The HLF Portraits: Karen Keskulla Uhlenbeck

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Video in TIB AV-Portal: The HLF Portraits: Karen Keskulla Uhlenbeck

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The HLF Portraits: Karen Keskulla Uhlenbeck
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Process (computing) Generating set of a group Block (periodic table) Multiplication sign Direction (geometry) Physicalism Student's t-test Peg solitaire Expected value Term (mathematics) Right angle Game theory Acoustic shadow Series (mathematics) Musical ensemble Family
Point (geometry) Computer programming Theory of relativity Process (computing) Multiplication sign Decision theory Physicalism 3 (number) Student's t-test Mathematics Many-sorted logic Energy level Normal (geometry) Right angle Extension (kinesiology) Family
Point (geometry) Trail Computer programming Polynomial Group action Sine Beta function Divisor Euler angles INTEGRAL Multiplication sign Decision theory Insertion loss Student's t-test Rule of inference Hypothesis Power (physics) Expected value Force Derivation (linguistics) Mathematics Goodness of fit Many-sorted logic Different (Kate Ryan album) Theorem Series (mathematics) Körper <Algebra> Algebra Curve fitting Social class Process (computing) Cohen's kappa Generating set of a group Moment (mathematics) Model theory Physicalism Linear algebra Calculus Faculty (division) Connected space Arithmetic mean Physicist Quantum mechanics Right angle Mathematician Statistical mechanics
Point (geometry) Axiom of choice Classical physics Finitismus Functional (mathematics) Group action Multiplication sign Direction (geometry) Archaeological field survey Student's t-test Perspective (visual) Dimensional analysis Hypothesis Frequency Partial differential equation Mathematics Mechanism design Many-sorted logic Term (mathematics) Different (Kate Ryan album) Operator (mathematics) Manifold Matrix (mathematics) Theorem Körper <Algebra> Nichtlineares Gleichungssystem Position operator Set theory Condition number Prisoner's dilemma Mathematical analysis Infinity Volume (thermodynamics) Calculus Price index Grand Unified Theory Calculus of variations Quantum mechanics Linearization Right angle Metric system Mathematician Bounded variation Funktionenalgebra Spacetime
Point (geometry) Group action Dynamical system Multiplication sign Student's t-test Hypothesis Mathematics Mechanism design Many-sorted logic Thermodynamisches System Term (mathematics) Boundary value problem Theorem Set theory Position operator Area Process (computing) Ordinary differential equation Physicalism 3 (number) Faculty (division) Differential geometry Proof theory Physicist Quantum Pressure Mathematician
Point (geometry) Geometry Trail Observational study Multiplication sign Gauge theory Neue Mathematik Student's t-test Regular graph Mereology Rule of inference Theory Hypothesis Mathematics Plane (geometry) Many-sorted logic Minimal surface Term (mathematics) Modulform Körper <Algebra> Series (mathematics) Algebra Position operator Process (computing) Moment (mathematics) Mathematical analysis Physicalism 3 (number) Maxima and minima Lattice (order) Calculus Perturbation theory Limit (category theory) Surface of revolution Sequence 19 (number) Sphere Faculty (division) General relativity Network topology Physicist Mathematical singularity Right angle Mathematician Family Spacetime
Point (geometry) Group action Process (computing) Multiplication sign Moment (mathematics) Physical law Student's t-test Rule of inference Flow separation Arithmetic mean Mathematics Right angle Spacetime
Mortality rate
[Music] you professor I hope we can start at the beginning relatively at 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 my I'm the eldest while 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 an 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 enhance your own involved I think was disapproved of by my parents my mother didn't care for the jigsaw puzzles Wow tell me 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 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 switch 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 yeah so my childhood was was overshadowed in some sense by the shadow of the depression on my parent right how this is the first of the questions we will see how many there are about the situation of being a woman in this case it's just the matter of parents expectations for you you are the oldest child and the oldest child 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 know 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 live rector sets that my brother had and and I was actually the tomboy and he actually had difficulty with sports and so in some sense we were reversed in roles which was very unfortunate for him in my case I benefited from from having the opportunities that he had and I was the one that played football with the touch football with it 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 let's put it that way so back to the relatively isolated in the best science person who could determine her own so there you are not necessarily playing all the time because you have the puzzles to do and so when 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 novels so you're not yet looking at physics textbook well I did when I got older but no one when I was young I was just reading I read there was this wonderful little series of books of biographies I don't either I've met some of the MacArthur fellows I know remember them they were orange mostly but everyone so others at turquoise one and there 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 who are wonderful safe little books that I read my way through
and wish there were many more isn't it fair to say it's 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 to do something worthy of biography yeah yeah I think so well it was 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 a relatively unintellectual surroundings and so and we went camping every summer and I mean the the camping every summer was something that stands out for everybody in my family my father who had a job and if not managing a foundry which was not suited to him at all would 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 yes 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 your other found as a 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 and 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 but people I was a good student and I was very energetic and very curious and very III do remember that I already had trouble keeping my mouth shut that is I'd get an idea and I want to talk about it right and it was much later in life I learned not to do that I think that I finally learned not to do that I can keep quiet but so I remember from from a childhood having difficulty having normal conversations because I'd get all interested in excited and want to talk about something and this was not the sort of thing that one did in suburban New Jersey right I think so too but so now I'm going to place you in the counselor's office at the end of your high school determining what what's next I mean how how do you decide if there was no one mentor you're 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 okay that was that that was given and I was interested in math and science and science math one 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 Hoyles books on cosmology and I read them I didn't I I still feel guilty for the fact that I didn't work through all the arithmetic I mean about about how stars form and all that but I was fascinated by and so I I wanted I wanted to study science I wanted to study well yeah that was that's interesting because for some I remember distinctly the the process because my father had gone to MIT is is his aunt had said him and so I applied to MIT I applied to Cornell because somehow or other Cornell with it 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 was influenced by my parents but it was for economic reasons I knew that my that would be hard for my parents to pay though would it have been extremely unusual for me 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 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 the the women there were different or the girls but they were self-reliant well more I don't know much less concerned with clothes in here my stuff like that'd be much right unless the barbary bother yeah yeah yeah I think so I think so or maybe that was just college but I if I if I remember correctly and of course it's your memory that counts you first opportunity to choose a major was physics I I went there thinking I would major in physics physics okay um although this may not be very interesting question what about physics in particular drew you well I I've been
fascinated by cosmology and I was fascinated by by quantum mechanics particle but and you know the kind of I I understood the Bohr model of the atom at that point and I was I was very interested but I I have to say that that the 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 might wasn't very interested or wasn't didn't have here the same attitude you didn't like that but so I know it's melodramatic to put it this way but you had a conversion experience the mathematic yes I did have a commodious yeah I should I should oh 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 to cut classes all the time but they took attention sin the physics lecture and I dropped out physics at that point but yeah I was converted to mathematics on my first semester and I want to hear about the conversion what happened well I was variant I still remember the first moment when I suddenly I 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 and so I didn't know I knew how to compute in some derivatives and integrals of polynomials so I wasn't I wasn't I picked that up but I remember going to a help session my professor was Maxwell Reid and I went to a help session and I still remember the name of the TA was Bertie burrows and at some point we'd done limits and at some point in this help session he showed us how to take a derivative and I remember that moment of excitement of saying can you really do this I mean is there a can is there a rule of are there rules and way thinking that allow one this kind of power over this kind of thought and I still remember well at this point it's remembering remembering I'm afraid but but but I still remember the excitement I remember turning to the the the the fellow next to man saying we really allowed to do that and so ok you know a convert what do you do about it you you formally take a mathematics major yes yes yes and actually I also was there since I was lived in New Jersey I remember being in Michigan over a holiday and bumping into a math professor in a art museum and he had me grading his linear algebra class before I had taken linear algebra and so and I 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 it 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 very interesting experience somebody is noticing you that's right and you know 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 and I think see I've been escaping into books my whole life and so I basically was escaping into mathematics at this point and I don't I believe that I was helped a great deal more than I was aware of a long time I mean I and of course I was not one of a group of people I was pretty much as a mathematical was a graduate student in mathematics so you know I felt I I fit into the culture yeah I fit into the community of mathematics but I didn't realize entrie aliy aware of the fact that there were a lot of people who were pulling for me and 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 if not no no no I I mean I had a whole series of completely different professors they were all different and they were all were encouraging though I don't actually remember anybody telling me that I shouldn't do mathematics because I was a woman till I got to graduate school really but if you looked around other mathematics major we're seeing many other there were there was 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'm not sure that and I I did lose track of them but there was no women and I don't remember any graduate students being women but I do remember you know my colleague Martha Smith at the University of Texas was I think two years behind me at Michigan as an again in the Honors Program and so there were women students and I remember the fact there were women students so we we weren't so strange as students there were no professors no professors and I don't remember any graduate students you are required as an undergraduate and the Honors Program to do with thesis no no no I didn't but I was in graduate courses as I said I actually sat in a graduate service course as a sophomore and I went 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 and it was a difference between lectures
you see in classes and in Michigan I got classes there I got these beautiful polished lectures German in German and your German was up to there I mean I'm not I do not have a good ear for languages but I took two years of German and I was fairly fluent in German by the time I spent a year in Germany okay so we're gonna graduate you we're going to assume that you graduated with honors I was yes I was now you face AI Beta Kappas now you face the decision of somebody who's quite serious about her future it's to where to go for graduate work right and I don't remember my I ended up going to NYU the the factors involved were very complex because my boyfriend was going to the to Harvard in the East Coast and why you had a very good reputation none for women there was a man named Lippmann varus there and he turned out a whole generation of women professors and my my and many of them who can you can talk to about that was he was quite a remarkable man he wasn't actually had left NYU by the time I went there but NYU had this very good reputation for women and after and 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 I 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 two mathematicians know my husband was a biophysicist his father was a very well-known physicist in fact you will still run across the Ornstein and breakfast is very important in statistical mechanics okay I'm gonna revise my question to say to people developing career yes thank you 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 you taking my viewpoints 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 so and so the idea that he was marrying somebody who was intent on a career as I assume you were well I wouldn't I don't think it was I don't think it was possible to be intent on a career call okay I mean you you know there was a professor and Kathleen marwat's at NYU and she was but she was somehow very protected by by the faculty they are and her father had been a well known mathematician and so she was seems somehow special so I I don't I don't really know what I saw at this point I didn't seem possible but then you know this was post The Feminine Mystique and Betty Ford and and changes 65 66 65 65 sisters oh yeah okay so so I I would say that I was I was just I was just taking one step ahead I got an NSF fellowship I had support from 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 wasn't really ambitious I was ambitious for the next step in doing mathematics very ambitious very ambitious but I was not and did not for I did not look down I would if you'd asked me if I would ever be a professor I would say oh no no no no that's not important if that had been important I couldn't have done it so I'm gonna go in a phrase and you tell me if it's right you're driven by curiosity I mean it's me what are the problems you're facing curiosity loss of 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 excitement's about it you understood what the Heine Borel theorem was and this was you know these are people who came generations before you and so there's there's more to just plain being curious it's fitting into some great picture because you said that I'm gonna 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 it's superseded but it strikes me with them many mathematicians I've had the opportunity to interview that you'll you live together with your antecedents I mean you have a an ongoing conversation across the ages yes I think that's correct yes that's really yes very much so very much so I I think one does and and and it changes with time and it never mean even in the 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've married yeah you're moving to Boston now because your husband is at Harvard what do you decide to do that I applied to Brandeis I I just was wary of going to Harvard or MIT III my team because of your father oh no no because it was I would have been I I recently sort of lucked out sort of understanding what it was I was wary of
I was wary of being the woman I didn't I want it to be the mathematician what 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 you I would just be exception that would be the exceptional not because I was smart not because I had ideas but because I was female right and I 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 sure they did and they said something the first week but yeah and so I got a little I got a flat I got flack but it disappeared very rapidly and you know my perfect I just had this insight my professors were Ted 15 years older than I was of that at Harvard they would have been 40 years older than me and have all this career would not have many women's students well I had young professors maybe didn't even have that many students and so a woman shows up well you know it's just 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 I made some very lucky choices that was let me assume you're being noticed at Brandeis yes yes are there particular professors who are influencing you in the direction you're gonna take well certainly my thesis adviser was a tremendous influence I mean Richard Pele and at that time and 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 differ two 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 the the field the field was developing but at that point it took a turn that really I'm still seeing the effects of some fifty years later really yeah and I don't it was a change in perspective and the the way I can describe it is is that functions instead of being regarded as the one variable dependent on 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 it at first as you see it already in quantum mechanics where where quantum mechanics is described in terms of functions but they're points in a Hilbert Urbana a Hilbert space and so you it had its origins already but I did nonlinear analysis and quite a mechanics is based on linear analysis but of course the work in linear analysis that was done was actually very found a foundational at that time and I mean the the exam I can give you examples of where how you saw this happen for instance there's the teasing or index theorem that says you can treat opera 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 this like matrices and there that's the very important point and my thesis adviser had been very involved in the development in fact he had written a survey set of lecture collected a bunch of lectures and witness survived volume on you teasing rated X theorem and he together with Steve snail developed a condition where calculus variations problems which are functions on an infinite dimensional space these calculus of variations problems could be treated like finite dimensional calculus problems oh did you determine the problem for your dissertation well my problem for my dissertation basically grew out of my thesis advisors interested 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 proofread or two so I wasn't good at everything thank you but anyway and so in the wake of that work there was a lot of technical things that I did in my thesis like putting metrics infinite dimensional manifolds and proving certain kinds of function satisfied certain conditions and so forth I don't think that 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 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 and okay now obviously you are now career oriented in having your 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 you a very general question about it 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 adviser is clear but are you surrounded by a group of graduate students and are you thinking together
are you thinking in isolation there are
some undergraduate students and maybe a young postdoc who were trained in the same kind of thinking I was but I don't remember I 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 husband's father knew 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 to me that my husband's father I became more and more interested in physics I mean I certainly for instance I did I actually strange strangely enough set to 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 I it what the opportunity was there and I did that so I I was already thinking in terms of I wasn't thinking narrowly I did not I I really I chose my thesis advisor and my thesis topic because it seemed a real really a lot of big opportunity I I do remember saying you know I I'd rather do this than prove some special case of some special boundary value problem for some technical things am I allowed to introduce the word ambition now why I I was I I was I've been ambitious for a long time but I was intellectually ambitious III you're 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 read I've always read most of my career I've always read a lot and I've always been interested in and every in a lot of things don't you want a job well I haven't I get well I was somebody's wife did I want a job I don't I want it I I did the next thing in their step at every step at this point I did the next thing well I got my PhD and I needed it I needed a temporary a job temporary job and that 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 instructor ships that I was a regular instrument I was a regular plebeian instructor there but but it as a mere instructor well what were you going to be doing it well I went to seminars and I I taught two semesters I taught I taught I taught I remember teaching ordinary differential equations and I went through 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 Koeppel there Nancy Koeppel was a more instructor and she had been Berkeley with and so I did there was another one suddenly there was another woman in this surrounding environment of global analysis is what it was called there 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 at the top of and very ambitious I should say as was appropriate for men Yeah right how are you now get me to a point where you actually can become a member of a faculty what is it what does it take how many years of intellectual wandering not in terms of your interests but in terms of your career well the introduction to the career really came at the University of California Berkeley which is where my my I went after one year at MIT I went to University of California Berkeley this is 1979 during 1969 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 and a lot of pressure about that went being women female I don't I don't know exactly and I said 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 Leonor bloom and myself we were both instructors or whenever you know position they gave two new PhDs and somehow or other there was controversy about everything well examine that people were saying these are brilliant people make them foolproof I mean give them all the opportunities and some of the people would say they should be home keeping house and having child this was he said in faculty environments yes 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 roses I felt it all I wanted it was said to me I'm getting the feeling that just because it 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 they're 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 climbed 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 it's and I'll just do the next thing and you know the 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 did he you know he was in a position where he could move up on the ladder on the glad he was in and so forth and I went in and I said why do I have any chances for staying on at 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 well look for a job somewhere else and we looked for jobs elsewhere together together isn't this against nepotism rules it was and we ran into that and that there's some unpleasant situation and by the way most of those repetition rules were only hearsay they were actually not legally on the books really yes anyway but I 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 and so I guess by now but by now we were thinking in terms of both having it both having a career right so we went to University of Illinois at champaign-urbana and there was some fuss about my job there too III 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 so the other women did not know it wasn't Sam or it wasn't well no I I won't want to say that doesn't support they were mostly older than I was and I ever became very friendly with the other women there but I don't I really didn't resist they did not resent me no no no no they did not resent me but I don't know on the other hand I was I was actually quite uncomfortable they're very there because there really wasn't any role for me except as a faculty wife that was that 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 year so by marriage broke up by 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 the singularities in space-time in 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 these but we walking in Penrose on this so I was part of it is that I've always my husband was a was very serious professionally serious and I was serious and what is the public publication sequence I did where you were 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 of this yeah public ID I published 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 I mean it wasn't like I was working with a bunch of people in solving a problem it was somehow or other I'd hit upon 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 was kind of nightmarish for me I mean I felt very isolated when I did it but I did it and and well somebody read it I it's there's a paper yes people people read it I mean and some of those and one of those papers very early papers is is still quoted when you go to seminars on eigenfunctions of problems how can I get you to a happier place in your career it's not working at this point in terms of the classic attack well I yeah III don't know it isn't working at this point and so at this point my marriage broke up and I acquired picked up a new math boyfriend my husband Robert Williams who was a quite a quite a mathematical character there's a holster he has an interesting story too but he was a little bit of a wild card he was a mountain climber and but also even more and very intellectual in fact of anything he's more intellectual now I have so we and we became drinking buddies and intellectual buddies and we traveled and I spent a cup of 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 I I the the the mathematician next door to me was how a maser who did type Miller theory and I started learning some mathematics that type Miller theory from him and so I was I was a comfortable when I was at the University of Illinois in Chicago it was it was a City University there are faculty wives were unheard of here 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 so oh I'm sorry I got tenure I got tenure from Urbana Champaign whoo yeah yeah yeah yeah I was okay so you went through I don't remember exactly whether I got it before I left her after I left but I mean any process of by moving around at that time I got just a tenured professor now wherever you go yeah yeah yeah well you know in fact I I'm I'm sorry but I 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 for for the rest of my life tenured in spite of herself yes I 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 two a breakthrough moment in in your mathematical inquiry and I need to get you to Texas okay well actually the brain the first breakthrough moment really came when I was at the end of my career in champaign-urbana a postdoc Jonathan Sacks from the University of California Berkeley he was I 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 for 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 and actually come up with solutions to the problem and this so this is this is really the bubbling process what happens is you have a 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 this solution doesn't converge and you look at them there's it is being bubbling and you actually look at it under microscope and lo and behold you can see a whole solution on the plane so this was for two I mean so I certainly feel like Jonathan sort of changed my life at this point and so this was this was the first breakthrough I had it feels like a breakthrough at the moment I mean where is it only later on when the implications oh I had no idea that it 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 the see I am talking about a revolution that I was part of in that form of mathematics that nonlinear analysis applied to geometry and topology and algebraic geometry and so forth came about through this process where I from when before I was a graduate student through my graduate student days and the subject you know it was very noticeable that in nineteen where about 1980 or so there were no 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 if 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 that that's and I solved a problem that the physicists really wanted to know the answer to so this gave this is this is I can go back into relationship math and physics here if we wanted to but and so at some point I got a job at the University of Chicago now this is the first big significant acknowledge is 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 so University of Illinois in 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 yes where you are right now as a visitor and he lowed the idea of graduates my question was basically don't you miss them yes I do miss them you do so tell me about graduate study in that bag you're from the point of view of the professor are your ideas helped my 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 is that I try to have some ideas and some problems that I even I I don't know that I think I might be able to do but I don't know and they look interesting and I was that I would think were worth doing meaning and not not something that I don't want it something that I don't not something I don't want to do but something that I really think you could pursue and I try to give it to the graduates to us and I sometimes you go through and it always changes it's never the same problem when it comes out the other end and so and let the graduate student do whatever with it and and the fact is is that your ideas are never right quite right but if if you're if you and the graduate student are lucky there's really something there and it'll also fit the students personality and interests directing the students and helping them right what about the intellectual blowback in your own work ah that it is affected by graduate students you know I don't know I've never asked that question to myself I haven't I haven't I haven't I have actually the answer is is if I'm thinking about it I tend I have a rule of God things that is I'm not allowed to think about the graduate students work unless I'm he's in or she is in the room I mean I 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 - right but but i but I'm not I'm not so the answer is 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 is 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 because oh that's fine because what I want is the launching and the thinking trying around there 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 want it to do for women so that they don't encounter some of the idiocy as you did at the 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 i I've actually worked at Texas also - on women's issues but the point is is that I think along with everybody else that when the law is changed in the 60s and 70s and so forth that the assumption was is 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 I stayed I I didn't want I didn't I didn't well I died I was just my experience at nearest California Berkeley was not good and but at 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 and but we looked around and we said where is the rest of them coming they're not the doors are not opened the the academia is not flooded by women or minorities for that matter and we those of us were disestablished of my career so I could do something and when the 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 and I also my collaborator Julian turn what came in and we worked together on it so I had I wasn't working by myself anymore I had somebody to work with which was a great experience it's a good question and not much time but you said you had to do something why weren't women fly and minorities flooding through because it's a very much more complicated question and law and I don't want to even pretend to enter into it but you can you can 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 I really I really think that to isolate and say women in science and separated from this is a real mistake I don't think there's any evidence that women in science and math have many more difficulties than women and other professions that's the last word thank you very much