Celebratio Mathematica

Kar­en Uh­len­beck is an avid lov­er of nature, a math­em­atician, and a mem­ber of the Amer­ic­an Academy of Arts and Sci­ences and the Na­tion­al Academy of Sci­ences. Her in­terest in math arose, in part, from her pref­er­ence to work alone, her nat­ur­al bent for ab­strac­tion, her love of ideas, and her lack of suc­cess in un­der­gradu­ate phys­ics. Al­though she faced blatant sex­ism early in her ca­reer, she nev­er took it per­son­ally, real­iz­ing that pre­ju­dice treats an in­di­vidu­al as a mem­ber of a class or group in­stead of as a per­son.

My first love is the out­doors — I en­joy moun­tain climb­ing, back pack­ing, hik­ing, ca­noe­ing, swim­ming, and bi­cyc­ling. Many of these in­terests I in­her­ited from my par­ents who, at age 83, are still hik­ing and back pack­ing. I am at home in nature and, when I can't be out in the wil­der­ness, I can of­ten be found in my garden at my home in Aus­tin. That's the real me. My day-to-day life is something very dif­fer­ent.

I am a math­em­atician. Math­em­aticians do exot­ic re­search so it’s hard to de­scribe ex­actly what I do in lay terms. I work on par­tial dif­fer­en­tial equa­tions which were ori­gin­ally de­rived from the need to de­scribe things like elec­tro­mag­net­ism, but have un­der­gone a cen­tury of change in which they are used in a much more tech­nic­al fash­ion to look at even the shapes of space.

Math­em­aticians look at ima­gin­ary spaces con­struc­ted by sci­ent­ists ex­amin­ing oth­er prob­lems. I star­ted out my math­em­at­ics ca­reer by work­ing on Pal­ais’ mod­ern for­mu­la­tion of a very use­ful clas­sic­al the­ory, the cal­cu­lus of vari­ations. I de­cided Ein­stein’s gen­er­al re­lativ­ity was too hard, but man­aged to learn a lot about geo­metry of space time. I did some very tech­nic­al work in par­tial dif­fer­en­tial equa­tions, made an un­suc­cess­ful pass at shock waves, worked in scale in­vari­ant vari­ation­al prob­lems, made a poor stab at three man­i­fold to­po­logy, learned gauge field the­ory and then some about ap­plic­a­tions to four man­i­folds, and have re­cently been work­ing in equa­tions with al­geb­ra­ic in­fin­ite sym­met­ries. I find that I am bored with any­thing I un­der­stand. My ex­cuse is that I am too poor an ex­pos­it­or to want to spend time on form­al mat­ters.

As a young aca­dem­ic I worked by my­self a lot. In fact, that was one of the at­trac­tions of math­em­at­ics. I am the eld­est of four chil­dren and I con­sider deal­ing with my sib­lings the hard­est thing I’ve ever done in my life. That had a great im­pact on my choos­ing a ca­reer — I wanted a ca­reer where I didn’t have to work with oth­er people. I’ve al­ways been com­pet­it­ive, but I find it dif­fi­cult to cope with the at­ti­tudes of people who lose. It is still at­tract­ive to work in an area where I com­pete only with my­self and don’t have to deal with the neg­at­ive as­pects of com­pet­i­tion. As my ca­reer ad­vanced, however, I found I had a lot to learn from oth­er people of all sorts. I have found it very re­ward­ing to deal with young­er math­em­aticians, and I now truly en­joy col­lab­or­at­ive pro­jects.

I can’t say that I was really in­ter­ested in math­em­at­ics as a child or ad­oles­cent, mostly be­cause one doesn’t really un­der­stand what math­em­at­ics is un­til at least halfway through col­lege. As a child I read a lot. I read everything, in­clud­ing all the books in our house three times over. I’d go to the lib­rary and then stay up all night read­ing. I used to read un­der the desk in school. My whole fam­ily were and still are avid read­ers; we lived in the coun­try so there wasn’t a whole lot else to do. I was par­tic­u­larly in­ter­ested in read­ing about sci­ence. I was about twelve years old when my fath­er began bring­ing home Fred Hoyle’s books on as­tro­phys­ics. I found them very in­spir­ing. I also re­mem­ber a little pa­per­back book called One, Two, Three, In­fin­ity by George Gamow, and I re­mem­ber the ex­cite­ment of un­der­stand­ing this very soph­ist­ic­ated ar­gu­ment that there were two dif­fer­ent kinds of in­fin­it­ies. I read all of the books on sci­ence in the loc­al lib­rary and was frus­trated when there was noth­ing left to read.

I grew up in New Jer­sey and, since there wasn’t a state uni­versity at the time, I went to the Uni­versity of Michigan. Since both of my par­ents were the first gen­er­a­tion of people in their fam­il­ies to go to col­lege — my fath­er was an en­gin­eer, my moth­er an artist — there was nev­er a ques­tion that I would go to col­lege. I wanted to go to MIT or Cor­nell, but my par­ents de­cided that those in­sti­tu­tions were too ex­pens­ive and the Uni­versity of Michigan was af­ford­able. I was lucky enough to get in­to the hon­ors pro­gram at Michigan. I had very ad­vanced courses as a fresh­man and re­ceived a su­perb edu­ca­tion. I had a ju­ni­or-level math course which I found very ex­cit­ing. I had in­ten­ded to ma­jor in phys­ics and de­cided to change ma­jors when they star­ted tak­ing at­tend­ance in the phys­ics lec­ture. I also had trouble with labs — I could not learn to look up an­swers in the back of the book and fudge the ex­per­i­ments. I could nev­er seem to get the labs to come out right. So I switched to math and have been in­ter­ested in it ever since.

There are three wo­men Ph.D. math­em­aticians from my fresh­man hon­ors class at Michigan. Some people at the Uni­versity of Michigan have a the­ory to ex­plain this phe­nomen­on of suc­cess rates of wo­men from their hon­ors pro­gram dur­ing this time peri­od: bright wo­men were not sent to ex­pens­ive, private col­leges, so they came to places like Michigan with hon­ors pro­grams. If we had been bright men, they sug­gest, our fath­ers would have forked out the money to send us to Ivy League schools.

After un­der­gradu­ate school I spent a year at New York Uni­versity’s Cour­ant In­sti­tute (1964), but then mar­ried a bio­chem­ist who was go­ing to Har­vard, so I switched to Bran­de­is. I had a Na­tion­al Sci­ence Found­a­tion gradu­ate fel­low­ship at that time, so four years of my gradu­ate school were paid for at a very lux­uri­ous rate. I was one of the people who be­nefited from Sput­nik. There was a hand­ful of wo­men in my gradu­ate pro­gram, al­though I was not close friends with any of them. It was evid­ent that you wouldn’t get ahead in math­em­at­ics if you hung around with wo­men. We were told that we couldn’t do math be­cause we were wo­men. If any­thing, there was a tend­ency to not be friendly with oth­er wo­men. There was blatant, overt dis­cour­age­ment, but also subtle en­cour­age­ment. A lot of people ap­pre­ci­ated good stu­dents, male or fe­male, and I was a very good stu­dent. I liked do­ing what I wasn’t sup­posed to do, it was a sort of le­git­im­ate re­bel­lion. There were no ex­pect­a­tions be­cause we were wo­men, so any­thing we did well was con­sidered suc­cess­ful.

I have al­ways known that I was a really good math­em­atician. I have a nat­ur­al bent for ab­strac­tion and I love ideas of all sorts. I value time to be by my­self and think, about math or oth­er things, it doesn’t mat­ter. The noise of the world is a dif­fi­cult thing for me to deal with. I have al­ways had a hard time hand­ling ex­tern­al stim­uli.

My first hus­band’s par­ents were older European in­tel­lec­tu­als and my fath­er-in-law was a fam­ous phys­i­cist. They were very in­flu­en­tial in my life. They had a dif­fer­ent at­ti­tude to­ward life than Amer­ic­ans. I re­mem­ber my moth­er-in-law read­ing Proust and giv­ing me her Eng­lish ver­sion when she learned to read it in French. My in-laws val­ued in­tel­lec­tu­al things in a way that my par­ents didn’t; my par­ents did value such things, but they be­lieved that mak­ing money was more im­port­ant. I don’t think I would have sur­vived at that stage of my ca­reer without the en­cour­age­ment from my first hus­band’s fam­ily.

After gradu­ate school I had two tem­por­ary jobs. I taught for a year at MIT while my hus­band was fin­ish­ing his Ph.D. in bio­phys­ics at Har­vard, and then I went for two years to the Uni­versity of Berke­ley dur­ing the Vi­et­nam War. I was not the only wo­man in those re­spect­ive de­part­ments, and I must say that all of these wo­men (my con­tem­por­ar­ies) suc­ceeded spec­tac­u­larly, prob­ably be­cause they had made up their minds to do what they chose.

I’m still pro­cessing a lot of what happened dur­ing those years. I think that some of the ori­gin of older wo­men’s lack of sym­pathy with fem­in­ists res­ul­ted from the fact that many of us were go­ing along fine in our ca­reers, and then some­body star­ted shout­ing that you were nobody and you wer­en’t sup­posed to be there. But there you were, and sud­denly there was all this fuss about wo­men. Now they had to hire wo­men. It be­wildered many of us. It’s nice to know that maybe some of the road­b­locks have been re­moved, but I bet that what ac­tu­ally happened was not very use­ful to any­body.

I was told, when look­ing for jobs after my year at MIT and two years at Berke­ley, that people didn’t hire wo­men, that wo­men were sup­posed to go home and have ba­bies. So the places in­ter­ested in my hus­band — MIT, Stan­ford, and Prin­ceton — were not in­ter­ested in hir­ing me. I re­mem­ber be­ing told that there were nepot­ism rules and that they couldn’t hire me for this reas­on. When I chal­lenged them on this is­sue years later, they didn’t re­mem­ber say­ing these things and, in­ter­est­ingly enough, there were no nepot­ism rules “on the books.” I would have rather they’d been hon­est and said they wouldn’t hire me be­cause I was a wo­man. I want to be val­ued for my work as a math­em­atician, not be­cause I’m a mem­ber of a par­tic­u­lar group.

At that point in time people were say­ing all kinds of things about wo­men, most of which had noth­ing to do with me per­son­ally. Pre­ju­dice is very rude be­cause it treats you as a mem­ber of a class or group in­stead of as a per­son. People were tre­mend­ously rude.

I ended up at the Uni­versity of Illinois, be­cause they hired me and my hus­band. In ret­ro­spect I real­ize how re­mark­ably gen­er­ous he was be­cause he could have been at MIT, Stan­ford, or Prin­ceton. I hated Cham­paign-Urb­ana — I felt out of place math­em­at­ic­ally and so­cially, and it was ugly, bour­geois and flat. I was lucky to re­ceive a Sloan Fel­low­ship and, in­stead of do­ing something math­em­at­ic­ally use­ful, I took time off from teach­ing to re­arrange my life. I had already met Les­ley Sib­n­er, who has served me since as role mod­el and ad­visor many years. I also star­ted to work Jonath­an Sacks and was taught Teich­mueller the­ory by Bill Abikoff. These were my first close math­em­at­ic­al con­tacts. I moved to Chica­go, es­tab­lished what has proven to be a long-term re­la­tion­ship with Bob Wil­li­ams (a some­what older math­em­atician), taught tem­por­ar­ily at North­west­ern and then per­man­ently at the Uni­versity of Illinois at Chica­go Circle. I also be­came friends with S. T. Yau, whom I cred­it with gen­er­ously es­tab­lish­ing me fi­nally and defin­it­ively as a math­em­atician.

I moved from Chica­go Circle, with some re­grets, to the Uni­versity of Chica­go in 1982, the same year I re­ceived a Ma­cAr­thur Fel­low­ship. It has been a struggle for me to come to grips with my own suc­cess. By look­ing around me at the fate of oth­er wo­men who wanted to be math­em­aticians, I can in­tel­lec­tu­ally, if not emo­tion­ally, un­der­stand that this is not so sur­pris­ing. Not that the fate of oth­er wo­men is sur­pris­ing, but I really don’t un­der­stand my suc­cess.

I think what has changed today is that people are tre­mend­ously more subtle, so that you don’t know what you’re up against. This is true not only for wo­men but for a lot of young people. Young people today are up against the fact that most of the young sci­ent­ists are com­ing from abroad, and so most of the people com­ing in­to aca­demia are be­ing trained some­where oth­er than the United States. No one ever talks about this phe­nomen­on of who is ac­tu­ally suc­ceed­ing in the sci­ences and en­gin­eer­ing — for­eign-born men and wo­men. I try to talk about this with my stu­dents. It’s dif­fi­cult, however, be­cause you’re not sup­posed to talk about it. In the large classes of en­gin­eer­ing stu­dents I teach, I’m see a lot more di­versity — wo­men, His­pan­ics, Afric­an-Amer­ic­ans. It can be done, not just by white, Anglo men.

I am cur­rently at the Uni­versity of Texas in Aus­tin, and there are three wo­men in the math de­part­ment, two full pro­fess­ors and one as­so­ci­ate pro­fess­or. I run a ment­or­ing pro­gram for wo­men in math­em­at­ics which is two years old. I am aware of the fact that I am a role mod­el for young wo­men in math­em­at­ics, and that’s partly what I’m here for. It’s hard to be a role mod­el, however, be­cause what you really need to do is show stu­dents how im­per­fect people can be and still suc­ceed. Every­one knows that if people are smart, funny, pretty or well-dressed they will are suc­ceed. But it’s also pos­sible to suc­ceed with all of your im­per­fec­tions. It took me a long time to real­ize this in my own life. In this re­spect, be­ing a role mod­el is a very un-glam­or­ous po­s­i­tion, show­ing people all your bad sides. I may be a won­der­ful math­em­atician and fam­ous be­cause of it, but I’m also very hu­man.