# Celebratio Mathematica

## Irving Kaplansky

### Letter to Section 11 [Mathematics] of the National Academy of Sciences

Just about ten minutes ago, I sat down to my email; I had looked at it at about 9:30 a.m. — be­fore the sad news about Kap ar­rived. So, I saw the mes­sage ap­pen­ded be­low (you have it as well) only a few minutes ago. I was shocked by the news. “Sad” really doesn’t be­gin to de­scribe my feel­ings; Kap was al­most as close, where I’m con­cerned, as a be­loved par­ent. Of all my gradu­ate school teach­ers (Stone, Zyg­mund, Chern, Span­i­er, Hal­mos, Segal, Weil, Graves, Hestenes, Mac Lane, Al­bert, etc.), and I revered each and every one of them, Kap was my fa­vor­ite. A half-hour-to-hour con­ver­sa­tion with him about math­em­at­ics gen­er­ated so much ex­cite­ment that I spent the rest of the day walk­ing on a cloud. Irv was im­mensely pop­u­lar with the gradu­ate stu­dents; he was al­ways ready to talk math with us and make good and use­ful sug­ges­tions for our work, but he was also some­what “scary” for many of the stu­dents. His “so­cial” be­ha­vi­or was even more pe­cu­li­ar than the “stand­ard” be­ha­vi­or of ded­ic­ated math­em­aticians. Most of us have an ex­ag­ger­ated sense of the “fu­til­ity” of small talk; Irv’s view of that had to be de­scribed as “ex­cess­ive”. For ex­ample, if you met him in the hall­way and stopped for a con­ver­sa­tion with him, when the con­ver­sa­tion was clearly over, he just walked on, turned and walked away, whatever — ab­so­lutely no de­com­pres­sion stage (or phrases, e.g., the cur­rently pop­u­lar, and al­most al­ways, fatu­ous “have a nice day” — re­cently in­flated to “have a great day”). Hand­shakes? For­get it! As fast and smart and cre­at­ive as he was, and all that (genu­ine, not af­fected) no-non­sense be­ha­vi­or of his, we loved (“wor­shipped” might be more ac­cur­ate) him. Chat­ting with him in his of­fice, after a few years, he asked me a nice ques­tion that had oc­curred to him, a fine blend of al­gebra and ana­lys­is (nil-po­tents of in­dex 2 and ap­prox­im­a­tion). I thought about it for fif­teen minutes or so that even­ing and didn’t see how to get star­ted. Be­ing busy with oth­er things I dropped it and didn’t get back to it un­til I met and talked to him a day or two later. He asked me if I had thought about the prob­lem. I said that I had, but hadn’t been able to get star­ted on it, and then asked him if he really thought it was true. His re­sponse was, “When God whis­pers a the­or­em in your ear, you should listen.” Now, of course I un­der­stood his “cute” way of giv­ing me some valu­able math­em­at­ic­al ad­vice, but I chose to mis­in­ter­pret it. When I re­por­ted this to the oth­er gradu­ate stu­dents, I told them the story and ad­ded that Ka­plansky had fi­nally re­vealed him­self, and as many of us had sus­pec­ted, he was God. In those very early years (end of the 1940s), Irv lived an aus­tere life. He ren­ted a single room in a house near the U. of Chica­go cam­pus, paid \$5 a week for it, if I re­mem­ber cor­rectly, and saved al­most all the rest of his salary. The word was that he was (re­l­at­ively) wealthy in those days. (Of course, that could mean any­thing from someone with a bank bal­ance of \$100 and up and no debts, in those days and our so­ci­ety.) Chel­lie (Rochelle), Irv’s wife of fifty-five years was tre­mend­ous fun, great sense of hu­mor. I had the im­pres­sion that she could wrap him around her little fin­ger, he knew it, and he en­joyed it. She entered the pic­ture in 1951. Some years later (about five), George Mackey was hav­ing din­ner with Kar­en and me at our apart­ment in Cam­bridge (we were vis­it­ing MIT that year). The con­ver­sa­tion turned to Irv. (Kap and George were great friends.) When the sub­ject of Kap’s pur­por­ted wealth came up, George told of a con­ver­sa­tion he and Chel­lie had had some little time back. He said that he had asked Chel­lie if she didn’t feel that she was lucky to have mar­ried a wealthy man — to which she replied, with a (feigned) sur­prised smile, “Oh, that — it was only about \\$30,000 and I went thru that in no time!” George paused after re­port­ing that, as­sumed a troubled, somber look and said, “Fair, sent a chill down my spine!” It prob­ably helps to know that, in those days, George was still a bach­el­or, and lived a frugal, aus­tere ex­ist­ence — com­pletely by choice. Both Kap and Mackey were per­fectly will­ing to spend their money when the oc­ca­sion war­ran­ted it. I’ve had many fine meals with each of them. Kap did not eat lunch with us dur­ing our gradu­ate stu­dent days, we took too long with it. I re­mem­ber a bunch of us walk­ing down the stairs of Eck­hart Hall on our way over to lunch at the Com­mons. Irv came boun­cing past us, evid­ently on the same mis­sion. The Com­mons is a few hun­dred meters from Eck­hart. We sauntered over ar­riv­ing in time to see Kap emer­ging from the Com­mons, lunch over. Chel­lie prob­ably slowed him down over the years. In my first years at Chica­go, Irv had no dis­cern­ible so­cial life. He liked swim­ming in Lake Michigan dur­ing the sum­mer and did so early each morn­ing. Then, in 1949 he had a few quar­ters off and went out for a stay at UCLA. The ru­mors flew back to Chica­go, Kap had bought him­self a con­vert­ible, now drank li­quor, so­cially, and smoked. One day it was said that the “new” Ka­plansky had re­turned. A day later, I happened on my dear pal and fel­low gradu­ate stu­dent, Arnold Sha­piro. He told me that he had just talked with Irv a few hours ago. I asked, “The new Ka­plansky?” Arnold’s reply was, “What new Ka­plansky? It’s just the old Ka­plansky — with a smile on his face.” Shortly after that, a few of us fin­ished our Ph.D. re­quire­ments. As tra­di­tion had it, we in­vited one and all to a party. Walk­ing around with a tray and two drinks (“high­balls”) on it, one primar­ily scotch and the oth­er bour­bon, I offered one of those drinks to Irv. His ques­tion for me was, “Which is the per­fume and which is the hair ton­ic?” That, ap­par­ently, was the “new” Ka­plansky. Of course, I could tell you so many more stor­ies about Irv, many of them that have some math­em­at­ic­al sig­ni­fic­ance. They are all memor­ies I treas­ure. Kap is one of the very few people I’ve known well most of my work­ing life of whom I can say that I have noth­ing but en­joy­able memor­ies.