The Princeton Mathematics Community in
Transcript Number 17 (PMC17)
© The Trustees of Princeton University, 1985
This is a written contribution, dated 5 September 1984, by Robert E. Greenwood.
Graduate student life in Princeton
In September 1936 I entered Princeton University. I stayed at the Graduate College. Our entryway there was used by 12 students; six of us were together a lot at mealtimes and on other occasions. They were Howard Richards (economist), Otto Haas, Jr. (chemist), and four mathematiciansJoseph Daly, John Giese, Ransom Whitney, and myself. In addition we associated with many others, for example, Ralph Traber, who was studying mathematics, and his roommate Conyers Herring, who was studying physics. I believe Traber entered the actuarial field and for many years was in the Buffalo, N.Y. area. I don't think he received a Ph.D. degree. Herring worked for Bell Labs for many years.
Joe Daly was quite friendly with Carl Allendoerfer, who worked in mathematical analysis. Carl was at Haverford College; he co-authored a successful textbook with Cletus Oakley and later went to the University of Washington. Joe Daly married in the summer of 1937, I believe. He and his wife Charlotte lived in Penns Neck while Joe continued his studies at Princeton.
All of us were friendly with John H.M. Olmsted. After his marriage he stayed in the Princeton area until he received a degree. He taught at several places in the Midwest.
One of Alex Mood's friends was a man named Robert Singleton. Singleton did not stay at the Graduate College, and I did not know him well.
There was a student at Princeton by the name of Billy Moore. I have only vague recollections of him at Princeton, but later he taught at Texas A&M University. He was variously interested in statistics, computer science, and other specialties. I have not heard from him in a dozen years or so.
Ralph Boas was at the Graduate College in the late '30s. It is likely that he was with the Institute rather than at Princeton. I knew him, but not well.
Paul Erdos lived in Princeton during some of the 1938-39 academic yea r. I met him once or twice in the time I was at Princeton for my final Ph.D. examination. I have seen him and corresponded with him many times since then.
Charles Tompkins, presumably Marston Morse's assistant, was in Princeton in the late '30s.
Fred Ficken was at the Graduate College and at Princeton in the late '30s. He later taught at the University of Tennessee and was on the editorial staff of the Monthly for several terms. He is now deceased.
Ralph Fox and C.H. Dowker were both topologists. I have mentioned them elsewhere. Fox, I think, was married when he was a student. Dowker became entranced with a certain Shirley Temple movie and is alleged to have gone to six consecutive daily showings at a local movie theater; this was about 1938.
Ed Begle came to Princeton circa 1937. Years later, when at Stanford, he grew a beard. I grew a beard, beginning in 1972. I saw a group picture of Ed Begle and others in the late '70shis picture looked a whole lot like my picture. One day, probably in 1982, a young lady came up to me in an Austin fast-food store, apologized for intruding, but said I looked a lot like a man she had worked for at Stanford, namely Ed Begle. She was then working as a secretary in the U.T. College of Fine Arts. By this time I had seen the picture of Ed Begle, and I told her that Ed and I had been at Princeton together.
In 1939 Thomas Doyle, Ralph Fox, and I gave a beer party, as was customary for people receiving their doctorates. I remember that Dean Eisenhart attended and asked for a glass of ginger ale. The party was at the Nassau Tavern. Two "notorious" tee-totallers, John Tukey and Robert Eddy (a chemist), also gave a final party that year, only their party was a milk party. They had some big milk jars, and they poured out milk for the attendees.
Occasionally it was said, sometimes of Einstein and sometimes of Church, that he sat on the concrete and meditated about the abstract. Turing was Church's pupil, I believe.
A group of mathematics and physics graduate-students (most of whom lived at the Graduate College) formed a play-reading group in the late '30s. One night a week they would meet in the quarters of one member, and the group would be provided with many copies of a play. Roles would be assigned, and each person would read his assigned part. I was not a regular member, but on one or two occasions I substituted for a member who had a part but could not attend that session.
In 1937, before mandatory college-entrance examinations, all graduate students at Princeton were asked, sometime in the fall of 1937, to volunteer to take a college-entrance examination. Many did so. When the results were announced it was learned that the mathematics students, as a group, led all other discipline classifications (doing very well not only in the mathematics and scientific part, but also in the liberal-arts part). This surprised the English majors. I believe the geologists received the lowest rating. It is not known how much the play-reading activity mentioned above helped those participants in their general knowledge of the arts.
About half of the walk between the Graduate College and Fine Hall (or Nassau Hall) was on a winding sidewalk bordered by some trees with low branches. If there had been a snowfall, a plow would remove the snow from the walk. One afternoon I was returning to Fine Hall, and Dean Eisenhart was on his way back to Nassau Hall. I am 6' 2" tall; Dean Eisenhart was of short physical stature. The Dean could proceed on the walk without having to dodge the low branches, which were covered with snow. But I had to stoop, and at times I shook snow off a branch. I casually remarked to Dean Eisenhart that the campus groundskeeper must be a short man. Two weeks later a crew came along and cut off many of the low branches over the walk, adding another eight inches or so to the clearance.
A comment or two about Witold Hurewicz. I believe he was the co-author, with Hank Wallman, of a topology book. He rented, I believe, a room in Princeton. One five successive days he was reported to have let the bathtub run over, much to the landlady's displeasure. Some of us would exercise and play on a field near the Graduate College. Hurewicz would sometimes watch us. He had such poor physical coordination that he couldn't swing a bat or run when he was supposed to run, much less return a fast serve on a tennis court. No doubt this lack of coordination had something to do with his fall off a pyramid in Mexico, which led to his death.
Another landlady story about Erdos. He was planning to leave Princeton; I think it was the spring of 1939. For some reason he decided to stay over a day. As he was leaving the grounds of the place where he had rented a room, he called back to the landlady, "I'll be sleeping with you again tonight," or something like that. The landlady's reaction to this is unknown to me.
One Sunday morning, probably in 1938, people were surprised to find a cow hitched to something in the inner courtyard of the Graduate College and contendedly grazing there. I don't believe the perpetrators of this prank were ever identified. I feel quite sure that at least one of them was a mathematics graduate-student at Princeton. It was not I, but I had heard some of the planning talk.
Topology seminars at Princeton
In the middle 1930s Princeton University and the Institute for Advanced Study were very strong in topology. I had no intention of becoming a topologist; I leaned toward the idea of pursuing a career in mathematical physics, which was later changed to a career in mathematics. Nevertheless, I considered it advisable to attend some of the meetings of the topology seminars. And, of course, if you attend, you are asked to contribute.
Early in my first year at Princeton, 1936-37, I attended a seminar for beginning graduate students in topology. I think the leader was Norman Steenrod. He was discussing the theorem that a countable collection of countable sets is countable. Perhaps I volunteered that the theorem is true, but I didn't volunteer to prove it. This was because of some earlier training of mine and points out a difference between two philosophies of mathematical instruction.
In the '30s, Robert Lee Moore of the University of Texas at Austin and Solomon Lefschetz of Princeton University were two of the leading topologists, particularly in graduate-school instruction. Both were able and effective, and both were also individuals. Moore based his approach on axiomatics and did not allow his students to read mathematical books and articles dealing with the subject matter of Moore's courses. Lefschetz was quite intuitive and was quite willing for his students to read and talk with others (provided they did not plagiarize) as long as they learned basic techniques and made these techniques a part of their own collection of mathematical tools.
I had a course from Moore at Texas in 1934-35. To some extent I had been influenced by himcertainly I did not particularly want to prove this theorem that Steenrod was talking about. To do so might deprive some other member of the seminar from discovering an original (to him) proof. But Steenrod asked me to give a proof. So I wrote out the beginnings of the countable sets in an array and showed several methods of counting through the entire array by a "diagonal progression."
Later, I was attending a more advanced topology seminar led by Professor Lefschetz. I was asked to choose a topic and address this seminar. I went to C.H. Dowker, who was further along in his studies than I, and together we selected a paper by Borsuk which proved that a ham sandwich (two slices of bread and a slice of ham) could be cut so that each slice of bread and the slice of ham were cut into two "equal" pieces. Dowker was quite generous with his help, and he had me give him a rehearsal speech before my actual talk. R.L. Moore would not have approved; Lefschetz would have approved. I learned a lot from preparing and delivering the talk. A few weeks later M.H.A. Newman from Cambridge University, then a visitor at Princeton, gave a popular talk. Someone asked him what mathematicians did. A part of his answer was that some mathematicians spent two sessions at a seminar proving that a ham sandwich could be cut exactly in half!
On another occasion I was talking to a seminar group about the properties of a certain set E. I had listed, in brief form, some of the properties of the set E. But Professor Lefschetz asked me to draw a picture of the set E. It so happens that I was somewhat nervous at the time of this talk, but I managed to trace out a set E, looking somewhat like the drawing below.
[GRAPHIC OF OUTLINE OF A WAVEY E WITH A WAVEY INDENTATION ON THE TOP LEFT EDGE, not immediately recognizable for what it is]
Everyone but I and Lefschetz laughed, and Lefschetz grinned. I didn't know what they were laughing at until I was talking with a friend later who told me that I had drawn a facsimile of the letter capital E on the board!
Although not a seminar occurrence, the following did happen at my doctoral oral examination. Professor Lefschetz was on my committee. In the examination room he received a message that he was wanted on the telephone. As he was leaving, he asked me to draw a pretzel on the blackboard. This I did, after a fashion. In a few minutes Lefschetz returned. When he saw what I had drawn, his jaw sagged. One of the other examiners spoke up in my behalf and said that I had been asked to draw a pretzel. Professor Lefschetz then apologized and said he had meant to say torus. So I drew a square, showing how to match up two sets of edges to form a torus, which is what Lefschetz wanted, and my final oral proceeded.
The H. Petard spoof
Sometime in 1936 or 1937 a group of mathematics and physics students at Princeton University decided to write a tongue-in-cheek article under an assumed name and get it published in a mathematical journal. This reporter was not a member of the group engaged in this project. This reporter will plead guilty to having, at that time, read a large number of detective stories (and probably was continuing to read them to the detriment of his progress in his mathematical program).
At some sort of a social function, the secretary of the Mathematics Department, Agnes Fleming, said that she had received, from various places, some letters addressed to one H. Petard asking that the letters be held for Petard's arrival in Princeton. Then, she said, she had received a letter from H. Petard himself, stating that his arrival in Princeton had been delayed, and asking if the Mathematics Department would forward to a new address any mail which might have arrived for him. Without being specifically asked for my opinion, I voiced the idea that this sounded very suspicious and that it might be a process of trying to build up a spurious identity. (In the previous decade there had been certain colleges which had granted admittance to 11 "manufactured" students with forged credentials.) One or two others at the social gathering thought by idea was farfetched, or at least said so. Then the conversation turned in another direction.
A day or two later I was visited by a couple of members of the group, one of whom had said my idea was farfetched, to ask why I had blown their "cover". I explained that the group should have taken me into their confidence, that I knew nothing about their proposal, and that they should have used more discreet methods. But I told them that I wouldn't give them away, at least not any time soon.
As I recollect and reconstruct the situation, the group had collectively written a paper with the title "A contribution to the mathematical theory of big game hunting". They wanted a Princeton address, presumably to receive the referee's report and reprints, if accepted and published. They didn't feel that they could directly involve the Mathematics Department secretary in this hoax. So they were trying to build up a false identity, get the false identity moved away from Princeton, and hoped to receive mail addressed to someone ostensibly still in Princeton with an implied connection with the Princeton Mathematics Department.
Well, it worked. The tongue-in-cheek article on big game hunting did appear in the American Mathematical Monthly, vol. 45 (no. 7, Aug-Sep 1938), pp. 446-447, under the authorship of H. Petard of Princeton, New Jersey. And some of the members of the group indicated that they now had more respect for my mental acumen and/or savvy.
The Princeton Mathematics Community in the 1930s