Celebratio Mathematica

Donald L. Burkholder

In memoriam: Donald Burkholder

University of Illinois Urbana-Champaign

Don­ald Ly­man Burk­hold­er, a renowned math­em­atician who helped to re­vo­lu­tion­ize in­ter­dis­cip­lin­ary stud­ies in the areas of prob­ab­il­ity the­ory and ana­lys­is and who spent his en­tire ca­reer as a pro­fess­or at the Uni­versity of Illinois, died in his sleep on Sunday, April 14, 2013, in Urb­ana, Illinois. He was 86.

He was born Janu­ary 19, 1927, in Octavia, Neb­raska, the fourth of five chil­dren of Elmer and Susan (Ro­throck) Burk­hold­er. His moth­er had been a school­teach­er, and his fath­er was a farm­er who served on the com­munity school board for many years. Edu­ca­tion be­came the fam­ily busi­ness: of the four boys, the old­est was a su­per­in­tend­ent of schools, the three young­est were col­lege pro­fess­ors, and many in the next gen­er­a­tion are edu­cat­ors.

In 1945, Don gradu­ated from high school, where he was cap­tain of the bas­ket­ball team and seni­or class pres­id­ent, an hon­or (as he loved to re­late) that came his way be­cause his three class­mates had all been pres­id­ent already. He was draf­ted and entered the Ci­vil­ian Pub­lic Ser­vice as a con­scien­tious ob­ject­or, serving as a cook at a camp for fight­ing forest fires in Ore­gon and as an or­derly at a men­tal hos­pit­al in New Jer­sey.

Fol­low­ing his dis­charge in Decem­ber, 1946, he ac­ted on the re­com­mend­a­tion of a friend and en­rolled at Earl­ham Col­lege, a pre­dom­in­antly Quaker col­lege in Rich­mond, In­di­ana. There he met his wife-to-be, Jean An­nette Fox, and they were both drawn to the field of so­ci­ology by the vis­ion and in­tel­lec­tu­al rig­or of a new fac­ulty mem­ber who had also served in the CPS, Bill Fus­on.

After their wed­ding in June 1950, Don and Jean at­ten­ded the Uni­versity of Wis­con­sin in Madis­on as gradu­ate stu­dents in so­ci­ology. In 1953 they went to the Uni­versity of North Car­o­lina at Chapel Hill, where Don had a fel­low­ship to study so­ci­olo­gic­al stat­ist­ics. He soon dis­covered that his real in­terest lay in math­em­at­ics, and he com­pleted a Ph.D. in stat­ist­ics in 1955 un­der the guid­ance of Prof. Wassily Hoeff­d­ing. That sum­mer, Don joined the Math­em­at­ics De­part­ment at the Uni­versity of Illinois in Urb­ana, where he be­came a pro­fess­or in 1964. In 1978 he was ap­poin­ted Pro­fess­or in the Uni­versity of Illinois’ Cen­ter for Ad­vanced Study. Don re­tired as pro­fess­or emer­it­us in 1998.

Soon after he came to Illinois, Don, in­flu­enced by his em­in­ent col­league Joseph Doob, turned to the study of mar­tin­gales and their con­nec­tions to oth­er areas of math­em­at­ics. The term mar­tin­gale is used in the dis­cip­line of prob­ab­il­ity to de­scribe a fair gambling game, in which the for­tunes of the gam­bler and the house are equally weighted. It is a mat­ter of bal­ance. As Don liked to point out, the study of mar­tin­gales is like study­ing cer­tain prop­er­ties of Al­ex­an­der Calder’s mo­biles, art­works whose parts hang in per­fect bal­ance.

It is now widely re­cog­nized that the concept of bal­ance em­bod­ied in mar­tin­gales is cent­ral for a large num­ber of ob­jects in math­em­at­ic­al fields seem­ingly un­con­nec­ted to prob­ab­il­ity. Don’s re­search, in­clud­ing a fruit­ful set of pa­pers with his col­lab­or­at­or Richard Gundy, pro­foundly ad­vanced mar­tin­gale the­ory and drove a re­volu­tion in the last third of the twen­ti­eth cen­tury that el­ev­ated prob­ab­il­ity the­ory to a ma­jor role in the study of ana­lys­is and dif­fer­en­tial equa­tions.

In his five-dec­ade ca­reer, Don gave sev­er­al hun­dred in­vited lec­tures and lec­ture series in Eng­land, France, Ger­many, Switzer­land, Is­rael, Den­mark, Sweden, Po­land, Hun­gary, Ja­pan, Singa­pore, Italy, Scot­land, Spain, and Canada and at uni­versit­ies across the United States. He was ed­it­or of the An­nals of Math­em­at­ic­al Stat­ist­ics (1964–67), pres­id­ent of the In­sti­tute of Math­em­at­ic­al Stat­ist­ics, a lead­ing in­ter­na­tion­al so­ci­ety (1975–76), and a mem­ber of many coun­cils, ad­vis­ory com­mit­tees, and gov­ern­ing boards. He was a ded­ic­ated teach­er and ment­ored 19 Ph.D. stu­dents.

He was elec­ted to the Na­tion­al Academy of Sci­ences in 1992, and was a Fel­low of the Amer­ic­an Academy of Arts and Sci­ences, the So­ci­ety for In­dus­tri­al and Ap­plied Math­em­at­ics, and the Amer­ic­an As­so­ci­ation for the Ad­vance­ment of Sci­ence. In Decem­ber 2012, he was among the first class named as Fel­lows of the Amer­ic­an Math­em­at­ic­al So­ci­ety.

In his early years at the Uni­versity of Illinois, Don was deeply in­flu­enced by his close col­league Joseph Doob. Half a cen­tury later, Don’s last ma­jor ef­fort as a math­em­atician was to edit a volume of math­em­at­ic­al art­icles in memory of Prof. Doob, which ap­peared in 2006. Sub­sequently, Don’s col­leagues honored him in turn with a col­lec­tion of his ma­jor art­icles (2011) and a volume of math­em­at­ic­al art­icles in his hon­or (2012). Don was de­voted to pos­it­ive so­cial change. Dur­ing one sum­mer in col­lege, he vo­lun­teered in a com­munity group ad­voc­at­ing hous­ing de­seg­reg­a­tion in Chica­go while earn­ing money in the Chica­go steel mills, lay­ing bricks in the fur­naces. He worked for civil rights with the Fel­low­ship of Re­con­cili­ation, foun­ded by Ba­yard Rustin. Throughout his life, he con­trib­uted to or­gan­iz­a­tions and polit­ic­al can­did­ates who cham­pioned so­cial justice, equal op­por­tun­ity, and lift­ing in­di­vidu­als and com­munit­ies at home and abroad out of the rav­ages of poverty. He shared these in­terests with his wife Jean, who has been act­ive in the Urb­ana-Cham­paign com­munity, work­ing with the League of Wo­men Voters and oth­er or­gan­iz­a­tions on hous­ing, in­teg­ra­tion, urb­an plan­ning, neigh­bor­hood pre­ser­va­tion, and edu­ca­tion, in­clud­ing ser­vice as the first chair of the Urb­ana Hu­man Re­la­tions Com­mis­sion and twenty-two years on the Urb­ana School Board.

Don is sur­vived by his wife of al­most 63 years, Jean An­nette (Fox) Burk­hold­er; his son J. Peter Burk­hold­er and son-in-law P. Douglas McKin­ney of Bloom­ing­ton, In­di­ana; his son Wil­li­am F. Burk­hold­er, daugh­ter-in-law Joanne (McLean) Burk­hold­er, and grand­daugh­ter Sylvie Kath­leen Burk­hold­er of Singa­pore; his sis­ter Helen Dale and broth­er-in-law Ernie Dale of Au­burn, Wash­ing­ton; his broth­er John Burk­hold­er and sis­ter-in-law Donna Burk­hold­er of McPh­er­son, Kan­sas; his sis­ters-in-law Anne Burk­hold­er of McPh­er­son, Kan­sas, and Le­ona Burk­hold­er of Madis­on, Wis­con­sin; and sev­en­teen nieces and neph­ews. His daugh­ter Kath­leen Linda Burk­hold­er died of a cereb­ral hem­or­rhage in 1981, and he was pre­de­ceased by his broth­ers Robert Burk­hold­er of Buhler, Kan­sas, and Wendell Burk­hold­er of Madis­on, Wis­con­sin.