The Princeton Mathematics Community in
Transcript Number 21 (PMC21)
© The Trustees of Princeton University, 1985
RECOLLECTIONS OF PRINCETON, 1939 - 1941
This is a written contribution, dated 30 December 1984, by Robert Hooke.
School had scarcely started when [Solomon] Lefschetz called the new graduate students into his office to give us an orientation lecture. He left out a lot, but it began our understanding of how a man can be lovable and terrifying simultaneously.
On the first day of classes I showed up at [Salomon] Bochner's course on complex variables and was surprised to see Lefschetz sitting in the front row. A few minutes into the class it developed why he was there. He stood up and announced that there was no textbook for the course and no official class notes had been done before, so he was calling for volunteers to take official notes. No volunteers were forthcoming, so he put on his most affable look and said, "Mr. Dolph and Mr. Hooke, why don't you volunteer?" He then appointed Brock McMillan, who already had his Ph.D. but was auditing the course for some reason, to oversee our work, which was a good thing. Later in the term, as Bochner's lectures grew more and more incoherent, we were heard a few times about the impossibility of making sense of them. These complaints were echoed by others in the class who were taking their own notes. To put us in our place, [Claude] Chevalley volunteered to interrupt his unending game of Go long enough to attend a class. At the end of the class he presented us with a complete set of notes for that lecture, written clearly in a precise hand, in ink, and in French. Years later I returned to Princeton and found that Bochner had become one of the most respected lecturers. It was said that his trouble in the fall of 1939 was that he still had family in Poland.
One vaguely irritating thing about that class was that if anyone was the best student in the class, it was a physicist. I felt better about this years later when Dick Feynman won the 1965 Nobel Prize in Physics.
By Christmas I was totally discouraged. I felt that everybody else was smarter than I was and had had a better collection of previous courses. Lefschetz had told us that the prelims were the only important exam we would have, and the courses that were offered, except for Bochner's, were not helping me make any progress toward learning what was needed for prelims. (A dozen or so years later Al Tucker told me that almost all students felt this way, but that didn't help me in 1939.) Fortunately for me, the majority of January was devoted to a "reading period", during which time I learned what I needed to know about real variables, point-set and combinatorial topology, and modern algebra. This also provided invaluable aid in learning how to learn mathematics without the aid of a professor.
At this time we could see the war coming into our lives, and I wanted very much to finish my Ph.D. before that happened. I had thought I would specialize in analysis, but I seemed to be far behind everyone else in that area. I had had a good course in continuous groups from Nathan Jacobson at North Carolina, however, and that gave me the feeling that I could get my degree faster in algebra than in anything else. So in the second semester I took [J. H. M.] Wedderburn's course in matrices and Chevalley's in algebraic geometry, in addition to Bochner's in measure theory.
Wedderburn's lecturing style was unique, to say the least. He was apparently a very shy man and much preferred looking at the blackboard to looking at the students. He had the galley proofs from his book Lectures on Matrices pasted to cardboard for durability, and his "lecturing" consisted of reading this out loud while simultaneously copying it onto the blackboard. Ernst Snapper, who claimed to be only the fourth person ever with the courage to write a dissertation under Wedderburn (and one of the other three had lost his mind) told me this story explaining why Wedderburn was a bachelor. It seems that an old Scottish tradition required that a man, before marrying, accumulate savings equal to a certain percentage of his annual income. In Wedderburn's case his income had gone up so rapidly that he had never been able to accomplish this.
Chevalley's lectures were very well prepared and very precise, so that the following event stands out in my memory. One day soon after his lecture began, he became stuck on a point in the proof he was giving. He stepped back a few paces from the board and stared at it. No one in the class knew how to help. After some 40 minutes of this completely silent cogitation, the bell rang and he walked out of the door without a word. I remember this well, not only because it made for a very long and memorable class, but also because the entire process was repeated a couple of weeks later.
In the spring Lefschetz stopped me in the hall one day and asked me why I was not taking prelims. I had considered that it would be at least a year before I was ready, and at first the thought of taking this one big exam with three weeks of preparation seemed ridiculous. But he was persuasive and in one of his affable moods, so I decided to do it. I secretly thought he must have believed I'd been there a year longer than I had, but I decided that since he thought I was ready he would do what he could to avoid being proved wrong. As it turned out, the prelims went very well, his confidence in me having had a very helpful effect.
One reason that I had not thought of taking prelims at this time was the infamous "Part Zero" exam. This was one of the things that Lefschetz had left out of his orientation talk at the beginning of the year. We heard rumors that in midwinter the new students would be notified to come around for this exam, with no prior notice given of the date. This seemed like such an unlikely way of doing things that we didn't believe it, treating the story as if it were a normal kind of upperclass teasing of freshmen. So when we found messages in our boxes to show up for this the next day, I was horrified. The purpose of the exam was to help determine what fellowships to give us, if any, the following year. I was very nervous for this exam and felt afterwards that I had disgraced myself and would no doubt be invited to look next year for an easier school to go to. However, it turned out that some others felt the same way, and I did get a fellowship for the following year, but it was not until my later conversation with Lefschetz that any of my confidence began to return. Incidentally, Lefschetz was not always so good at inspiring confidence. Just before we took our prelims that year he got us all together for a little pep talk. One of the things he told us was about the famous mathematicians who had flunked their first attempts to pass Princeton prelims. Actually, I think he thought this would alleviate our worries about flunking, but all it did was to make us think how hard the exam must be.
After passing my prelims I wanted to get started on a thesis so that I could work on it over the summer. If I were to write in algebra there were two people under whom I could do it, Wedderburn and Chevalley. Chevalley was young and inclined toward acid commentary, but Snapper had warned me about the perils of working under Wedderburn, so I collected myself and went to ask Chevalley if I could work under him. So far as I knew, Gerhard Hochschild was the only one who had done this. Chevalley was very helpful and gave me a bunch of topics to try out. I selected a conjecture of Zassenhaus to work on.
One small event that sticks with me from the following fall has to do with a party, which was a slightly-more-than-usually-festive tea that I believe was given in the department to introduce new students and the faculty to one another. I was talking with H.F. Bohnenblust and telling him how sorry I was that he had been on a leave of absence the previous year. (I had heard that he was an excellent lecturer.) In the midst of the conversation I looked up and saw a very nice looking young woman coming in the door. This was such an unusual event that it called for comment, so I said to Bohnenblust, "Who is the good-looking woman?" "You asked the wrong man," he answered. "That's my wife."
Having passed my prelims, there was no need, officially, to take any further courses, so I concentrated on my thesis. The loose Princeton system, however, allowed us to sit in on whatever courses we wanted to try, just for general education. One of those that I attended for a while was Chevalley's course in differential equations. On the first day the classroom was packed with people wondering what he would say on the subject. People soon started dropping out, however, and eventually I joined them. At the end of the semester I knew Hochschild was still going, so I asked him how many others were also doing so. His answer was that the only others were Hermann Weyl and John von Neumann.
I soon found that Zassenhaus's conjecture was false, and I wrote a paper proving it was. Chevalley thought it could be considered a thesis, but the rule was that no negative theses were accepted, so I began to work on another of his topics. By spring (1941) 1 had made enough progress to start looking for a job for the following year, so I talked to Dean Eisenhart and asked for advice on how to go about it. The Depression was still on, but the war had caused it to abate a little, so I hoped he had heard of an opening or two. He knew of no openings, but he suggested that I attend some upcoming meetings in Chapel Hill, and since I had come from there he thought I might be able to unearth something. (By contrast to today's methods, this minimal advice was the only counseling I ever received from any school, except for being told at Chapel Hill that Princeton was the place to go for graduate study.) The dean must have given the same help to others, since most of those I knew returned to their home states to teach. I did go to the meeting, hoping to find something at Duke or Chapel Hill, but they had no openings. Instead I heard of a job at North Carolina State, which I eventually took.
One day Lefschetz stopped me and asked what I was planning to do the following year. I told him I was looking for a job. He strongly advised staying in Princeton and offered me a teaching assistantship for whatever the going rate was then. (I think it was $750 a year. It was certainly no more.) I told him I wanted to get married and that was not enough to support a wife. "Nonsense," he said, "she could get a job, and you could do very well." This might have been true, but I doubt it; besides, she had another year of college to go, and I was ready to leave school. Later when I got the job at N.C. State I told Lefschetz, and he asked what they were going to pay me. When I answered $1800 he said, "You can't support a wife on that!" Annis and I were married in June, and we spent the summer in Princeton while I finished my thesis. In September we went to Raleigh, I returned at Thanksgiving to take my final exam, and she finished college in Raleigh.
As I've said, I felt hurried during those two years, and except for the mentioned snatches of conversation with Lefschetz my contacts with the faculty were largely brief and formal, and I didn't come away with any particularly, warm feelings toward them. Ten years later, though, I became interested in statistics by teaching a course to students who had asked for something they could use without becoming teachers; at the same time, postwar inflation was making it hard to live on a professor's salary, so I decided to move into statistics myself. I wrote back to Princeton for advice and received valuable help from John Tukey, Sam Wilks, and Al Tucker, who made it possible for me to spend three years in Princeton with two research groups. During those three years we came to know Princeton much better, and I am very grateful to Princeton for being so helpful to me in making this change that so affected my life.
The Princeton Mathematics Community in the 1930s