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Under certain conditions specified in the law, libraries and archives are authorized to furnish a photocopy or other reproduction. One of these specified conditions is that the photocopy or other reproduction is not to be “used for any purpose other than private study, scholarship or research.” If a user makes a request for, or later uses, a photocopy or other reproduction for purposes in excess of “fair use,” that user may be liable for copyright infringement. The Princeton Mathematics Community in the 1930s Transcript Number 18 (PMC18) © The Trustees of Princeton University, 1985 ISRAEL HALPERIN (with ALBERT TUCKER) This is an interview of Israel Halperin at Princeton University on 25 May 1984. The interviewer is Albert Tucker. Tucker: Would you tell me how it was that you came to Princeton as a graduate student? Halperin: Well, came in 1933. Prior to that I had done a year's graduate work at the University of Toronto. Before the end of that year I applied to a number of institutions in the United States with graduate schools of high repute for an opportunity to go there to do Ph.D. work. I was accepted at several places including Princeton, so it was just a case of choosing which I preferred. Since one of Toronto's graduates, Albert Tucker, had gone to Princeton, that was a place that I knew something about. Tucker: There was a second one. Halperin: That's true, but Albert Tucker had not only been there but he, by this time, had taken his Ph.D. and gone on to higher things. The reputation of the Princeton staff had become rather solid at Toronto. Yes, there was a second one, Malcolm Robertson, who was in the course of doing his Ph.D. That was enough for me. It was also so that another student with whom I was in close touch at Toronto-we were close friends-had an offer to go to Princeton to do graduate work in physics. Tucker: That was John Blewett? Halperin: Yes. Together we decided we would go to Princeton. (PMC18) 1 Tucker: Do you remember your first days at Princeton? Halperin: Oh yes. Of course we were very poor. We were all very poor in those days, and we came by bus. We arrived at the bus station at the edge of Princeton, as it was then. So I phoned Al Tucker and said, "We're here, what should we do?" He said, "Stay right there, I'll come." So he came and took us to a place where we could have a room. He had been there, a place called Brown Hall, a residence of the Theological Seminary. Tucker: Of course by then, Fine Hall was in use. Fine Hall opened for business in the fall of 1931 as I recall. Halperin: It is very interesting that to those who had been there, this was a rather new building, but to someone like myself who had just arrived, it might as well have been there 100 years. Tucker: From whom did you take courses in your first year? Do you remember? Halperin: Oh, I remember very well. I got the impression I wasn't taking courses. But those of us who were in our first year of graduate work were apparently expected to take [Luther P.] Eisenhart's tensor-calculus course. When I started that course, it was all very dull because I had been through all of this with [John L.] Synge in Toronto. Tucker: Yes. Halperin: I got rather fed up, in spite of the fact that Eisenhart was the dean and a stern-looking gentleman, and I just didn't go to lectures after a few. The other courses were so casual that I sort of dropped out of them too. I went to Bohnenblust's lectures for a while, but I had had most of the stuff from Professor William J. Webber in Toronto. But the one person whose lectures I had not had before was von Neumann, and I wouldn't have missed any of that. Tucker: What was he lecturing on that year? Halperin: Well, I recall the story I heard later. Someone is said to have asked Eugene Wi_gner, "What is von Neumann lecturing on this year?", and Wigner replied, "I don't know what he'll call it, but it will be Hilbert spaces." Yes, he was lecturing on Hilbert spaces, on the spectral theorem. At first I couldn't understand how you could have Hilbert spaces with complex numbers. I had never heard of such a thing. I asked Malcolm Robertson, "How do you define the inner product if you have complex numbers?", and he told me. Tucker: Did you participate in the activities that went on, such as those in the common room?·· Halperin: Oh yes. The common room was a wonderful place. As I said, we were all poor-all the students were poor-but I didn't see any (PMC18) 2 trace of competition or friction. It seemed to me we were all monks in a monastery, all working with the purest motives to discover mathematics and to share it with others. The common room was a very lively place. Those were the days when refugees were coming out of Europe, and those in mathematics seemed to head first for Princeton, because the Institute and the University's math department were both there. It was a tremendous concentration of talent. There was hardly a day that in the common room we wouldn't see a new face and ask who that was, and the answer would be some mathematician we'd heard of, who was a great researcher. Tucker: Was [Stan] Ulam around at that time? Halperin: He. wasn't around when I came; he arrived later. In fact, when he arrived I was deputized to show him around. I remember taking him, among other places, to the gym where you could go swimming. I enjoyed swimming enormously, so with great satisfaction I showed Ulam the possibilities of going swimming. He turned his nose up at that; he wasn't interested. Tucker: I think Veblen had me meet Ulam when he arrived by boat. Might you have come along with me on that trip? Halperin: No, the first time I saw Ulam was when I was called by Lefschetz and told to take Ulam around and show him the University. Tucker: Before that I was told to meet him. Halperin: So you went to New York to find him? Tucker: He was in Hoboken, as I recall. I think a Polish-American liner had arrived in Hoboken. Halperin: I see. Tucker: Have you heard that Ulam died just recently? Halperin: I heard that just yesterday. I was quite surprised because I had been in correspondence with Ulam. I was out of touch with him for many years, but then I sent him a copy of the 1981 American Math Society Memoir by von Neumann. After that we were in correspondence a bit. I was going to meet him in Washington, but it turned out that I was there the week before he got there. I wrote him after that, but I did not get a reply before he died. Tucker: When did you start working on your thesis? Halperin: In those days, as is perhaps still the case, the graduate student was expected to qualify in what were called prelims. Tucker: Yes. (PMC18) 3 Halperin: There wasn't much expectancy of getting involved with the research topic until then. Bochner wasn't very happy about that; he once said to me rather vigorously, "You should be working on a problem." I was just accumulating information the first year. I passed my prelims in the fall at the beginning of my second year. Tucker: Whom did you have on your prelims committee? Halperin: That was a remarkable situation. The committee consisted of Solomon Lefschetz, H.F. Bohnenblust, and T. Y. Thomas. I had been told that the examination was to start at 3:30. At 3:00 Boni was going by a lecture room and saw me in the room, and he said, "Why aren't you at your prelims?" I said, "It doesn't start until 3:30." "No," he said, "it starts at 2:30." So he took rrie ·down to the room, and there Lefschetz and Thomas were, waiting and talking. So my prelims got started. It had gone on for about 15 minutes when Thomas got up and said, "I've got to go to tea," and out he walked. Tucker: Lefschetz and Boni went on? Halperin: That's right. It was a very casual affair. It wasn't what I had anticipated.