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Celebratio Mathematica

Irving Kaplansky

Algebra  ·  U Chicago

In memoriam: Irving Kaplansky (Professor of Mathematics, Emeritus, UC Berkeley, 1917–2006)

by David Eisenbud and Tsit-Yuen Lam

Irving Ka­plansky, known to his friends as Kap, was born on March 22, 1917 in Toronto, the young­est of four chil­dren. His par­ents had re­cently emig­rated from Po­land, where his fath­er Samuel had stud­ied to be a rabbi. In Toronto Samuel worked as a tail­or, while Kap’s moth­er es­tab­lished a chain of Health Bread Baker­ies that ul­ti­mately sup­por­ted the whole fam­ily. Kap died on the 25th of June 2006, at his son Steven’s home, in Sher­man Oaks, Cali­for­nia.

Kap’s math­em­at­ic­al tal­ent was ap­par­ent early. From 1938 to 1939 he at­ten­ded the Uni­versity of Toronto, where he got his bach­el­or’s and mas­ter’s de­grees (1938–39). He was one of the two Put­nam Fel­lows in 1938, the first year of that most pres­ti­gi­ous of all North Amer­ic­an un­der­gradu­ate math­em­at­ic­al com­pet­i­tions. Kap went to Har­vard Uni­versity and re­ceived his Ph.D. there in 1941, work­ing un­der Saun­ders Mac Lane. He was Ben­jamin Peirce In­struct­or at Har­vard from 1941 to 1944, and then joined the Ap­plied Math­em­at­ics Group do­ing war work at Columbia Uni­versity from 1944 to 1945.

After the war, Kap joined the Math­em­at­ics De­part­ment at the Uni­versity of Chica­go, where he was chair of the de­part­ment from 1962 to 1967 and George Her­bert Mead Dis­tin­guished Ser­vice Pro­fess­or from 1969. He re­tired from the Uni­versity of Chica­go in 1984 in or­der to be­come the second dir­ect­or of the Math­em­at­ic­al Sci­ences Re­search In­sti­tute (MSRI) in Berke­ley, es­tab­lished just a few years be­fore by Shi­ing-Shen Chern (its first dir­ect­or), Calv­in C. Moore, and Is­ad­ore M. Sing­er. He was ap­poin­ted as pro­fess­or of math­em­at­ics at UC Berke­ley at the same time. In 1985–86, he served as pres­id­ent of the Amer­ic­an Math­em­at­ic­al So­ci­ety.

Dur­ing his life­time, Kap re­ceived many pro­fes­sion­al hon­ors and re­cog­ni­tions. These in­clude the Quan­trell Award for Ex­cel­lence in Un­der­gradu­ate Teach­ing at the Uni­versity of Chica­go (1961) and the Steele Prize (Ca­reer Award) from the Amer­ic­an Math­em­at­ic­al So­ci­ety (1989). Kap was elec­ted to the Amer­ic­an Academy of Arts and Sci­ences in 1965, and to the Na­tion­al Academy of Sci­ences in 1966. He re­ceived two hon­or­ary de­grees: Doc­tor of Math­em­at­ics from the Uni­versity of Wa­ter­loo, and Doc­tor of Sci­ence from Queen’s Uni­versity, both in 1968.

Kap was proud of the fact that he was one of the first to sug­gest to the Na­tion­al Sci­ence Found­a­tion (NSF) the found­ing of new math­em­at­ics re­search in­sti­tutes bey­ond the In­sti­tute for Ad­vanced Study in Prin­ceton. Already in the 1960s he had told an NSF pan­el that the growth of U.S. math­em­at­ics made the cre­ation of such in­sti­tutes in the Mid­w­est and on the west coast an im­port­ant pri­or­ity. Kap led MSRI un­til 1992, over­see­ing its move from its tem­por­ary quar­ters to its spec­tac­u­lar per­man­ent loc­a­tion above the cam­pus, and put­ting many MSRI tra­di­tions in place. Among his many long-term con­tri­bu­tions to the life of the in­sti­tute was the cre­ation in 1986 of a group of Friends of MSRI that in­cluded James H. Si­mons, Wil­li­am Ran­dolph Hearst III, El­wyn R. Ber­lekamp, and Steven Wolfram, three of whom sub­sequently be­came trust­ees and ma­jor con­trib­ut­ors to MSRI.

Kap re­tired as dir­ect­or of MSRI and as pro­fess­or of math­em­at­ics in 1992, but came to his of­fice at MSRI to do re­search every day and at­ten­ded every col­loqui­um at Berke­ley un­til he be­came ill in 2005. A man of ex­traordin­ar­ily reg­u­lar life­time habits, he un­fail­ingly took the same bus down from MSRI for his daily swim. He re­mained act­ive in math­em­at­ic­al re­search and pub­lic­a­tion un­til just eight months be­fore his death.

In all Kap wrote some 151 journ­al art­icles (the last pub­lished in 2004) and 11 books. His math­em­at­ic­al in­terests were ex­traordin­ar­ily broad, and his pa­pers touch on to­po­lo­gic­al al­gebra and op­er­at­or al­geb­ras, the arith­met­ic and al­geb­ra­ic as­pects of quad­rat­ic forms, com­mut­at­ive and ho­mo­lo­gic­al al­gebra, non­com­mut­at­ive ring the­ory and dif­fer­en­tial al­gebra, Lie the­ory, com­bin­at­or­ics and com­bin­at­or­i­al num­ber the­ory, in­fin­ite abeli­an groups, lin­ear al­gebra, gen­er­al al­gebra, game the­ory, prob­ab­il­ity and stat­ist­ics. Among his most im­port­ant pa­pers were those on to­po­lo­gic­al al­gebra and op­er­at­or the­ory pub­lished in 1948–1952, and those on non­com­mut­at­ive ring the­ory, such as the clas­sic “Rings with a Poly­no­mi­al Iden­tity” (Bul­let­in of the Amer­ic­an Math­em­at­ic­al So­ci­ety, 1948), which star­ted a whole field. His books be­came le­gendary for their clar­ity, style and brev­ity.

The in­terest and skill that Kap showed in teach­ing is sug­ges­ted by his books, but demon­strated by his ment­or­ing of Ph.D. stu­dents. Fifty-five re­ceived their de­grees from him between 1950 and 1978, and their work proved fer­tile: as of this writ­ing (sum­mer 2007) Kap’s “math­em­at­ic­al fam­ily,” con­sist­ing of stu­dents, grand-stu­dents…, has at least 627 mem­bers. Joe Rot­man, one of Kap’s stu­dents, wrote:

Every course, in­deed, every lec­ture, was a de­light. Courses were very well or­gan­ized, as was each lec­ture. Res­ults were put in per­spect­ive, their ap­plic­a­tions and im­port­ance made ex­pli­cit. Hu­mor and droll asides were fre­quent. Tech­nic­al de­tails were usu­ally pre­pared in ad­vance as lem­mas so as not to cloud the main ideas in a proof. Hy­po­theses were stated clearly, with ex­amples show­ing why they were ne­ces­sary. The ex­pos­i­tion was so smooth and ex­cit­ing; I usu­ally left the classroom feel­ing that I really un­der­stood everything. To deal with such ar­rog­ance, Kap al­ways as­signed chal­len­ging prob­lems, which made us feel a bit more humble, but which also ad­ded to our un­der­stand­ing. He was a won­der­ful teach­er, both in the short term and for the rest of my math­em­at­ic­al ca­reer. His taste was im­pec­cable, his en­thu­si­asm was con­ta­gious, and he was the mod­el of the math­em­atician I would have been happy to be.

Kap was not a nat­ur­ally so­ci­able per­son be­fore his mar­riage, but his world was vastly en­riched when he mar­ried Chel­lie Bren­ner in 1951. Chel­lie and Kap had three chil­dren, Steven, Alex and Lucy. Chel­lie was Kap’s op­pos­ite in terms of out­go­ing open warmth. Chel­lie brought streams of friends and col­leagues in­to their home, and in the years of Kap’s dir­ect­or­ship at MSRI she presided as a moth­er hen over the many vis­it­ors as well as over Kap him­self. When Chel­lie be­came ill in the last part of Kap’s life the tables were turned, and he nursed her faith­fully.

Kap was en­tranced by mu­sic very early. He wrote,

At age 4, I was taken to a Yid­dish mu­sic­al, Die Goldene Kala. It was a rev­el­a­tion to me that there could be this kind of en­ter­tain­ment with mu­sic. When I came home I sat down and played the show’s hit song. So I was rushed off to pi­ano les­sons. After 11 years I real­ized there was no point in con­tinu­ing; I was not go­ing to be a pi­an­ist of any dis­tinc­tion….  I en­joy play­ing pi­ano to this day. […] God in­ten­ded me to be the per­fect ac­com­pan­ist — or bet­ter, the per­fect re­hears­al pi­an­ist. I play loud, I play in tune, but I don’t play very well.

Nev­er­the­less, his play­ing was greatly en­joyed by his friends and fam­ily, and later by his col­leagues at MSRI, where he would play at Christ­mas parties and oth­er oc­ca­sions. His daugh­ter Lucy be­came a well-known folk­sing­er-song­writer, and he some­times ac­com­pan­ied her con­certs, for ex­ample at Berke­ley’s Freight and Sal­vage. She wrote that “[f]rom as early as I can re­mem­ber I would sing while he played the pi­ano. He taught me dozens of songs from the 1930s and ’40s, as well as from Gil­bert and Sul­li­van oper­et­tas. I still re­mem­ber most of these songs.”

Kap’s mu­sic­al in­terest was centered on Gil­bert and Sul­li­van, and on pop­u­lar songs of the “golden age”, about 1920–1950. He com­posed a num­ber of songs and was proud of a mu­si­co­lo­gic­al ob­ser­va­tion about songs of this peri­od:

Most had the form \( \mathrm{AABA} \). I no­ticed there was a second form (“Type 2”) \( \mathrm{AA}^{\prime}\mathrm{BAA}^{\prime}\mathrm{BA}^{\prime\prime} \). \( \mathrm{A} \): 4 bar theme; \( \mathrm{A}^{\prime} \), \( \mathrm{A}^{\prime\prime} \): vari­ants; \( \mathrm{B} \): con­trast­ing 8 bar theme. (Though I as­sumed any jazz mu­si­cian knew about this, noth­ing about it was found in the lit­er­at­ure.) Type 2 is really bet­ter for songs. (In Woody Al­len’s Ra­dio Days, the ma­jor­ity of the 20 songs are Type 2.) As proof I tried to show that you could make a pass­able song out of such an un­prom­ising source of them­at­ic ma­ter­i­al as the first 14 di­gits of \( \pi \).

En­id Rieser pro­duced lyr­ics, and Lucy of­ten per­forms this song on her tours. Kap is sur­vived by his wife Chel­lie, his chil­dren Alex, Lucy and Steven, and by his grand­chil­dren Aaron and Molly.

The au­thors are grate­ful to Hy­man Bass, from whose ac­count many of the quotes and facts above are taken.