Celebratio Mathematica

Karen Uhlenbeck

Michigan Great Karen K. Uhlenbeck:
Pioneer in mathematical analysis — and for women mathematicians

by Lee Katterman

Kar­en K. Uh­len­beck stud­ied math­em­at­ics for many years, well in­to gradu­ate school, be­fore she fi­nally ac­know­ledged that a ca­reer in this field was right for her. “Even when I had my Ph.D. for five years,” she said, “I was still strug­gling with wheth­er I should be­come a math­em­atician. I nev­er saw my­self very clearly.”

Today, Uh­len­beck, hold­er of the Sid W. Richard­son Found­a­tion Re­gents Chair in Math­em­at­ics at the Uni­versity of Texas at Aus­tin, is widely ac­claimed as a tal­en­ted and cre­at­ive math­em­atician as well as someone who takes very ser­i­ously her ob­lig­a­tion to ment­or young wo­men math­em­aticians. Through her re­search, Uh­len­beck has made sig­ni­fic­ant con­tri­bu­tions to our un­der­stand­ing of the fun­da­ment­al prop­er­ties of mat­ter. In her pro­fes­sion­al life, she has demon­strated a per­sever­ance that en­abled her to suc­ceed in sci­ence in spite of the dis­cour­aging road­b­locks she en­countered.

Uh­len­beck was born in 1942 in Clev­e­land, Ohio, and spent her teen years in rur­al New Jer­sey. Her act­ive par­ti­cip­a­tion in sports and phys­ic­al activ­ity was un­con­ven­tion­al for the times — girls were ex­pec­ted to be in­ter­ested in dat­ing, mar­riage, and hav­ing and rais­ing chil­dren.

Her life path, Uh­len­beck says, was in­flu­enced by strong and in­de­pend­ent wo­men in her fam­ily. Her grand­moth­er, for one, raised 12 chil­dren al­most single-handedly and lived to be 103 years old. Her moth­er — Car­o­lyn Keskulla — had a fiercely in­de­pend­ent streak as an artist, in­tel­lec­tu­al and non­con­form­ist. Out of this, Kar­en Uh­len­beck de­cided early on that she prob­ably would be­come “a forest ranger or some kind of sci­ent­ist,” al­though she nev­er ima­gined dur­ing high school that math­em­at­ics was in her fu­ture.

Uh­len­beck came to the Uni­versity of Michigan in 1960 as an Hon­ors Pro­gram stu­dent. It was dur­ing these years that Uh­len­beck dis­covered her pas­sion for math­em­at­ics. In fact, she switched her ma­jor from phys­ics to math­em­at­ics be­cause she was do­ing poorly in phys­ics lab courses and flour­ished un­der a cre­at­ive free­dom she felt in her hon­ors math­em­at­ics courses. But even then, Uh­len­beck didn’t yet see her­self pur­su­ing a ca­reer in math­em­at­ics.

She did de­cide to at­tend gradu­ate school — but mainly be­cause her boy­friend and oth­er friends were do­ing so. Her boy­friend was go­ing to Har­vard, yet Kar­en, whose gradu­ate stud­ies were sup­por­ted by fel­low­ships from the Na­tion­al Sci­ence Found­a­tion and Woo­drow Wilson Found­a­tion, did not give ser­i­ous thought to the school. Ini­tially, she at­ten­ded the Cour­ant In­sti­tute in New York City, which had an ex­cel­lent math­em­at­ics pro­gram, but was con­sidered less pres­ti­gi­ous be­cause of its “ap­plied math” fo­cus.

After get­ting mar­ried in 1965, Uh­len­beck trans­ferred to Bran­de­is to be closer to her hus­band. “For someone like me, Bran­de­is was a su­per place to be a gradu­ate stu­dent be­cause the fac­ulty were all ex­tremely young,” Uh­len­beck re­calls. She now real­izes that the young fac­ulty provided role mod­els she wouldn’t have found at top tra­di­tion­al math­em­at­ics schools.

After re­ceiv­ing her Ph.D. in 1968, she fol­lowed her bio-phys­i­cist hus­band to Mas­sachu­setts In­sti­tute of Tech­no­logy and then Berke­ley, where she worked as a non-ten­ure track lec­turer be­cause the schools in­ter­ested in her hus­band were not in­ter­ested in her. In 1971, Uh­len­beck was offered an as­sist­ant pro­fess­or­ship at the Uni­versity of Illinois, Urb­ana-Cham­paign. This time her hus­band moved with her. However, the mar­riage ended a few years later, at which time Uh­len­beck joined the fac­ulty at the Uni­versity of Illinois–Chica­go.

A few col­leagues at Urb­ana-Cham­paign and Chica­go provided more role mod­els (in­clud­ing her first wo­man fac­ulty col­league) that helped Uh­len­beck put her ca­reer in­to a high­er gear. In 1982, she re­ceived a Ma­cAr­thur Fel­low­ship, the so-called “geni­us” award. She fur­ther de­veloped her re­search as a vis­it­ing pro­fess­or at Berke­ley, Har­vard, the Max Planck In­sti­tute and Uni­versity of Cali­for­nia–San Diego. In 1986, at age 44, Uh­len­beck be­came the first wo­man math­em­atician elec­ted to the Na­tion­al Academy of Sci­ences. Since then, only two oth­er wo­men math­em­aticians have been elec­ted to the Academy — both in the last two years — out of a total of 111 math­em­aticians who are cur­rent mem­bers.

In an­noun­cing her elec­tion to the Na­tion­al Academy of Sci­ences, the Academy said: “Uh­len­beck has been the fore­most pi­on­eer in de­vel­op­ing and ap­ply­ing hard ana­lyt­ic meth­ods in the cal­cu­lus of vari­ations and non­lin­ear par­tial dif­fer­en­tial equa­tions to the study of the math­em­at­ic­al struc­ture of the gauge field the­or­ies of present-day fun­da­ment­al phys­ics.”

In 1995, Uh­len­beck re­ceived the Com­mon Wealth Award for Sci­ence and Tech­no­logy from Sigma Xi, the na­tion­al re­search hon­or­ary so­ci­ety, and, in 1984, was named Alumna of the Year by the U-M.

Al­though Uh­len­beck says she entered math­em­at­ics be­liev­ing she could simply work by her­self and hide from the pres­sures wo­men faced in aca­demia, Uh­len­beck ul­ti­mately forged a num­ber of col­lab­or­a­tions that helped her work. She also learned that she truly en­joyed ment­or­ing stu­dents. She is es­pe­cially proud of her role as one of the founders of the Park City Math­em­at­ics In­sti­tute at the In­sti­tute for Ad­vanced Study at Prin­ceton. Un­der the aus­pices of this In­sti­tute, Uh­len­beck has or­gan­ized a ment­or­ing pro­gram for wo­men math­em­aticians. Over a two-week peri­od, the wo­men par­ti­cip­ate in sem­inars, work­ing prob­lem groups, and ment­or­ing and net­work­ing ses­sions. They also have an op­por­tun­ity to meet and con­verse with math­em­aticians in res­id­ence at the In­sti­tute for Ad­vanced Study.

Kar­en Uh­len­beck has blen­ded her unique in­terests, a curi­os­ity for math­em­at­ics and in­quiry, and a dog­ged­ness to sur­pass the so­cial hurdles she has en­countered to cre­ate a suc­cess­ful ca­reer as a ment­or and sci­ent­ist.