Celebratio Mathematica

Irving Kaplansky

Student memories of Kap

by Joseph Rotman

As a gradu­ate stu­dent at the Uni­versity of Chica­go, I at­ten­ded many of Ka­plansky’s ele­ment­ary courses: com­plex vari­ables, group the­ory, set the­ory, point-set to­po­logy; later, I at­ten­ded more ad­vanced courses: com­mut­at­ive al­gebra, Hil­bert’s fifth prob­lem, abeli­an groups, ho­mo­lo­gic­al al­gebra. 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 that 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 my thes­is ad­visor. I worked in abeli­an groups (at the same time, he had five oth­er ad­visees: two in ho­mo­lo­gic­al al­gebra and three in func­tion­al ana­lys­is). He set weekly ap­point­ments for me. When I entered his of­fice, he was usu­ally sit­ting com­fort­ably at his desk, of­ten with his feet up on the desk. He’d greet me with “What’s new?” I would then talk and scribble on the black­board as he listened and asked ques­tions. Once I had ax­io­mat­ized a proof of his and Mackey’s, en­abling me to gen­er­al­ize their res­ult. “How did you think of that?” he asked. I replied that that was the way he had taught me to think; he smiled.

Both of us spent a sab­bat­ic­al year in Lon­don at Queen Mary Col­lege. Of course, I con­tin­ued to en­joy his math­em­at­ics, but I saw an­oth­er side of him as well. N. Div­in­sky was an­oth­er sab­bat­ic­al vis­it­or (as was per­son{H. Flanders}), and I was dubbed Rot­mansky to go along with Ka­plansky and Div­in­sky. Kap dis­covered crick­et, and of­ten went to Lord’s Crick­et Grounds. But Kap really loved Gil­bert and Sul­li­van. He ar­ranged an even­ing in which we per­formed Iolanthe. Kap was at the pi­ano, Div­in­sky did the pat­ter songs, Flanders was on the re­cord­er, and I was Stre­p­hon.

There are few gi­ants in the world, and now there is one less.