Celebratio Mathematica

Kenneth Ira Appel

In memoriam: Kenneth Appel

by the Department of Mathematics, University of Illinois

Ken­neth I. Ap­pel, 80, of Dover, New Hamp­shire, and formerly of Urb­ana, died Fri­day, April 19, 2013, in Dover after a short hos­pit­al­iz­a­tion. He had been dia­gnosed with eso­pha­geal can­cer in Oc­to­ber. Fu­ner­al ser­vices were held on April 22 in Dover.

From 1961 to 1993 he was a math­em­at­ics pro­fess­or at the Uni­versity of Illinois, where he and his col­league Wolfgang Haken solved one of the most fam­ous prob­lems in math­em­at­ics, the Four Col­or Con­jec­ture. They answered this ques­tion: Is it true that any map can be colored with just four col­ors so that con­tigu­ous coun­tries have dif­fer­ent col­ors? Their proof that four col­ors are suf­fi­cient, an­nounced in 1976, was the first ma­jor math­em­at­ic­al the­or­em to be proved with the aid of a com­puter. This solved a prob­lem first posed in 1852 by Fran­cis Gu­thrie which had been at­tacked without suc­cess by many math­em­aticians.

Ken­neth Ira Ap­pel was born in Brook­lyn, NY, on Oc­to­ber 8, 1932, and grew up in Queens, NY, the son of Ir­win Ap­pel and Lil­lian Sender Ap­pel. He re­ceived a bach­el­or’s de­gree in math­em­at­ics from Queens Col­lege in 1953. After work­ing briefly as an ac­tu­ary, he served two years in the U.S. Army, at Fort Ben­ning, Geor­gia, and in Baum­hold­er, Ger­many.

He re­ceived his Ph.D. in math­em­at­ics from the Uni­versity of Michigan in 1959. In Phil­adelphia that year he mar­ried Car­ole S. Stein. They moved to Prin­ceton, NJ, where Ken worked for the In­sti­tute for De­fense Ana­lyses, do­ing re­search in cryp­to­graphy.

After join­ing the Uni­versity of Illinois at Urb­ana, he taught math­em­at­ics and did re­search on group the­ory and com­put­ab­il­ity the­ory. In the 1980s he served as As­so­ci­ate Chair of the de­part­ment of math­em­at­ics and dir­ec­ted the pro­gram in ac­tu­ar­ial sci­ence. He also served on the Urb­ana city coun­cil and later on the city’s zon­ing board.

In 1993, he re­tired from the Uni­versity of Illinois to chair the math­em­at­ics de­part­ment of the Uni­versity of New Hamp­shire. In New Hamp­shire he also served as treas­urer of the county Demo­crat­ic Com­mit­tee and a mem­ber of the school board. He re­tired from the Uni­versity of New Hamp­shire in 2003.

The solu­tion of the four-col­or prob­lem by Ken Ap­pel and Wolfgang Haken was re­por­ted in the press world-wide, in­clud­ing Time magazine and Sci­entif­ic Amer­ic­an. The New York Times wrote in 1976,

Now the four-col­or con­jec­ture has been proved by two Uni­versity of Illinois math­em­aticians, Ken­neth Ap­pel and Wolfgang Haken. They had an in­valu­able tool that earli­er math­em­aticians lacked — mod­ern com­puters. Their present proof rests in part on 1,200 hours of com­puter cal­cu­la­tion dur­ing which about ten bil­lion lo­gic­al de­cisions had to be made. The proof of the four-col­or con­jec­ture is un­likely to be of ap­plied sig­ni­fic­ance. Nev­er­the­less, what has been ac­com­plished is a ma­jor in­tel­lec­tu­al feat. It gives us an im­port­ant new in­sight in­to the nature of two-di­men­sion­al space and of the ways in which such space can be broken in­to dis­crete por­tions.

In 1979 the Amer­ic­an Math­em­at­ic­al So­ci­ety and the Math­em­at­ic­al Pro­gram­ming So­ci­ety awar­ded the Del­bert Ray Fulk­er­son prize to Ap­pel and Haken. In 2012 Ken was elec­ted a Fel­low of the Amer­ic­an Math­em­at­ic­al So­ci­ety.

Ken Ap­pel was pas­sion­ate about math­em­at­ics edu­ca­tion, at all levels from ele­ment­ary school to gradu­ate school. At every stage of his life, he sought op­por­tun­it­ies to teach — as a gradu­ate stu­dent in Michigan, as a vo­lun­teer lec­turer at Prin­ceton Uni­versity, in more than fifty years as a pro­fess­or, and in re­tire­ment as a vo­lun­teer in math­em­at­ics en­rich­ment pro­grams in Dover and south­ern Maine pub­lic schools. He par­tic­u­larly be­lieved that stu­dents should be af­forded the op­por­tun­ity to study math­em­at­ics at the level of their abil­ity, even if it is well above their grade level. To that end, he en­joyed work­ing with gif­ted high school stu­dents on the kind of math prob­lems he would give to his gradu­ate stu­dents.

He was an avid ten­nis play­er un­til his fifties, a ser­i­ous swim­mer, a lifelong stamp col­lect­or, a skill­ful play­er of the game of Go, a baker of bread. He was a lov­ing hus­band, fath­er, and grand­fath­er.

Ken­neth Ap­pel is sur­vived by his wife Car­ole S. Ap­pel, son An­drew W. Ap­pel and his wife Maia Gins­burg, of Prin­ceton, NJ; son Peter H. Ap­pel and his wife Bárbara Zamora-Ap­pel, of Al­ex­an­dria, VA; by grand­chil­dren Avi and Joseph Ap­pel, Re­becca and Nath­aniel Weir, and Car­men Ap­pel; and his sis­ter Lois Green and her chil­dren. Car­ole and Ken’s daugh­ter Laurel F. Ap­pel, a bio­lo­gist at Wes­ley­an Uni­versity, died on March 4 this year at the age of 50 and is sur­vived by her hus­band, Mi­chael P. Weir.