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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 29 (PMC29) © 1:he Trustees of Princeton University, 1985 ALBERT TUCKER THE MATHEMATICS COMMUNITY AT PRINCETON BEFORE 1930 This is an interview with Albert Tucker in his office at Princeton University on 10 April 1984 conducted by William Aspray of the Babbage Institute. Th is session deals with the Princeton mathematical community in the period before 1930. Aspray: Professor Tucker would you begin by telling us something about the American mathematics community as it developed in the late-19th and early-20th centuries, prior to the '30s. Tucker: Well, before 1900 there were really only three places in the United States where graduate education in mathematics, to the doctorate level, took place. The first of these chronologically was Johns Hopkins University, and the other two were the University of Chicago, which was founded as a graduate institution about 1890, and Clark University in Worchester, Massachusetts, which at that time was also a graduate institution. Nowadays it is an undergraduate institution, quite different from what it was in those days. In the 19th century most of the leading mathematicians in the United States got their doctor's degrees abroad, especially in Germany .. In a certain sense the Ph.D. system as we now know it evolved in Germany and then was copied elsewhere. The important figure in Princeton mathematical history is Henry Burchard Fine. He studied in Germany with Felix Klein and Leopold Kronecker. He studied at two or three different German universities. Aspray: This was roughly when? Tucker: About 1885. The first Ph; D. that was given in mathematics at Princeton was given in about 1900. (PMC29) 1 Aspray: Do you remember who this was to? T'ucker: believe it was Henry Norris Russell, who had a distinguished career in astronomy at Princeton. A spray: How regularly were Ph.D. s granted then, in this period between 1900 and 1930? Tucker: Oh, about every other year in the first decade of the 20th century and then more frequently except for the period of World War I. A distinguished mathematician by the name of Robert Carmichael took a Princeton Ph.D. with Oswald Veblen along about 1910, and James Waddell Alexander, the Princeton topologist, took a degree about 1915, not with Veblen as most people think, but with a Swedish-American mathematician by the name of G ronwall, T. H. ·G ronwall. There is an amusing story that goes with that. Alexander had al ready published one or two papers with Veblen, basic papers in analysis situs. Veblen advised Alexander that he ought to do his Ph.D. thesis in a more canonical field, that perhaps analysis situs was just a passing fad. So the thesis was actually done in complex variables, an examination of univalent functions. It was one of the first papers on the subject of univalent functions. Then in the '20s there were probably one or two Ph.D.s each year, about half of them were Ph.D.s of Veblen, and the others were mainly Ph.D. s of Luther Eisenhart. Veblen had come to Princeton from the University of Chicago in 1905, as one of the preceptors of the system that was inaugurated by Woodrow Wilson, president of Princeton at that time, in an effort to upgrade the undergraduate education at Princeton. A spray: Specifically the undergraduate education? Tucker: Yes. The graduate education at Princeton has really always been an appendage. The main business has been undergraduate education. Aspray: Was it really Fine's doing that Princeton developed such a good mathematics department in the early years? Tucker: Yes, Fine was an excellent mathematician, but not a research mathematician. He had an uncanny knack for. spotting mathematical talent. The preceptor system-and he happened to have been a very close friend of President Wilson and a keen supporter of the upgrading of undergraduate education at Princeton~gave Fine an opportunity to bring in prom1s1ng young mathematicians. Two of these who were brought here from the University of Chicago and served as preceptors were Gilbert Ames Bliss, who later became the leader of mathematics at Chicago, and Oswald Veblen, who became leader of mathematics at Princeton. Others were George David Bi rkhoff, who became the leader at Harvard, and John Wesley Young, who moved to Dartmouth. Not very often mentioned is the fact that Robert Lee Moore, the famous point-set topologist of the University of Texas, was here for a year or two in the first decade of the 20th century. And from England, Sir James Jeans was brought here as a professor in mathematical physics. (PMC29) 2 It was in some sense Jeans who established the tradition in mathematical physics, a joint thing between mathematics and physics departments that has persisted through the years. Another famous physicist who was here at that time was Owen Richardson, who was later head of the Physical Laboratory at the University of London. Indeed Oswald Veblen married Richardon's sister. Aspray: May we go back for a moment to the preceptor system? This was introduced by Wilson in 1905, is that correct? Tucker: Yes. Aspray: Could you describe what this system was and what kind of bearing it had on mathematical opportunities? Tucker: Up until that time at Princeton the lecture system had been used. In a given course there would be a set of lectures. Perhaps there would be 200 students in the course, and their only contact with the professor or with the faculty was through the lecture. Aspray: I see. Tucker: The idea of the preceptor system was to have small discussion groups of eight or ten students. The students would prepare papers and discuss them in the precepts, so that it was a much more intimate form of teaching. It was designed to imitate things that went on at the British universities. Aspray: I see. Tucker: Now, in mathematics it was found that this system didn't work very well for the elementary courses, that they should still be taught pretty much in a one-way form, but in small classes of about 20. When I came to Princeton and was a part-time instructor in 1929, I taught two of these 20-student sections. It would be in the same course, so I would teach the same thing in both sections. There might be a dozen or even twenty sections in a course with a professor who was in charge and. who taught a hand-picked section of students. The rest of the teaching was done by the instructors. However, to counterbalance this, the lack of one-to-one learning that was supposed to occur in the precepts, the mathematics department set up a system of help sessions that was known by the students as the Missouri Club. This name was given to it because the students came with a "show-me" attitude. Aspray: I see. Tucker: One or two young mathematicians were on duty each night in the week, Monday through Friday, for from 7:00 to 10:00 in a certain room in McCosh Hall. This was a large room with blackboards on three sides of the room. The standard practice was that a student would come in, usually to get help doing homework problems, and the (PMC29) 3 instructor would tell the student to go take a section of the board and try working his assignment on the board. Then the instructor would circulate around the room giving attention for a minute or two to each student. It was something that worked very well, but depending a great deal on the personality of the instructor. Aspray: Now the impact that this had on the growth of a research faculty at the university was mainly that it provided more positions, is that correct? Tucker: That's right. Aspray: Presumably these had to be positions at a fairly low level. The school couldn't afford to hire a large number of senior people, even if they were available. Tucker: That's right. I suppose that was a principal ,reason why such people as Birkhoff and Bliss and Moore went on to positions elsewhere. There were only a few senior positions, and those were filled. Aspray: One might say then that Fine's achievement was making a virtue out of a necessity.