I had a second breakthrough when I started working on gauge field theory and I solved a problem that the physicists really wanted to know the answer to. So I could go back into the relation of math and physics here if we wanted to.

And so at some point, I got a job at the University of Chicago. Now this is the first big significant acknowledge. It's the University of Chicago. The University of Chicago made me an offer and I was living in Chicago and I liked my job at Chicago, University of Illinois-Chicago,

Chicago Circle we called it. But I wanted graduate students. And so I went to the University of Chicago and I did get graduate students and that was... I interviewed one mathematician in this series who loved, who was at an institute much like this,

where you are right now as a visitor, and he loathed the idea of graduate students. My question was basically, don't you miss them? Yes, I do miss them. You do? So tell me about graduate study from the point of view of the professor.

Are your ideas helped by graduate students? Are you mostly just encouraging them in their own inquiry? I guess I have a very special view about it. And that is that I try to have some ideas

and some problems that I even... I don't know, that I think I might be able to do, but I don't know. And they look interesting, and that I would think were worth doing. Meaning, not something that I don't want to do,

but something that I really think you could pursue. And I try to give it to the graduate student. And sometimes you go through... It always changes. It's never the same problem when it comes out the other end. And let the graduate student do whatever with it.

And the fact is that your ideas are never quite right, but if you and the graduate student are lucky, there's really something there. And it will also fit the student's personality and interests and so forth.

That is directing the student and helping them. Right. What about the intellectual blowback in your own work? Do you find that it is affected by graduate students? You know, I don't know. I've never asked that question to myself.

I haven't. Actually, the answer is if I'm thinking about it, I tend... I have a rule about things. That is, I'm not allowed to think about the graduate student's work unless he or she is in the room.

I mean, I don't want to get in the way. I want to be there. And I'm allowed to think about it for that hour or two. Right. But I'm not... So the answer is that it helps you intellectually, just overall. It helps you... I mean, it helps you like...

Look, I love going to hear a Beethoven quartet. Right. And all this, I think, contributes. I don't think that my mathematical brain is in any way separate from the rest of my brains. But I don't see the immediate interaction with students as contributing to the problem that I'm working on at the time.

We're almost at the end of our time, so I'm not going to get you to Texas, but that's fine. That's fine, because what I want is the launching and the thinking around the key moments. But I want to ask a question of you, and this is about what you think you have done or helped to do or wanted to do for women

so that they don't encounter some of the idiocies you did at your younger point. I mean, you've actually taken an active role in creating... Was it at this institute?

Yes, yes, yes. It was here. I've actually worked at Texas also on women's issues, but the point is that I think, along with everybody else, that when the laws changed in the 60s and 70s and so forth, that the assumption was that women and minorities would simply march through the doors and take their rightful places in academia.

And I was not involved in women's issues. You didn't want the category. Well, my experience at the University of California Berkeley was not good.

But around 1990 and so forth, myself and other women... So when I entered into academia, I was with a group of women who got jobs at that time. But we looked around and we said, where are the rest of them coming?

The doors are not open. The academia is not flooded by women or minorities, for that matter. And those of us, well, I was established in my career, so I could do something.

And when somebody like the Institute for Advanced Study gives you secretarial help, money and space and support and so forth, you're crazy to turn it down. And I also, my collaborator, Julianne Turn, came in and we worked together on it, so I wasn't working by myself anymore.

I had somebody to work with, which was a great experience. It's a big question and not much time, but you said you had to do something. Why weren't women and minorities flooding through? Because it's a very much more complicated question than law. And I don't want to even pretend to enter into it.

But you can, well, it's interesting, here I've heard several talks by women about women advancing in the art world and so forth, where the social justice issue is much more closely tied to it.

But there are a lot of people who have said a lot of things about why women are not represented. And I do think that the question of women being represented in math and science versus, say, the senate or the art world or the composers and symphony conductors,

I really think that to isolate and say women in science and separate it from this is a real mistake. I don't think there's any evidence that women in science and math have any more difficulties than women in other professions. That's the last word. Thank you very much.