Celebratio Mathematica

Dr. Kar­en K. Uh­len­beck, a pro­fess­or of math­em­at­ics at The Uni­versity of Texas at Aus­tin, has been awar­ded the Na­tion­al Medal of Sci­ence. She is one of 12 renowned Amer­ic­an sci­ent­ists and en­gin­eers to re­ceive the hon­or, which will be presen­ted at an awards din­ner sched­uled for Fri­day (Dec. 1) in Wash­ing­ton, D.C.

In an­noun­cing the Year 2000 Na­tion­al Medal of Sci­ence win­ners, Pres­id­ent Bill Clin­ton paid trib­ute to this group of sci­entif­ic lead­ers, who have set new dir­ec­tions in so­cial policy, neur­os­cience, bio­logy, chem­istry, bioen­gin­eer­ing, math­em­at­ics, phys­ics and earth and en­vir­on­ment­al sci­ences.

“These ex­cep­tion­al sci­ent­ists and en­gin­eers have trans­formed our world and en­hanced our daily lives,” Pres­id­ent Clin­ton said. “Their ima­gin­a­tion and in­genu­ity will con­tin­ue to in­spire fu­ture gen­er­a­tions of Amer­ic­an sci­ent­ists to re­main at the cut­ting edge of sci­entif­ic dis­cov­ery and tech­no­lo­gic­al in­nov­a­tion.”

Uh­len­beck, who holds the Sid W. Richard­son Found­a­tion Re­gents Chair in Math­em­at­ics, con­ducts re­search in geo­metry and par­tial dif­fer­en­tial equa­tions and stud­ies ap­plic­a­tions of geo­metry to large-scale prob­lems in high-en­ergy phys­ics. She also is in­ter­ested in the ways that new com­plex math­em­at­ic­al con­cepts find uses in re­search in oth­er areas of sci­ence, such as eco­logy, mo­lecu­lar bio­logy and the struc­ture of ma­ter­i­als.

“I am grate­ful to both the math­em­at­ics de­part­ment of The Uni­versity of Texas and to the gen­er­ous be­ne­fact­ors who en­dowed the Re­gents Chair. With this sup­port and money, I have been able to ac­com­plish quite a lot, both in the sub­ject of math­em­at­ics and in sup­port­ing and en­cour­aging the next gen­er­a­tion of math­em­aticians,” Uh­len­beck said.

The Na­tion­al Medal of Sci­ence is some­times re­ferred to as Amer­ica’s No­bel Prize. Uh­len­beck re­ceived her medal for her pi­on­eer­ing con­tri­bu­tions to glob­al ana­lys­is and gauge the­ory that res­ul­ted in ad­vances in math­em­at­ic­al phys­ics and the the­ory of par­tial dif­fer­en­tial equa­tions. Spokes­men for the Na­tion­al Sci­ence Found­a­tion, which ad­min­is­ters the Na­tion­al Medals of Sci­ence for the White House, said Uh­len­beck stands out as one of the founders of geo­metry based on ana­lyt­ic­al meth­ods.

The NSF also cited her lead­er­ship as a ment­or for wo­men and minor­it­ies in math­em­at­ics edu­ca­tion. She and her cowork­er, Chuu- Li­an Terng, are the or­gan­izers of a ment­or­ing pro­gram for wo­men math­em­aticians, which is held at the In­sti­tute for Ad­vanced Study each spring.

“I feel very humble, as many great­er sci­ent­ists have re­ceived this award. I hope that my ac­cept­ance will serve as en­cour­age­ment to young wo­men sci­ent­ists and math­em­aticians,” Uh­len­beck said. Uh­len­beck said it is not easy to de­scribe her work in geo­metry in non-tech­nic­al lan­guage, a prob­lem she has in com­mon with most re­search math­em­aticians.

“Math­em­at­ics is a dis­cip­line which takes ideas from all branches of sci­ence and ex­tends, con­structs and de­vel­ops fur­ther these ideas in­to a body of res­ults that we usu­ally refer to as the­or­ems. These ideas can be used in­de­pend­ently as a lan­guage to de­scribe new pro­cesses that have noth­ing to do with the ori­gin­al source,” she ex­plained. “For ex­ample, I study bubbles, that ori­gin­ate with soap bubbles. But I use them in ab­stract con­texts, where they can be used to in­vest­ig­ate the shape of space or to study the struc­ture of ma­ter­i­als.

“A ba­sic idea in high en­ergy phys­ics is part of the de­scrip­tion of col­or and charm (gauge the­ory). I study this ab­stractly, and have found ways to use this in the study of waves and mag­net­ic ma­ter­i­als. Oth­er math­em­aticians have used my work in the study of space-time and in string the­ory,” she said.

Uh­len­beck said the group she works with at UT Aus­tin “spe­cial­izes in look­ing for new ideas in math­em­at­ics in the work of oth­er sci­ences. While our primary work is the­or­et­ic­al phys­ics, we have a mem­ber who thinks about how DNA coils. I have been fas­cin­ated by a num­ber of equa­tions I learned about from phys­i­cists who study plasma and flu­id flow.” She ad­ded that “in com­mon with all ba­sic re­search­ers, math­em­aticians do not ex­pect im­me­di­ate ap­plic­a­tions, al­though we do ex­pect the ideas we de­vel­op to be around for cen­tur­ies. The kinds of math­em­at­ics that are used in ap­plic­a­tions have be­come di­verse, and we don’t try hard to second guess what will be use­ful next year.”

Uh­len­beck, who was awar­ded a Ma­cAr­thur Found­a­tion fel­low­ship in 1983, has taught at UT Aus­tin since 1987. She was born in Clev­e­land and grew up in New Jer­sey. She gradu­ated from the Uni­versity of Michigan and earned her Ph.D. at Bran­de­is Uni­versity, with a Na­tion­al Sci­ence Found­a­tion gradu­ate fel­low­ship. Ten of the 12 sci­ence medal­lists this year, in­clud­ing Uh­len­beck, re­ceived NSF sup­port for por­tions of their aca­dem­ic or re­search ca­reers.

She was a Woo­drow Wilson Fel­low, a Sloan Fel­low and an Al­bert Ein­stein Fel­low at the In­sti­tute for Ad­vanced Study. She is a re­cip­i­ent of the Com­mon Wealth Award for Sci­ence and In­ven­tion, and a mem­ber of the Amer­ic­an Academy of Arts and Sci­ences and the Na­tion­al Academy of Sci­ence. Uh­len­beck is co-au­thor of In­stan­tons and Four-Man­i­fold To­po­logy, pub­lished in 1983, and her work has con­trib­uted to the dis­cov­ery of a new four-di­men­sion­al space-time. She is a mem­ber of the Texas In­sti­tute for Com­pu­ta­tion­al and Ap­plied Math­em­at­ics.