Celebratio Mathematica

In ask­ing math­em­aticians around the coun­try who they thought should be in­ter­viewed for this book, al­most every­one named Kar­en Uh­len­beck. Uh­len­beck is con­sidered one of the top math­em­aticians in the coun­try; she has re­ceived many dis­tin­guished awards, in­clud­ing the Ma­cAr­thur “geni­us” award, and a nom­in­a­tion to the Na­tion­al Academy of Sci­ences. Her pi­on­eer­ing work in math­em­at­ic­al ana­lys­is has earned her tre­mend­ous re­spect as a tal­en­ted and cre­at­ive math­em­atician.1 One of the in­gredi­ents of Uh­len­beck’s suc­cess is that she is ex­tremely in­de­pend­ent. She is proud of the way she was ba­sic­ally self-taught, pur­sued her own in­terests, and for a great deal of her pro­fes­sion­al life “didn’t need any­one.” Over time, however, Uh­len­beck gradu­ally be­came aware that such de­term­ined in­di­vidu­al­ism can lead to isol­a­tion, and can have a neg­at­ive im­pact on pro­fes­sion­al growth. As her ca­reer de­veloped, com­munity be­came es­sen­tial to suc­cess.

At the same time, for many wo­men, do­ing math is not “an auto­mat­ic thing.” It is more dif­fi­cult for wo­men to en­vi­sion them­selves in such a role, and this lack of vis­ion can have an ef­fect on many levels. It makes it less likely for wo­men to pur­sue math­em­at­ics, and even those who be­gin such a path are more eas­ily di­ver­ted if they do not have a clear sense of where it will lead or how they would fit in. Con­sequently, wo­men are more likely to choose al­tern­at­ive tra­ject­or­ies that present them­selves. Moreover, even those wo­men who do stay in math have trouble see­ing them­selves as math­em­aticians. As Kar­en Uh­len­beck says, “Even when I had had my Ph.D. for five years, I was still strug­gling with wheth­er I should be­come a math­em­atician. I nev­er saw my­self very clearly.” This dif­fi­culty in ima­gin­ing one­self as a math­em­atician arises in part from the strong so­cial ste­reo­types about wo­men, as well as from the lack of role mod­els to present al­tern­at­ives to these tra­di­tion­al ex­pect­a­tions.

Most strik­ing is the fact that even some of the most tal­en­ted wo­men in math­em­at­ics — those who are clearly gif­ted and who love math­em­at­ics — can still feel like out­siders in the math­em­at­ics com­munity. As Uh­len­beck said, “I’m not able to trans­form my­self com­pletely in­to the mod­el of a suc­cess­ful math­em­atician be­cause at some point it seemed like it was so hope­less that I just resigned my­self to be­ing on the out­side look­ing in.”

What are the factors that con­trib­ute to this feel­ing of be­ing “on the out­side look­ing in”? And how does this sense of mar­gin­al­iz­a­tion com­plic­ate wo­men’s re­la­tion­ship to pub­lic awards and re­cog­ni­tion?

From an early age, Uh­len­beck had a healthy dis­reg­ard for the so­cial ex­pect­a­tions of wo­men. The roles for wo­men in the 1950s, the dec­ade in which she came of age, were quite lim­ited. In the pre­vi­ous dec­ade, wo­men had been ex­posed to a wide range of op­por­tun­it­ies be­cause so many men were away at war. Their skills were needed in factor­ies and man­age­ment, and they dis­covered that they could be weld­ers, truck drivers, pro­fes­sion­al base­ball play­ers — al­most everything that needed to be done was done by wo­men. Later, in the six­ties and sev­en­ties, the wo­men’s move­ment and sweep­ing so­cial change opened many doors for wo­men, al­low­ing them to en­vi­sion and pur­sue new paths. It be­came in­creas­ingly com­mon for wo­men to be­come doc­tors, law­yers, sci­ent­ists, or busi­ness ex­ec­ut­ives. But the dom­in­ant, and un­ques­tioned, roles for white middle-class wo­men in the fifties were clear: their fo­cus was on get­ting mar­ried, hav­ing and rais­ing chil­dren, and caring for the home. Wo­men were not sup­posed to be act­ive in sports, ex­cept as cheer­lead­ers, and be­ing in­tel­lec­tu­ally ori­ented made one an out­cast. As Uh­len­beck said, “I did not feel like I was sup­posed to do any­thing in­ter­est­ing ex­cept date boys. That was what girls did.”

Kar­en, however, pre­ferred to play foot­ball and climb trees. “I was very much a tom­boy. The boy down the street and I played foot­ball and base­ball for the bet­ter part of my life, right through high school. It was not a very re­spect­able thing to do.” So en­trenched were these roles and ex­pect­a­tions that even her moth­er, who was far from the paradigm of con­ven­tion, had dif­fi­culty ac­cept­ing her daugh­ter’s un­will­ing­ness to con­form to gender roles.

But des­pite her moth­er’s dis­com­fort with Kar­en’s un­con­ven­tion­al ways, Kar­en’s whole fam­ily in many ways paved the way for her be­ing dif­fer­ent. In the rur­al com­munity in north­ern New Jer­sey where she grew up, her par­ents were no­tice­ably dif­fer­ent — her fath­er, an en­gin­eer, and her moth­er, an artist, were Demo­crats and went to a Unit­ari­an church, while most people were con­ser­vat­ive, Re­pub­lic­an, and either Cath­ol­ic or Prot­est­ant. Her par­ents were also ar­dent con­ser­va­tion­ists. For their hon­ey­moon they went hik­ing in the moun­tains of the West, and later, even with four chil­dren (of which Kar­en was the old­est), the fam­ily would go camp­ing every sum­mer for two weeks in the Ad­iron­dacks. This back­ground in the out­doors was an es­sen­tial part of Kar­en’s de­vel­op­ment.

Her fam­ily provided many mod­els of strong and in­de­pend­ent wo­men. Her grand­moth­er, an im­pos­ing six feet tall, raised twelve chil­dren al­most single-handedly and lived to the age of 103. Kar­en’s moth­er, also ex­tremely act­ive and en­er­get­ic, “a kind of su­per­wo­man,” had a fiercely in­de­pend­ent streak as an artist, an in­tel­lec­tu­al, a mav­er­ick in her own right. She be­lieved in do­ing everything her­self, and as Kar­en says, “I think I get a lot of my char­ac­ter from her.”

Grow­ing up in a rur­al en­vir­on­ment helped Uh­len­beck avoid in­tense peer pres­sure to con­form. She found al­tern­at­ive forms of com­pan­ion­ship in the un­struc­tured world of the coun­try; by play­ing in the fields and help­ing in the garden, she grew fa­mil­i­ar with birds, flowers, and trees. And she found al­tern­at­ive vis­ions of the world by im­mers­ing her­self in books. She read everything she could find, par­tic­u­larly bio­graph­ies (there were very few on wo­men, “mostly pres­id­ents’ wives”), and books on math, sci­ence, and fron­ti­er life. These early in­flu­ences began to shape her vis­ion of what she wanted to do with her own life, a vis­ion that would en­able her to es­cape the un­com­fort­able ex­pect­a­tions of who she was sup­posed to be.

I was either go­ing to be­come a forest ranger or do some sort of re­search in sci­ence. That’s what in­ter­ested me. I did not want to teach. I re­garded any­thing to do with people as be­ing sort of a hor­rible pro­fes­sion. … I felt that I didn’t get along with people very well. I al­ways had a lot of girl­friends, but I nev­er had very many boy­friends; I didn’t feel com­fort­able. I nev­er felt like I was really a part of any­thing. I went my own way, without really want­ing to, but I nev­er did un­der­stand the trick of do­ing things like you were sup­posed to do.

“Not do­ing things like you were sup­posed to” may have been a li­ab­il­ity in ad­just­ing to so­cial norms, but it would ul­ti­mately be­come an as­set in her pi­on­eer­ing re­search as a math­em­atician.

By the time Uh­len­beck fin­ished high school, she had no idea that she would go on in math­em­at­ics. Her early school­ing had not been par­tic­u­larly stim­u­lat­ing; in­deed, she had spent most of her time read­ing nov­els un­der her desk. Col­lege, however, turned out to be a strik­ing con­trast.

Uh­len­beck’s fam­ily as­sumed that Kar­en would go to col­lege, but where she went was less im­port­ant. She chose the Uni­versity of Michigan be­cause it was re­l­at­ively in­ex­pens­ive; spend­ing money on a wo­man’s edu­ca­tion was not con­sidered a high pri­or­ity. The year was 1960.

Kar­en en­rolled in the hon­ors pro­gram at the Uni­versity of Michigan, which provided her with an ex­cel­lent edu­ca­tion; her strong train­ing in math­em­at­ics there was to prove very use­ful in gradu­ate school. In­ter­est­ingly, this hon­ors pro­gram pro­duced a large num­ber of wo­men math­em­aticians. Be­cause it was so rig­or­ous, many people dropped out of the math­em­at­ics por­tion, but for Kar­en it was a peri­od of blos­som­ing, both per­son­ally and in­tel­lec­tu­ally. She had lots of friends, and felt more com­fort­able with wo­men from the Mid­w­est than with those from the East Coast be­cause they seemed to her more open and friendly. There was a large con­tin­gent of New York­ers as well. She also began to have boy­friends, most of whom also stud­ied math­em­at­ics or sci­ence. Dur­ing her ju­ni­or year, she went abroad to study in Ger­many. The world un­fol­ded bey­ond her wild­est dreams. The dis­cip­line of the classes and the pol­ished lec­tures (giv­en in Ger­man) were stim­u­lat­ing to her. She traveled around Europe, learned to ski, went to the op­era, and got to see parts of the world that were dra­mat­ic­ally dif­fer­ent from her home town in New Jer­sey. She es­pe­cially en­joyed be­ing totally on her own.

It was dur­ing col­lege that Uh­len­beck first dis­covered how much she en­joyed math­em­at­ics. Her first math class in the hon­ors pro­gram at the Uni­versity of Michigan was an ex­tremely chal­len­ging ana­lys­is course. Kar­en flour­ished and de­cided to switch her ma­jor from phys­ics to math­em­at­ics. “I got to col­lege and dis­covered that I could do math­em­at­ics, and I nev­er even saw my­self as do­ing it, but I re­cog­nized that I was par­tak­ing in something that I en­joyed. … I just thought the idea of di­vid­ing things up in­to in­fin­ite amounts seemed really far out.” She par­tic­u­larly liked the ex­cite­ment that came from con­nect­ing with math­em­at­ics dir­ectly in­stead of “just do­ing what the book says.” And she “found it really neat that you could think through these ar­gu­ments and get them right just like the book.” Per­haps most im­port­ant, she dis­covered in the dis­cip­line of math­em­at­ics an in­cred­ible sense of free­dom, a cre­at­ive free­dom not un­like that ex­pressed by po­ets who work with haiku or oth­er highly struc­tured forms of po­etry. As Uh­len­beck says, “If you obey the rules, you could do al­most any­thing you wanted.”

However, des­pite the fact that Uh­len­beck loved math­em­at­ics, she did not as­sume that she would pur­sue it in gradu­ate school or go on to be a math­em­atician. As Uh­len­beck points out, for wo­men, pur­su­ing math­em­at­ics is not “an auto­mat­ic thing.” And she was no ex­cep­tion. She simply could not ima­gine her­self in such a role. Ul­ti­mately, it was the fact that her boy­friend and oth­er un­der­gradu­ate friends were go­ing to gradu­ate school that drew her in­to it — an early in­dic­a­tion of how sig­ni­fic­ant ties to a com­munity can be. But she still had no vis­ion of where she was go­ing or what steps were in­volved.

I think if someone from in­dustry had come and in­ter­viewed me and wanted to hire me, I might have been in­clined, be­cause I don’t think my par­ents were par­tic­u­larly en­thu­si­ast­ic about my go­ing to gradu­ate school. No oth­er op­tion came up and said we want you, and I was be­ing pressed by people in math. All the people I knew were go­ing to gradu­ate school. And I met my fu­ture hus­band as a seni­or and he was go­ing to gradu­ate school (in bio-phys­ics). … It wasn’t something that I had been geared up to do­ing all along. It was just that my life grew in­to that, es­pe­cially when I star­ted see­ing him ser­i­ously. He was go­ing to gradu­ate school, so what was I go­ing to do?

Kar­en re­ceived sev­er­al fel­low­ships, in­clud­ing a Na­tion­al Sci­ence Found­a­tion and Woo­drow Wilson Fel­low­ship, which made it easi­er for her to pur­sue math­em­at­ics. Not only did it provide the fin­ances to go on, it also en­cour­aged her psy­cho­lo­gic­ally. While she couldn’t ima­gine her­self as a math­em­atician, the fel­low­ships at least im­plied that oth­er people thought she had po­ten­tial.

Des­pite the fact that she had re­ceived highly coveted fel­low­ships and that her boy­friend was go­ing to Har­vard, Kar­en nev­er thought ser­i­ously about ap­ply­ing to the most elite schools, such as Har­vard or MIT (Prin­ceton was still not ad­mit­ting wo­men). She chose in­stead to at­tend Cour­ant In­sti­tute in New York City, which has pro­duced a num­ber of wo­men Ph.D.’s. Al­though this was a strong pro­gram, its fo­cus was on ap­plied math­em­at­ics, which was con­sidered less pres­ti­gi­ous than the “pure” math fo­cus of the Ivy League schools.

When Uh­len­beck mar­ried, she de­cided to trans­fer to a gradu­ate pro­gram closer to her hus­band. Again she did not ap­ply to Har­vard or MIT, but in­stead chose Bran­de­is. It was not so much a lack of con­fid­ence in her math­em­at­ics abil­ity as a sense of how prob­lem­at­ic the at­mo­sphere would be for her as a wo­man.

It was self-pre­ser­va­tion, not lack of con­fid­ence. I was pretty sharp, without be­ing con­scious of it, of how dif­fi­cult things were for pro­fes­sion­al wo­men. (I knew all about be­ing so­cially awk­ward!) At the time, I may have thought that if I were bril­liant enough, I would suc­ceed at Har­vard. Now I do not be­lieve that — I be­lieve the so­cial pres­sures of sur­viv­ing in an en­vir­on­ment that would ques­tion every move would have done any wo­man in, un­less she were par­tic­u­larly in­ter­ested in the com­bat. I knew I was not in­ter­ested in the battle of prov­ing so­cial things, so I (wisely in ret­ro­spect) avoided it.

At this point Kar­en had no real role mod­els: no oth­er wo­men with whom she could identi­fy, and who could help her en­vi­sion her­self as a math­em­atician. Trans­fer­ring to Bran­de­is did help, however, by at least provid­ing her with young role mod­els. “For someone like me, Bran­de­is was a su­per place to be a gradu­ate stu­dent be­cause the fac­ulty were all ex­tremely young. My thes­is ad­visor was barely over thirty years old. … It was ex­cit­ing to hob-nob with the ju­ni­or fac­ulty in my last year.” Bran­de­is was just be­gin­ning a new and rig­or­ous gradu­ate pro­gram modeled after Prin­ceton’s. Kar­en was in the first year of the new pro­gram. Many gradu­ate stu­dents with weak­er back­grounds had trouble sur­viv­ing, but Uh­len­beck’s train­ing at the Uni­versity of Michigan and her one year at the Cour­ant In­sti­tute served her well. For such a small school, Bran­de­is pro­duced many strong gradu­ates, and wo­men in par­tic­u­lar.

Dur­ing gradu­ate school, Uh­len­beck still had no clear vis­ion of where she was go­ing with math­em­at­ics, or even what sub­ject area she would pur­sue. “I think that my ca­reer was more marked by a wan­der­ing. … I would de­cide that I really liked something and I’d be kind of bored with it by the end of the course, and then I would de­cide that I really liked something else and I would get bored with it. It sort of wandered around.” In the end, however, this wan­der­ing was good train­ing, for her re­search crosses the bound­ar­ies of many math­em­at­ic­al fields.

In choos­ing an ad­visor, Kar­en based her de­cision on what mattered most to her at the time: who was do­ing what seemed like ex­cit­ing math­em­at­ics. Dick Pal­ais was work­ing on ma­ter­i­al that seemed new and dif­fer­ent. In­deed, it was his field and his clar­ity that drew her to him; per­son­al com­pat­ib­il­ity was less im­port­ant.

I thought he was an ex­traordin­ar­ily clear lec­turer. I still re­mem­ber I went in and said, “Tell me about the heat equa­tion,” and I got an hour lec­ture. That was all I needed to know about the heat equa­tion for twenty years. He really is very clear. For me, I’m much mud­di­er, and I ap­pre­ci­ated that kind of a teach­er. So he was an ex­tremely good choice for me.

For a long time we were very un­com­fort­able with each oth­er. He frankly ad­mits that he didn’t want to take me as a stu­dent when I ap­peared. I think his ini­tial re­ac­tion was that I would just have chil­dren and give up. But in fact after me he had a lot of wo­men stu­dents. I don’t think [his re­sponse] was a per­son­al one, it was just an auto­mat­ic re­sponse of the time. He wasn’t neg­at­ive. But I didn’t choose him be­cause I got along really well with him. I liked the kind of math­em­at­ics he did, and he was really a clear lec­turer.

Thus, Uh­len­beck’s gradu­ate years were char­ac­ter­ized by an al­most para­dox­ic­al com­bin­a­tion of traits — her lack of vis­ion about where she was go­ing, in­deed the al­most ac­ci­dent­al way she stumbled in­to math­em­at­ics, along­side a strong in­de­pend­ent spir­it. She pur­sued what she wanted, with whomever she wanted, and with little guid­ance from ex­tern­al au­thor­it­ies. Even in her thes­is work, she chose a sub­ject that her ad­visor knew little about, so that in the end she was able to teach him some of the ma­ter­i­al, rather than the oth­er way around. But both this tent­at­ive com­mit­ment to math­em­at­ics and her highly in­di­vidu­al­ist­ic nature con­trib­uted to the prob­lems she began to face as a young pro­fes­sion­al.

Up un­til this point, be­ing a wo­man did not con­flict with her role as a stu­dent, par­tic­u­larly at Bran­de­is, where there was a sig­ni­fic­ant pres­ence of wo­men. If there was any dis­crim­in­a­tion, she was (“per­haps stub­bornly”) ob­li­vi­ous to it. The clearly struc­tured roles of stu­dent and teach­er made it easy for Kar­en to plug in­to stu­dent life as both an un­der­gradu­ate and a gradu­ate stu­dent. Though she was un­usu­al, she did not feel like an “out­sider,” or what she would later de­scribe as be­ing “oth­er.”

But in go­ing from be­ing a stu­dent to be­ing a pro­fes­sion­al, Uh­len­beck found her life chan­ging in im­port­ant ways. Be­ing a wo­man was to play a sig­ni­fic­ant role in how she saw her­self and how oth­ers saw her. She was be­gin­ning to hit ter­rit­ory where very few wo­men had gone be­fore. She be­came more of an an­om­aly, and so­cial ex­pect­a­tions of what it meant to be a wo­man would be­gin to con­flict with her role as a pro­fes­sion­al.

It is this stage of her ca­reer that also be­gins to demon­strate the sig­ni­fic­ance of com­munity in shap­ing the life of a math­em­atician: what hap­pens when there is a lack of pro­fes­sion­al com­munity, the dif­fer­ent forms of com­munity that are im­port­ant in one’s pro­fes­sion­al de­vel­op­ment, and the un­ex­pec­ted ways that com­munity can sus­tain one through dif­fi­cult per­son­al and pro­fes­sion­al times.

When Uh­len­beck fin­ished gradu­ate school in 1968, she fol­lowed her hus­band (a bio-phys­i­cist), Olke Uh­len­beck, for two years, tak­ing a one-year ap­point­ment at MIT and then a two-year ap­point­ment at the Uni­versity of Cali­for­nia at Berke­ley. When she was offered a per­man­ent ap­point­ment at the Uni­versity of Illinois at Cham­paign–Urb­ana, her hus­band agreed to move there, rather than to Prin­ceton or Pa­lo Alto, where she would not have a good job. Though it was un­usu­al for a man to take his wife’s ca­reer so ser­i­ously, it was be­gin­ning to be seen as pres­ti­gi­ous to have a pro­fes­sion­al/in­tel­lec­tu­al wife, and he was proud of her in that way. But even as they fol­lowed this non-tra­di­tion­al path, tra­di­tion­al norms and ex­pect­a­tions still had a power­ful ef­fect on Kar­en’s life. Though she was a full-time fac­ulty mem­ber, she was per­ceived, and per­haps per­ceived her­self, primar­ily as a fac­ulty wife. She did not yet have a clear vis­ion of her­self as a pro­fes­sion­al.

I felt like I was in a cage. I did not like be­ing a fac­ulty wife. I re­mem­ber that feel­ing very well. We mostly so­cial­ized with people in my hus­band’s de­part­ment. I re­mem­ber eat­ing din­ner in the fac­ulty club one time, and I went in the ladies’ room and cried. I really didn’t feel at home.

I had an as­sist­ant pro­fess­or­ship, but I was still try­ing to be a good wife. Maybe I thought of my­self as that way. It’s so hard to know what is go­ing on, but it didn’t work at all, and I think it was partly pro­fes­sion­al. I think it was much more pro­fes­sion­al than I real­ized at the time. I was very good friends with my of­ficemate and one or two oth­ers in the fac­ulty, but I didn’t feel like it was a place where I could live. At that point, I really didn’t know what I was do­ing, math­em­at­ic­ally or per­son­ally. I didn’t like teach­ing that much; I nev­er saw it as a ca­reer. And I was try­ing to work by my­self, really in isol­a­tion.

It nev­er oc­curred to me that this was not the place for me. I al­ways did what people ex­pec­ted of me and kept some part of my­self for what I really wanted to do. I’ve nev­er been one to fight ex­tern­al battles. It’s a waste of time. [At Cham­paign-Urb­ana] I really didn’t have any­body. I did get dis­cour­aged. Be­fore that I had al­ways thought that I could over­come all the obstacles.

Per­son­al and pro­fes­sion­al is­sues are in­tim­ately en­twined for wo­men. Even Kar­en had dif­fi­culty de­term­in­ing how much of her un­hap­pi­ness was tied to her role as a wife, and how much of it came from dis­sat­is­fac­tion with how her math­em­at­ic­al life was go­ing. Moreover, all the sig­nals of the time were sug­gest­ing that wo­men’s lives are about be­ing wives, moth­ers, and, if they are pro­fes­sion­als, at least something like teach­ers. But these roles did not mesh with Kar­en’s ori­ent­a­tion. She was not in­clined to play the role of the “good wife,” she did not par­tic­u­larly like teach­ing, and be­cause they did not have chil­dren, she was not de­fin­ing her­self as a moth­er. But she had not yet de­veloped a strong enough iden­tity as a math­em­atician to fall back on that for a sense of strength and mean­ing in her life, and to use it as a way to in­ter­act with the com­munity. The cage she felt trapped in by these per­son­al is­sues per­meated her math life, and so she felt caged math­em­at­ic­ally as well. At the same time her ca­reer un­hap­pi­ness may have con­trib­uted to the per­son­al un­hap­pi­ness.2 Kar­en and her hus­band ul­ti­mately split up. In 1976 she de­cided to leave the Uni­versity of Illinois at Cham­paign-Urb­ana and start a new job at the Uni­versity of Illinois in Chica­go, after a semester at North­west­ern Uni­versity. “That was a good move. I nev­er had any doubt. \( \dots \) It was hard to de­cide wheth­er it was pro­fes­sion­ally bet­ter or per­son­ally bet­ter. I think the city seemed like more free­dom.” Dur­ing this peri­od, Uh­len­beck’s re­la­tion­ship with her pro­fes­sion­al com­munity began to change. For one thing, it was the first time she was on her own and needed to sup­port her­self eco­nom­ic­ally. For­tu­nately she re­ceived a Sloan Fel­low­ship, which played an im­port­ant role in the trans­ition she was go­ing through. “It’s pos­sible that lots of people’s ca­reers wouldn’t sur­vive if they didn’t have some sort of sup­port dur­ing a bad peri­od in life.”

[Hav­ing the Sloan Fel­low­ship] made a big dif­fer­ence to me dur­ing this peri­od be­cause I think I al­ways felt that I owed something to the pro­fes­sion. When your per­son­al life gets all shot, you’re glad that you have something pro­fes­sion­al. That’s when you sud­denly real­ize that this isn’t a game, that study­ing math­em­at­ics and go­ing along and do­ing the next step is for real, and if you didn’t have a way to sup­port your­self you would be in a very in­ter­est­ing po­s­i­tion.

In­deed, this peri­od was the first time Uh­len­beck ar­tic­u­lated any sense of re­spons­ib­il­ity to the pro­fes­sion; she also sud­denly began to see her­self as a pro­fes­sion­al. This link between eco­nom­ics and one’s at­ti­tude about one’s work is sig­ni­fic­ant; it is one of the factors that have con­trib­uted to wo­men’s more tent­at­ive com­mit­ment to their work. To a large de­gree, many of the wo­men who pur­sued aca­dem­ic work came from re­l­at­ively priv­ileged back­grounds. Those who mar­ried of­ten did not see their in­come as es­sen­tial to their fam­ily’s se­cur­ity, which gave them the op­tion of see­ing them­selves as either “am­a­teurs” or “pro­fes­sion­als.” This pat­tern is only now chan­ging in fun­da­ment­al ways, as even mar­ried wo­men’s salar­ies are in­creas­ingly seen as es­sen­tial to the eco­nom­ic sta­bil­ity of their fam­il­ies.

Though a lot of Uh­len­beck’s un­hap­pi­ness dur­ing the peri­od in Cham­paign-Urb­ana came from try­ing to con­form to roles that were not suited to her, much of it was also due to the stifling of her math­em­at­ic­al de­vel­op­ment. She had ac­cess to a pen, pa­per, and lib­rary, but math­em­at­ics is much more than an in­di­vidu­al pur­suit. Some kind of com­munity is es­sen­tial for cross-fer­til­iz­a­tion and the sus­tained stim­u­la­tion of the math­em­at­ic­al ima­gin­a­tion. And com­munity is what Uh­len­beck began to find both at the Uni­versity of Illinois and at the In­sti­tute for Ad­vanced Study.

Leav­ing Cham­paign-Urb­ana was a ma­jor turn­ing point in Uh­len­beck’s life. It was to sig­nal a sig­ni­fic­ant shift, a fi­nal let­ting go of try­ing to con­form to an ex­tern­al im­age of a wo­man’s life: wife, moth­er, teach­er. As she let go of these iden­tit­ies, she was free to ex­plore and em­brace dif­fer­ent parts of her­self, and she began to blos­som pro­fes­sion­ally.

At the Uni­versity of Illinois in Chica­go, Uh­len­beck was very happy with her new en­vir­on­ment. A primary factor was the pro­fes­sion­al and per­son­al re­la­tion­ships she es­tab­lished on her own. She no longer spent most of her time with her hus­band’s col­leagues, cre­at­ing in­stead a com­munity of her own. A par­tic­u­larly im­port­ant part of that was the ca­marader­ie, both pro­fes­sion­al and so­cial, that she de­veloped with oth­er wo­men math­em­aticians.

I had a fe­male ment­or [Vera Pless] for the first time. I don’t know wheth­er she ever real­ized it, but she sort of saved me. She would give me pa­per clips and tell me what to do in trivi­al situ­ations. It’s really the only time I had some­body help me out. I re­mem­ber that very much — be­ing very re­lieved. She helped me over all the little de­tails of a new job in a new place where you don’t know any­one. I would go across the hall and bug her at least two or three times a week. She would tell me about the people on the fac­ulty. I don’t know if I would have sought her out, but she was right there, and she was there a lot of the time.

Later she says of Vera, “I felt like we were liv­ing on the same plan­et any­way.” This kind of in­tim­ate sup­port is ex­tremely im­port­ant, a kind of in­vis­ible sup­port that men of­ten take for gran­ted, and that wo­men of­ten have less ac­cess to — it helps one identi­fy the un­writ­ten rules of a de­part­ment, a uni­versity, a pro­fes­sion­al com­munity. It is also a bond that can tra­verse the bound­ar­ies between per­son­al and pro­fes­sion­al life. For wo­men this of­ten hap­pens more eas­ily with oth­er wo­men.

Kar­en also very much iden­ti­fied with Louise Hay, an­oth­er math­em­atician who had got­ten a di­vorce, and be­cause of that she very much ap­pre­ci­ated her Ph.D. in math­em­at­ics, and her abil­ity to be eco­nom­ic­ally in­de­pend­ent. For Hay, as for Uh­len­beck, the ser­i­ous­ness of be­ing able to sup­port her­self be­came real only after her di­vorce. With Hay, Uh­len­beck could dis­cuss de­tails of her life that would not arise for her male col­leagues, small but sig­ni­fic­ant is­sues such as wheth­er to keep her mar­ried name.

Uh­len­beck stayed at the Uni­versity of Illinois in Chica­go for sev­en years. Dur­ing that time she also had vis­it­ing ap­point­ments at sev­er­al re­search in­sti­tutes, in­clud­ing the Uni­versity of Cali­for­nia at Berke­ley, the In­sti­tute for Ad­vanced Study at Prin­ceton, the new Math­em­at­ics Re­search In­sti­tute at Berke­ley, and Har­vard Uni­versity. Both the Uni­versity of Illinois and es­pe­cially Prin­ceton brought her in con­tact with oth­er col­leagues she greatly en­joyed work­ing with.

The middle year when I was at the Uni­versity of Illinois, I got in­vited and went for a year to the In­sti­tute of Ad­vanced Study, which was a spe­cial year in dif­fer­en­tial geo­metry. Shing Tung Yau, Rick Schoen, Le­on Si­mon, and J. P. Bour­guignon vis­ited. I learned a lot of math­em­at­ics that I hadn’t learned, of a dif­fer­ent kind, and got more in the main­stream of math­em­at­ics. I re­mem­ber that it took me a few months be­fore I would talk to any­body. I felt very much out of it when I came, but after I was there for a whole year — I worked with Rick Schoen dur­ing that peri­od of time and dur­ing that sum­mer — that was really the be­gin­ning of my suc­cess.

This group is one she con­tin­ued to work with for a long time. Dur­ing this peri­od a gradu­ate stu­dent from Har­vard, Cliff Taubes, also came down to work with her, and thus began an­oth­er im­port­ant math­em­at­ic­al re­la­tion­ship. As she says of this peri­od, “I don’t think I be­came a bet­ter math­em­atician, but I be­came bet­ter able to give sem­inars and could say things that wer­en’t totally in­com­pre­hens­ible to every­body.”

Al­though Kar­en had al­ways had some con­tact with oth­er math­em­aticians, re­l­at­ively speak­ing, she worked quite in­de­pend­ently. This lim­ited math isol­a­tion, in com­bin­a­tion with what Kar­en would de­scribe as her “messy think­ing,” made it dif­fi­cult for her to com­mu­nic­ate clearly with oth­er math­em­aticians. She de­scribes her in­ter­ac­tion with a young math­em­atician at the Uni­versity of Illinois named Jonath­an Sacks, who would beat her door down un­til he un­der­stood what she was say­ing. “I was hard to un­der­stand. I still am hard to un­der­stand. I was not so­cial­ized.” The year at the In­sti­tute, there­fore, was very use­ful in teach­ing her how to com­mu­nic­ate and work with oth­er math­em­aticians. It was the be­gin­ning of her trans­ition from a kind of monk­ish math life to work­ing, com­mu­nic­at­ing, and in­ter­act­ing with oth­ers in her field. In ad­di­tion to teach­ing her how to com­mu­nic­ate, this ex­pos­ure helped steer her to “main­stream” prob­lems in her field. In the end, this in­ter­ac­tion was nour­ish­ing for her in­tel­lec­tu­ally as well as emo­tion­ally.

It was from this group, Shing Tung Yau in par­tic­u­lar, that she also re­ceived the kind of sup­port she needed to gain con­fid­ence in her­self as a math­em­atician, and to be­gin to see her­self as such. “I could tell that Yau thought I was a good math­em­atician. I don’t think that had happened to me be­fore. He was ob­vi­ously ex­tremely bright. \( \dots \) He’s a very re­mark­able and en­er­get­ic per­son\( \dots \). I really cred­it him a large amount. I’m not say­ing that oth­er people haven’t tried to sup­port me. My thes­is ad­visor has al­ways been a large sup­port­er. It was more real. I could tell that Yau thought I was a good math­em­atician. That was hard for me to ac­cept.”

But these con­nec­tions did more than simply boost her con­fid­ence and bring her in­to the main­stream of math­em­at­ic­al ideas. They also be­came cru­cial ad­voc­ates in her pro­fes­sion­al life. The sig­ni­fic­ance of such ad­voc­ates be­comes ap­par­ent when Uh­len­beck talks about one of her two older ment­ors, a wo­man about five years older than Kar­en who is in roughly the same field:

We still have a very close re­la­tion­ship. She provides real sup­port to me. \( \dots \) She’s a typ­ic­al ex­ample of a wo­man who is a very good re­search math­em­atician but who is not re­cog­nized. She is at a tech­nic­al in­sti­tute. The only good thing about the job is that she peri­od­ic­ally gets good gradu­ate stu­dents. She is un­der­paid and teaches a lot. I said Yau is really the per­son that I hold re­spons­ible for my suc­cess. You know, it’s true — to be really suc­cess­ful you have to be pro­tec­ted, and there is no way to do it any oth­er way. I think about this all the time.

Her ex­per­i­ences have helped her re­cog­nize how im­port­ant it is for young math­em­aticians to make con­tacts in the com­munity — something that she missed out on at the be­gin­ning of her ca­reer. As she ac­know­ledges, giv­en her in­de­pend­ent streak, this was prob­ably in­ev­it­able. However, her more re­cent and fruit­ful in­ter­ac­tion with young­er col­leagues and stu­dents is, in a sense, mak­ing up for what she missed at the early stage of her ca­reer.

I tell my stu­dents that the most im­port­ant thing, if you want to keep do­ing math­em­at­ics, is that you es­tab­lish math­em­at­ic­al con­tacts. Even if you don’t need to work with them, you’re go­ing to get de­pressed soon­er or later and you’re go­ing to need some sort of in­put\( \dots \). Wheth­er people stay as re­search math­em­aticians or not, I think the big item is that they have some con­tact in the math­em­at­ics com­munity of a per­son­al nature. That sounds weird be­cause math­em­aticians are crazy. They work by them­selves and you sort of think of them as sit­ting in their room work­ing by them­selves, but every math­em­atician hits bad points and how do you get over it? Some­body has got to come along and say, “Cut it out, kid.” Or some­body has to come in with a new idea and hit you on the head with it.

I see young people who al­ways think they want to go to a place where there’s a lot of ac­tion and a lot of ideas go­ing on. I think the only be­ne­fit they really get from that is that they make strong re­la­tion­ships. Some math­em­aticians are so­cial. Some math­em­aticians work to­geth­er, but a lot don’t. What hap­pens to the people who go out and work in isol­a­tion? I think noth­ing, ex­cept that you’re bound to hit a bad point, and then how are you go­ing to get over it? If you’re on good terms with your thes­is ad­visor, you call your thes­is ad­visor up and the thes­is ad­visor says to cut it out or gives you some feed­back. [On the oth­er hand] I don’t want my stu­dents do­ing that. They need to find their own re­la­tion­ships. \( \dots \) There are people who sail through and noth­ing ever goes wrong. Nor­mal people aren’t like that. We have all sorts of aw­ful things go­ing on.

For wo­men and minor­it­ies, this is par­tic­u­larly im­port­ant, not be­cause they ne­ces­sar­ily have more prob­lems, nor even ne­ces­sar­ily dif­fer­ent prob­lems, but they of­ten have less ac­cess to the sup­port sys­tems that help math­em­aticians through the tough peri­ods. For those who feel more isol­ated, small obstacles can be­come enorm­ous. Col­leagues and friends can help put them in per­spect­ive.

We see, then, the subtle ways that the math­em­at­ic­al com­munity can be very im­port­ant in the de­vel­op­ment of one’s ca­reer: it ex­poses one to main­stream prob­lems and new ideas, teaches one how to com­mu­nic­ate with oth­er math­em­aticians, in­stills con­fid­ence, provides sup­port dur­ing dif­fi­cult peri­ods, and fa­cil­it­ates re­cog­ni­tion and pro­fes­sion­al op­por­tun­it­ies. We also see the many levels of math­em­at­ic­al com­munity. There is one’s im­me­di­ate work en­vir­on­ment, and as Kar­en’s life il­lus­trates, through her dif­fer­ent ex­per­i­ences at the Uni­versity of Illinois in Cham­paign-Urb­ana, the Uni­versity of Illinois in Chica­go, and later the Uni­versity of Chica­go, these com­munit­ies can fun­da­ment­ally af­fect one’s im­age of one­self, one’s vis­ion of the math com­munity, and one’s re­la­tion­ship to that com­munity. In this way they can pro­foundly in­flu­ence one’s im­age of one­self as a math­em­atician. Kar­en had the op­por­tun­ity to go bey­ond these im­me­di­ate com­munit­ies and meet oth­er math­em­aticians who worked in fields close to her own. The In­sti­tute for Ad­vanced Study brought to­geth­er top re­search­ers in her field and greatly ex­pan­ded her in­ter­ac­tion with the lar­ger math com­munity. This ex­pos­ure to Yau’s group was pro­foundly in­flu­en­tial in the de­vel­op­ment of her ca­reer, lead­ing to pub­lic re­cog­ni­tion and pres­ti­gi­ous awards.

Though Kar­en was happy in Chica­go at the Uni­versity of Illinois, a num­ber of factors made her de­cide to leave: money was lim­ited, she wanted to be work­ing with gradu­ate stu­dents, and fi­nally she “wanted her ca­reer to go some­where.” She ac­cep­ted a job at the Uni­versity of Chica­go, which was more pres­ti­gi­ous; there was more money avail­able for re­search, and the school had a first-rate gradu­ate pro­gram. But in ret­ro­spect she says, “Leav­ing the Uni­versity of Illinois and go­ing to the Uni­versity of Chica­go was prob­ably a mis­take.”

At the Uni­versity of Illinois she had had a num­ber of close col­leagues with whom she could work, math­em­aticians who were not ne­ces­sar­ily dir­ectly in her field but were close enough that they had a lot to share and teach each oth­er. They were also young, and she found them easy to re­late to. The Uni­versity of Chica­go, on the oth­er hand, was not a stim­u­lat­ing re­search en­vir­on­ment for her; she did not find col­leagues to work with — “It wasn’t con­geni­al there.”

The uni­versity was go­ing through a peri­od of trans­ition at that time. The older gen­er­a­tion of well-known math­em­aticians had all re­tired, and there was a young­er group who were not yet as well es­tab­lished. The gradu­ate pro­gram had not had much suc­cess with wo­men stu­dents. But the mis­match between Kar­en and the Uni­versity of Chica­go went deep­er than these is­sues. The at­mo­sphere and tra­di­tions of the uni­versity were ali­en to her on many levels.

I simply nev­er be­came friendly with people. Most were edu­cated in fancy in­sti­tu­tions. There was this air of real elit­ism. I had got­ten a de­gree from Bran­de­is. I’d been teach­ing at the Uni­versity of Illinois. But they seemed to have lived their whole lives in pres­ti­gi­ous in­sti­tu­tions. A lot of people there hadn’t taught un­der­gradu­ate courses. I’d been teach­ing re­medi­al cal­cu­lus to busi­ness ma­jors. A dif­fer­ent world. They also didn’t do the kind of math­em­at­ics that I did. This is not to say those things are in any way re­lated to each oth­er, but it was the double thing.

These vari­ous factors — the lack of col­leagues to work with, the air of elit­ism, a long com­mute — all con­trib­uted to the dis­tance and ali­en­a­tion she felt from the in­sti­tu­tion.

I just didn’t feel at home, I guess that’s the biggest thing. I kept telling my­self that I should give it a little longer, that I should do something dif­fer­ent, but it’s dif­fi­cult to know how to change it. Chica­go had a bad repu­ta­tion among the wo­men math­em­aticians in the Chica­go area — it did not have a repu­ta­tion as a friendly place. I just really didn’t think those things were im­port­ant. I now think those things are really im­port­ant.

For wo­men es­pe­cially, the at­mo­sphere of the work­place can have a very sig­ni­fic­ant im­pact on their work, their im­age of them­selves, their im­age of the math­em­at­ic­al com­munity, and wheth­er they fit in­to it. In Kar­en’s case, the Uni­versity of Chica­go func­tioned to fur­ther po­lar­ize her from a kind of tra­di­tion­al, main­stream math­em­at­ic­al com­munity. It re­in­forced a vis­ion of “them” as “oth­er,” an im­age she could not ima­gine con­form­ing to.

Kar­en’s evolving vis­ion of the sig­ni­fic­ance of one’s pro­fes­sion­al en­vir­on­ment, par­tic­u­larly for wo­men, had a strong in­flu­ence on later ca­reer de­cisions. She has been offered pres­ti­gi­ous po­s­i­tions and de­clined them be­cause she felt they would not be pos­it­ive en­vir­on­ments for her pro­fes­sion­ally. And she ul­ti­mately chose in­stead an of­fer from the Uni­versity of Texas at Aus­tin, where she now holds a Sid Richard­son Found­a­tion Re­gents’ Chair in Math­em­at­ics.

Kar­en has a fairly un­usu­al re­cord with re­spect to teach­ing. In her early years she taught mostly low-level cal­cu­lus and fi­nite math courses. Later she taught primar­ily gradu­ate courses. She has had little ex­per­i­ence with any­thing in between, i.e., stand­ard un­der­gradu­ate courses or up­per-level (math ma­jor) courses; there­fore many of her thoughts about teach­ing emerge primar­ily from work­ing with gradu­ate stu­dents.

Teach­ing has al­ways been dif­fi­cult for Kar­en. Even when she was young and planned to be “a forest ranger or a sci­ent­ist,” she did not see her­self as a teach­er. The in­tens­ive so­cial skills in­volved in teach­ing and the abil­ity and pa­tience needed to ex­plain com­plex ideas in a simple man­ner were not Kar­en’s strengths. In fact, her quick mind in many ways hindered her abil­ity to teach. She dis­covered early on that the way she learned, and the way she thought about math, did not help her at all in teach­ing oth­er people. “As far as teach­ing goes, it really is true that it takes me years to un­der­stand the dif­fi­culties stu­dents have. I just nev­er com­pre­hend that you have to say something twice. It took me a long time to un­der­stand that say­ing something once is es­sen­tially not say­ing it.” Fur­ther­more, Kar­en was in many ways self-taught, both as a stu­dent and as a math­em­atician. This made it harder to know how to teach oth­er stu­dents; and there were no teach­ers that she was striv­ing to emu­late. Fi­nally, the very traits that are as­sets in her re­search — in­clud­ing her non-lin­ear way of think­ing — can be prob­lem­at­ic in the con­text of teach­ing.

The way I learned is totally use­less for teach­ing. So you have to start again. I have no love of or­gan­iz­a­tion. The ap­peal that math­em­at­ics has for me is not that I can or­gan­ize it; I think many suc­cess­ful teach­ers en­joy this or­gan­iz­a­tion. They like get­ting the ma­ter­i­al in a straight line, and I think that many stu­dents en­joy that kind of present­a­tion. In fact, when I’ve had teach­ers who do that, I of­ten find that it is a very ef­fi­cient, neat way to learn ma­ter­i­al. But the kind of math­em­at­ics I do is very sloppy math­em­at­ics. I was dis­cuss­ing this with a col­league who said that non-lin­ear ana­lys­is seemed so wild or un­tamed com­pared to lin­ear ana­lys­is, and the kind of math­em­at­ics I do is really not a very or­gan­ized kind of thing. So I think I have dif­fi­culties in teach­ing, but that kind of math­em­at­ics is go­ing to be like that. Stu­dents who like things to be or­derly and neat would be crazy to go in­to this kind of math­em­at­ics, where you have to learn an im­mense amount, not quite un­der­stand all sorts of stuff, and put a lot of things to­geth­er that are com­pletely dif­fer­ent. I think it’s prob­ably hard to lec­ture on.

What emerges from Uh­len­beck’s style and ex­per­i­ence is a very per­son­al ap­proach to work­ing with her stu­dents. Since each stu­dent has a unique voice, she in­ter­acts with each of them dif­fer­ently. Rather than try­ing to find a com­mon de­nom­in­at­or, or to teach stu­dents in the same way, she fo­cuses on what is dif­fer­ent about them. “First I de­cided that the stu­dents were so dif­fer­ent that the idea that one would im­pose an out­side the­ory of how they should learn was crazy. Then I de­cided that im­pos­ing an out­side the­ory of how I should teach was also crazy.”

When I star­ted hav­ing gradu­ate stu­dents it was an eye-open­er, be­cause I con­sider my­self a six­ties lib­er­al, and we were all in­ter­ested in teach­ing dif­fer­ently and giv­ing people the right ideas and not be­ing so form­al. But when I star­ted hav­ing more than one gradu­ate stu­dent, maybe around my fourth gradu­ate stu­dent, I real­ized that the­or­ies of learn­ing are prob­ably just non­sense be­cause people think so dif­fer­ently. My first four stu­dents were all Amer­ic­ans. They all went through school, they all came from a sim­il­ar cul­ture, they were all in­ter­ested in math­em­at­ics, they were all in­ter­ested in roughly the same kind of math­em­at­ics, and they were all com­pletely dif­fer­ent.

Some of them think ab­stractly, so much so that I don’t ever un­der­stand any­thing they say be­cause I write dif­fer­ently. Some of them were so con­crete; they had to start with the simplest case and work up. There’s just this ter­rif­ic vari­ety between think­ing ab­stractly, think­ing by ex­amples, think­ing con­cretely. The bril­liant stu­dent I had who was half phys­i­cist was a very loose thinker. Some of them are very tight thinkers. They all have something very dif­fer­ent to con­trib­ute to math­em­at­ics if you prod them enough.

They all got in­ter­ested. I nev­er had a stu­dent who didn’t get in­ter­ested. I can’t ima­gine try­ing to get a stu­dent through a Ph.D. when they wer­en’t in­ter­ested. But they’re all dif­fer­ent. When you’re go­ing to teach kids, fresh­men, any­body else \( \dots \) if there’s that much vari­ation of gradu­ate stu­dents in math­em­at­ics, how much vari­ation is there go­ing to be in the gen­er­al pop­u­la­tion?

Kar­en’s primary task as an ad­visor, there­fore, is to help stu­dents find their unique styles and con­tri­bu­tion. As she says, “In or­der to be a good math­em­atician, you’ve got to fig­ure out what you can do and find out the way you think. I don’t think it’s so easy. You have to find your own way of do­ing things.”

At the same time, she also ap­pre­ci­ates that help from oth­ers at crit­ic­al times can make a tre­mend­ous dif­fer­ence. When her stu­dents get dis­cour­aged, for ex­ample, she re­minds them that every­one gets dis­cour­aged and re­com­mends tricks that can help: hav­ing an easy prob­lem and a hard prob­lem to work on, try­ing something dif­fer­ent for a thes­is top­ic, tak­ing a va­ca­tion, read­ing an art­icle if you’re tired of banging your head against the wall, or giv­ing a sem­in­ar.

But the en­cour­age­ment and stim­u­la­tion does not go just one way. Uh­len­beck con­siders her stu­dents her math­em­at­ic­al chil­dren; work­ing with them is a very re­ward­ing part of her life. Many of them have also been great teach­ers for her, and a ma­jor source of in­spir­a­tion. Her early gradu­ate stu­dents were par­tic­u­larly im­port­ant; they would take courses, for ex­ample in al­geb­ra­ic to­po­logy, and would even­tu­ally learn more than she knew, so they could teach her, mak­ing the re­la­tion­ship a re­cip­roc­al one. “My gradu­ate teach­ing is so suc­cess­ful partly be­cause I have ar­ranged it so that I learn from them.”

In­deed, when she is asked about who has been most in­flu­en­tial on her math­em­at­ic­al de­vel­op­ment, she says, “I think I’ve been in­flu­enced by some of my stu­dents more than any­thing. I had a really good, bright stu­dent who was in between phys­ics and math­em­at­ics, and when he left Chica­go, I knew I was go­ing to miss him. So I would go over to the phys­ics sem­inars.” She re­calls that he said of their dis­cus­sions, “It’s really strange, you go in there and she talks and talks and talks and you nev­er quite un­der­stand, but after a while something hap­pens and it’s worth it.”

Uh­len­beck’s re­search blends geo­metry, to­po­logy, phys­ics, and ana­lys­is. At the time of the in­ter­view, it in­volved find­ing con­nec­tions between math­em­at­ics and the new phys­ics. For ex­ample, she com­bines geo­met­ric con­cepts with de­tailed ana­lys­is of par­tial dif­fer­en­tial equa­tions to de­scribe ob­jects as var­ied as soap bubbles, black holes, and cer­tain kinds of quantum tun­nel­ing.

She is of­ten torn now about how to use her time: do­ing prob­lems, de­vel­op­ing ideas that she’s already been work­ing on, or learn­ing new ma­ter­i­al which could lead to new prob­lems and a lar­ger pic­ture of how pieces fit to­geth­er. It is her will­ing­ness to con­stantly ex­plore new ter­rit­ory that has kept her math­em­at­ic­ally vi­brant and alive.

There is the pleas­ure of do­ing math­em­at­ics and this real de­sire to learn what the phys­i­cist Ed Wit­ten is do­ing. They are pulling me in op­pos­ite dir­ec­tions. I would like to do math­em­at­ics, but I also want to know what’s go­ing on over there, and the two are really dif­fer­ent. I can’t leave these new ideas alone. This is where the ac­tion is, and I feel that I really have to learn all this. I’m in a field that has had a lot hap­pen in the last fif­teen years. For me this is very ex­cit­ing. As one of my stu­dents said, “It’s like be­ing a pi­on­eer and walk­ing on some area that nobody had ever walked be­fore.”

But for Uh­len­beck, a new kind of pleas­ure has emerged from do­ing math­em­at­ics, one for which age and ex­per­i­ence are as­sets.

I still get a kick out of do­ing math­em­at­ics. It’s harder to come by now be­cause many of my stand­ards are high­er. But now there’s a new kind of pleas­ure of try­ing to fit things to­geth­er, mak­ing something match something else. When I was young­er I had no in-depth know­ledge of math­em­at­ics. By now I know an aw­ful lot of math­em­at­ics, and I’m really fas­cin­ated by con­nec­tions.

One char­ac­ter­ist­ic of Uh­len­beck’s re­search that is dis­tinct­ive is not only the sub­ject mat­ter she pur­sues, but also how she thinks.

[How I think] is not lin­ear. When I write a pa­per, it’s much bet­ter to just have the ba­sic ideas, and then I can pick them out and fill them in. If I just write this thing that goes lin­early, I get con­fused. I’ve dis­covered that there are ba­sic­ally two types of math­em­aticians, those that really do go from point to point and get real up­set if pa­pers aren’t writ­ten that way and write their pa­pers that way and want the lec­tures that way, and then there are people like me who prefer the ideas to be giv­en and the filling in [is sec­ond­ary] — it’s just struc­tured dif­fer­ently in my mind.

I think some people are very sur­prised that a math­em­atician would be like this. They think of math­em­at­ics as be­ing ordered and care­ful and so forth. And in­deed many oth­er math­em­aticians are like this. Maybe more of them are very or­derly as a whole. But it’s not the way I think, and it’s not the way I learn. In fact, there’s really no way to get in­to com­mu­nic­a­tion with mod­ern phys­ics without just sit­ting through a lot of it so that it stops sound­ing like garbage. You can’t lo­gic­ally work your way through this non­sense. You just sit through enough and sud­denly what they’re say­ing seems lo­gic­al and starts fit­ting to­geth­er. It’s a dif­fer­ent lan­guage.

In the end, Uh­len­beck’s unique in­terests, curi­os­ity, and style have all con­trib­uted to her suc­cess. And while Uh­len­beck is de­lighted by her math­em­at­ic­al suc­cesses, the ex­tern­al re­cog­ni­tion that has ac­com­pan­ied this suc­cess has not been un­mit­ig­ated pleas­ure — something that is hard for many people to un­der­stand. Awards such as the Ma­cAr­thur Fel­low­ship and elec­tion to the Na­tion­al Academy of Sci­ences are coveted by most every­one in the pro­fes­sion, but for Uh­len­beck they raise dif­fi­cult is­sues about her iden­tity.

I didn’t mind be­ing a wo­man do­ing math, not sup­posed to be do­ing it, work­ing on the fringes, suc­ceed­ing in a small way, and sort of be­ing in­com­pre­hens­ible and not hav­ing many stu­dents. In many ways that was much more com­fort­able. I was really sort of do­ing it for my­self. Then [when I star­ted get­ting awards and pub­lic re­cog­ni­tion] I had to make a ma­jor ree­valu­ation of who I am. Get­ting the Ma­cAr­thur is really sort of trau­mat­ic in some ways. I just nev­er thought of my­self in any way like that.

There are sev­er­al factors that con­trib­ute to the dis­com­fort Uh­len­beck has with this re­cog­ni­tion. There is of course the prac­tic­al is­sue of how time-con­sum­ing such awards can be: par­tak­ing in ce­re­mon­ies, giv­ing talks, so­cial­iz­ing with oth­er award win­ners and academy fel­lows. But the sense of bur­den is much deep­er and more com­plex for Uh­len­beck than just in­creas­ing de­mands on her time.

Like many math­em­aticians, Kar­en is a very private per­son who chose to pur­sue math­em­at­ics in part be­cause it was a world apart from the pub­lic arena. “You choose to do your own thing [in math­em­at­ics], and what you do is very private and per­son­al, and three oth­er people in the world may un­der­stand that.” That pri­vacy is what Uh­len­beck is most com­fort­able with, and it is what she lost as she gained re­cog­ni­tion. Be­cause of the awards she sud­denly be­came a pub­lic fig­ure, a far cry from what drew her to math­em­at­ics.3 Moreover, the awards forced her to pub­licly see her­self, and re­cog­nize that oth­er people saw her, as a wo­man math­em­atician, not just a math­em­atician. Since so many people began to ad­dress ques­tions of wo­men in sci­ence to her, she sud­denly had to speak for all wo­men. This was an un­com­fort­able role for Uh­len­beck. She does not see her­self as a typ­ic­al wo­man, nor does she think she makes a very good role mod­el for wo­men. In fact, be­cause she found her pas­sage a dif­fi­cult one, she does not want her story to be ex­em­plary.

Fur­ther­more, be­ing cast in­to the role raises con­flicts in her strategy for deal­ing with gender prob­lems. To a large de­gree Uh­len­beck felt that she was ob­li­vi­ous to gender bi­as, and her way of deal­ing with prob­lems was of­ten to ig­nore them. But when she hears the dis­cour­aging ex­per­i­ences of many oth­er wo­men, she feels a heightened sense of re­spons­ib­il­ity. “I’m not sens­it­ive to my­self at all, but I am sens­it­ive on be­half of young­er wo­men.” In her pub­lic role, par­tic­u­larly when she is seen as a rep­res­ent­at­ive of wo­men in math, she could no longer ig­nore the prob­lems. “I think you’ll find lots of older wo­men, even though they may not say they’re fem­in­ists, who will get furi­ous [about the kinds of prob­lems wo­men con­front]. You won’t find that in young wo­men who have any hope in suc­ceed­ing. It’s self-pre­ser­va­tion.” At the same time, tak­ing these prob­lems on can be ex­tremely frus­trat­ing, par­tic­u­larly when there is little one can do about them. “Once I be­came a mem­ber of the math­em­at­ic­al elite I found it a pain \( \dots \) to be a wo­man. There are two choices for me. I can either ig­nore the fact that I’m a wo­man or I can be­come a ra­bid an­im­al. \( \dots \) I don’t see any in-between re­ac­tion to the situ­ation.”

In her own life, though she did to some ex­tent “ig­nore the fact” that she was a wo­man, Uh­len­beck de­veloped mech­an­isms to cre­ate an en­vir­on­ment in which she felt com­fort­able. She cre­ated a niche by de­fin­ing her­self in op­pos­i­tion to the very group she felt ex­cluded by. In this way she was able to em­brace what was dif­fer­ent about her­self, and in the pro­cess to lib­er­ate her­self from the need for ex­tern­al af­firm­a­tion. Woody Al­len quipped that he nev­er reads re­views of his work be­cause if he took the good re­views ser­i­ously and was pleased by them, then he would have to ac­cept the bad re­views and get de­pressed by them. Uh­len­beck, too, did not seek out or have much in­vest­ment in af­firm­a­tion from the lar­ger math com­munity. But this strategy made it con­fus­ing to main­tain her iden­tity when she sud­denly found her­self be­ing defined as “one of them.”

I prob­ably had al­ways been look­ing out­ward in\( \dots \). You say “those guys” and here you are, your whole ca­reer you’re look­ing from the out­side in and say­ing “those guys” and then you’re sud­denly one of them. But you’re not, be­cause you’ll nev­er be. I found it ex­tremely hard to re­ad­just everything. \( \dots \) I’m not able to trans­form my­self com­pletely in­to the mod­el of a suc­cess­ful math­em­atician be­cause at some point it seemed like it was so hope­less that I just resigned my­self to be­ing on the out­side look­ing in. It will take a long time, if ever, be­fore I can see my­self as be­ing really suc­cess­ful be­cause I’m so con­di­tioned to do it be­cause I want to do it and to get along with life.

Uh­len­beck’s life is a re­mind­er that tra­di­tion­al meas­ures of suc­cess can be viewed quite dif­fer­ently by wo­men. This is not to say that wo­men should not get these re­wards, nor that they don’t want them. It does, however, make us more sens­it­ive to the fact that even “suc­cess” for wo­men in tra­di­tion­ally male fields is a com­plex is­sue. There are two sides to these bless­ings, and while it is nice to have ex­tern­al re­cog­ni­tion, the at­tend­ant bur­dens and re­spons­ib­il­it­ies are weighty.

Uh­len­beck’s life ex­em­pli­fies the fact that what hinders wo­men in math­em­at­ics is not ne­ces­sar­ily lack of tal­ent. Many factors con­trib­ute to the dif­fi­culty wo­men face in feel­ing like equal mem­bers of the math­em­at­ics com­munity. While Uh­len­beck has the tal­ent and the in­de­pend­ence to pur­sue math­em­at­ics on her own, her suc­cess was sig­ni­fic­antly tied to her con­nec­tions with­in the math­em­at­ics com­munity. But es­tab­lish­ing these ties can be more dif­fi­cult for wo­men. In some cases, wo­men are more likely to be seen as fac­ulty wives rather than pro­fes­sion­als in their own right. In oth­ers they may just be seen as dif­fer­ent, not fit­ting the im­age of what a math­em­atician or a col­league is sup­posed to be.

For Uh­len­beck, es­tab­lish­ing ties to the com­munity was also made more dif­fi­cult by her in­de­pend­ent nature, and the fact that she thought quite dif­fer­ently than many of her col­leagues. She was not so­cial­ized to “speak the same lan­guage.” While this very trait of in­de­pend­ence is what en­abled Uh­len­beck and oth­er wo­men to pur­sue math­em­at­ics in the first place, in some ways it can also later be­come a hindrance.

Many people have sug­ges­ted that the dif­fi­culties wo­men face in math­em­at­ics are partly due to wo­men’s lack of con­fid­ence, but Uh­len­beck sug­gests that the prob­lem is more one of a lack of fit. “I some­how feel that it’s not so much a lack of con­fid­ence as not feel­ing in the right place. Wo­men have plenty of con­fid­ence. The wo­men that I’m talk­ing about can do any­thing. That’s the prob­lem. They’re sur­viv­ors of life. They know they can find something else in­ter­est­ing to do.” For this reas­on, Uh­len­beck ar­gues that many very tal­en­ted wo­men choose to leave math­em­at­ics. But even those who stay can also ex­per­i­ence that sense of not be­long­ing, or not fit­ting in. This was true for Uh­len­beck, both at Cham­paign-Urb­ana and at the Uni­versity of Chica­go. In dif­fer­ent ways gender played a role in mak­ing her feel like an out­sider, a sense of dis­tance that can be fur­ther ex­acer­bated by oth­er dif­fer­ences such as race, class, or eth­nic back­ground. In the end, even someone as highly self-suf­fi­cient as Kar­en Uh­len­beck dis­covered that one’s pro­fes­sion­al en­vir­on­ment can play an im­port­ant role in one’s sense of be­long­ing. As she says, “There are all these trivi­al things which have noth­ing to do with your math­em­at­ic­al abil­ity [which in­flu­ence your math­em­at­ic­al life]. Math­em­at­ic­al abil­ity is such a small part.”

Kar­en Uh­len­beck works on a vari­ety of prob­lems which defy pi­geon­hol­ing in­to a unique math­em­at­ic­al field. The terms “glob­al ana­lys­is” and “par­tial dif­fer­en­tial equa­tions” prob­ably come closest, but they do not con­vey the im­port­ance that ideas from the­or­et­ic­al phys­ics play in her work and in this field gen­er­ally. “Dif­fer­en­tial equa­tions” are ex­pressed in terms of cal­cu­lus, which was in­ven­ted by New­ton and Leib­n­iz in the sev­en­teenth cen­tury. New­ton was mo­tiv­ated by the study of mo­tion, par­tic­u­larly mo­tion of the plan­ets. Much of Uh­len­beck’s work deals with equa­tions whose ori­gins lie in mod­ern ver­sions of New­ton’s the­ory of mech­an­ics and grav­ity. Though I stress the phys­ic­al ori­gins of the equa­tions, one must real­ize that math­em­aticians study these equa­tions in a man­ner much dif­fer­ent than phys­i­cists. Of­ten we ap­ply these equa­tions in new con­texts, and we use them to teach us about oth­er math­em­at­ic­al struc­tures. Such is the case with the “Yang–Mills equa­tions,” whose study oc­cu­pied Uh­len­beck dur­ing much of the pre­vi­ous dec­ade. Her fun­da­ment­al first work on these equa­tions en­abled oth­er math­em­aticians, par­tic­u­larly Si­mon Don­ald­son, to use them to re­vo­lu­tion­ize the field of four-di­men­sion­al to­po­logy. Her later work had rami­fic­a­tions in the field of al­geb­ra­ic geo­metry. Without dis­cuss­ing the tech­nic­al de­tails, one can still ap­pre­ci­ate the cent­ral­ity of her work, which con­nects on the one hand to the­or­et­ic­al phys­ics and on the oth­er to more ab­stract fields of math­em­at­ics. Uh­len­beck has done sem­in­al work on many oth­er equa­tions as well, and her cur­rent work is in yet an­oth­er new dir­ec­tion — the the­ory of “in­teg­rable sys­tems” — and prom­ises to yield ex­cit­ing res­ults.