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From the collections of the Seeley G. Mudd Manuscript Library, Princeton, NJ These documents can only be used for educational and research purposes (“Fair use”) as per U.S. Copyright law (text below). By accessing this file, all users agree that their use falls within fair use as defined by the copyright law. They further agree to request permission of the Princeton University Library (and pay any fees, if applicable) if they plan to publish, broadcast, or otherwise disseminate this material. This includes all forms of electronic distribution. Inquiries about this material can be directed to: Seeley G. Mudd Manuscript Library 65 Olden Street Princeton, NJ 08540 609-258-6345 609-258-3385 (fax) [email protected] U.S. Copyright law test The copyright law of the United States (Title 17, United States Code) governs the making of photocopies or other reproductions of copyrighted material. 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 36 (PMC36) © The Trustees of Princeton University, 1985 ALBERT TUCKER OVERVIEW OF MATHEMATICS AT PRINCETON IN THE 1930s This is an interview on 8 October 1984 of Albert Tucker in Princeton, New Jersey. The interviewer is William A spray. Aspray: In this session we will try to give an overview of the important developments in Princeton in the 1930s. In an earlier discussion off tape, we talked about four major kinds of contributions of the Princeton mathematical community: (1) the Ph.D.s produced; (2) the overall environment for visitors to get inspiration and, for a time, to do research; (3) the research of the faculty members; and (4) the opening up of new areas of research. I am hoping to get some perspective on which of these you see as the most important contributions. And perhaps you will talk a bit about what the particular contributions were. Tucker: The thing that strikes me first is the research program at the graduate student level, in other words, the training of graduate students in mathematical research. At Princeton this was a broadly exercised effort. The students were carefully selected for admission. No students were admitted just to get a master's degree; all admissions were for the doctor's degree or for mathematical research beyond the doctor's degree. These students seemed to live and breathe their mathematical work. The library was right there in the building and was open all hours. There were recreational facilities in the common room, and indeed there were external recreational facilities, such as on the tennis courts, and showers in the building. So Fine Hall was not only a study place, and it was not only the place where-lectures and seminars occurred. It was also a place where people met for tea in the afternoon. It was a mathematical club. (PMC36) 1 Aspray: To get a good understanding of this we might differentiate Fine Hall from some other place. You say that one thing unique about Princeton as a training ground for mathematical research is that. it's a place where people do their research in a supportive social and intellectual environment. There were a number of other centers in the United States at this time that were producing large numbers of math Ph.D.s: Harvard, Johns Hopkins, Chicago, Cornell, Columbia, Yale, ... Tucker: Illinois, Michigan, Pennsylvania. Aspray: How does Princeton differ from any of these other places? Tucker: The main difference I was able to observe was the fact that mathematics was· concentrated in one building. Whenever you wished to be involved in mathematics, all you had to do was to go into that building and participate. The students learned a great deal from one another, and students often wrote their theses using a variety of advisers. A student could, if he wished, stick to one advisor, but he could use any of the faculty members. And he could use his fellow students. There was always a room where you could go and use a blackboard and argue things out with another student or faculty member. Aspray: Let's take an example. You spent some time in the early 1930s at Harvard. Tucker: I was at Harvard in the spring term of 1933. Aspray: Would you compare the situation at Harvard with the situation at Princeton? Tucker: At Harvard it seemed as though the mathematical activity was decentralized and disorganized, because the professors had offices various places. There was no common place where there were mathematics offices. The graduate students had nothing like the Fine Hall common room. A student's social activities were not organized around mathematics, but around the people in his dormitory or boarding house. While I was there I had no mathematical activities except when I went to see my supervisor Marston Morse or when I attended the weekly mathematics colloquium or when I sat in on a course that Marston Morse was giving. I would see other people in the classroom, but the moment the class was over we all went our separate ways. Most of my time was actually spent either by myself or with people who were not mathematicians. Aspray: Some outsiders might think that mathematical research ·is a solitary activity. What kind of impact did the Princeton environment have? What was the outcome of having people there breathing and talking mathematics all the time? Can you make any differentiation between the Ph.D. s from Princeton and those from Hopkins or Harvard or Chicago? ( PMC36) 2 Tucker: My belief-and I think this can be backed up by statistics-is that the Princeton Ph.D. s in mathematics were, by and large, more productive in the writing of papers and monographs and so on. I think they often became mathematical leaders in the universities where they got positions. I think that this was so because.of the close contact that the graduate students and post-docs had with members of the faculty, with Veblen, von Neumann, Eisenhart, Lefschetz. Through their seniors they began to acquire what you might describe as mathematical statesmanship. And when they took positions elsewhere they tried to carry some of this Princeton excitement with them. Aspray: You mentioned statistics a moment ago, and when we were talking before this interview you cited a particular study. Tucker: You mean the study of the productivity of mathematicians that was made somewhere around 1960? Aspray: That's correct. Tucker: In this study-we should look up the reference-the mathematics Ph.D.s who had been out so many years from their Ph.D. were put in classes according to the number of papers that they had published. These classes were then related to the institutions that had given the Ph.D.s. Princeton was spectacularly highest in the most productive of the Ph.D.s, even though it was not at all at the top in the total number of Ph.D.s. Aspray: In addition to productivity in the sense measured by the number of papers written, let's talk about productivity in the sense of finding new ways of looking at things, or of forming new fields, or of crossing disciplines. Do you think the way that education went on at Princeton, where one wasn't closely tied to an advisor but had a whole smorgasbord of mathematics to experience, somehow translated itself into mathematicians who were more willing to go outside the narrow confines of traditional discipline-boundaries? Tucker: Oh, yes. Among the Princeton Ph.D.s there were unusually many who went into things that were on the edge of traditional mathematics-or altogether outside of traditional mathematics. Aspray: Can you give some examples? Tucker: Well, Henry Wallman is an example. He took his Ph.D. at Princeton in the late '30s, and then became involved in war-work at M.l.T. During the war this work was classified, but I think it had to do with radar. It was at any rate work in electronics. After the war he was at M.l.T. for a while, but then was appointed to a professorship in Sweden. He was professor of "electrotechnics" at the Chalmers Institute of Technology in Gothenburg, Sweden. There was another Princeton math-Ph.D. who went into engineering, Paco Lagerstrom. He became professor of aeronautical engineering at Cal Tech, but was trained in mathematical analysis. ( PMC36) 3 Asp ray: He continued to use his mathematical training in his later work? Tucker: Oh yes. Aspray: ls John Tukey another example? Tucker: John Tukey is a good example. His Ph.D. was in topology with Lefschetz, but in his wartime work he became very much interested in statistics as well as in data structures. So after the war it was appropriate that he should take a position that was half-time at Princeton University and half-time at Bell Labs. At a later time when the Statistics Department at Princeton separated off from Mathematics Department, he was the first chairman of the Statistics Department. And I think that he became some sort of deputy director of research in mathematics, statistics, and information processing at Bell Labs. Aspray: One more example might be Marvin Minsky. Tucker: Marvin Minsky came later, in the early '50s.
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