A Conversation with George A. Barnard

generalized, axiomatic treatments of everything. So I really had to learn it all again. I was to take a Ph.D. at Princeton and I always remember that I had to go over the syllabus of my preliminary exam with Lefschetz. I went over the algebra, and I had to learn vast quantities of algebra because we had virtually no abstract algebra at Cambridge. It just wasn't taught. And function theory was all done in terms of special functions and so on, and I had to know general function theory, and Hilbert space, and all that sort of thing. It was totally new to me. We got as far as projective geometry and I said, "Well now, projective geometry, that's really something that I think I do know. " Because H. F. Baker had written a five-volume work on projective geometry. He was the senior professor, the Lowndean Professor, at Cambridge at the time. They said, "Well, what do you know? " So I said, "Well, I reckon I've covered more or less the first four volumes of Baker's book. " They just said, "Good God, you don't call that projective geometry. " [Laughs] Of course, what they meant by projective geometry was abstract projective geometry in terms of Galois fields instead of the ordinary number field. That sort of thing is totally different from what Baker talked about. So I really had to learn that sort of mathematics from scratch, and that took me the best part of the first year I was there. Then in the second year, I did go to some lectures by Alonzo Church, but he was a very difficult person to approach. I used to go and knock on his door and hear him talking to somebody, so I would go away. I did this for quite a period. It wasn't until about half way through the year that I discovered that the person he was talking to was himself. Turing was there at the same time, and we sort of saw each other socially, Church, Turing and I. We were the only three people working in logic at that time. Though von Neumann was slightly interested, he didn't lecture on that aspect. He was interested in the logic of quantum mechanics, and he was working with Garrett Birkhoff on that. In fact, I spent a lot of time talking to von Neumann and other people, and not so much really to Church, so I learned a lot. Now coming back to statistics, Sam Wilks was there. I met him very early on because he always made a point of inviting any Britisher who arrived at Princeton to his home the very first week he arrived. I was then really supposed to be working in logic. Wilks hadn't written his book, and he wasn't at that time giving a course, but I went to some seminars with him. For example, I remember Hotelling coming and talking about multivariate analysis at one of the seminars. So I was just sort of not forgetting about statistics, but not really learning any. I went back to England in the summer of 1939 expecting to come back to Princeton to finish my Ph.D., but the war started so I stayed there. At the beginning of the war the navy obviously realized there was a shortage of mathematicians for the fleet-somebody decided this-and an advertisement appeared saying that mathematics graduates were required to serve as instructor lieutenants, the functions of the instructor lieutenant being to teach the midshipmen basic mathematics and also to advise the captain on tactics in battle. [Laughs] Practically the whole of my contemporaries and I showed up as applicants for this job, including, for example, Fred Hoyle. We were introduced first of all to Instructor Commander Somebody-or-other who asked us about our mathematics-what did we specialize in. When I said, "Topology," he said, "That's some kind of n-dimensional geometry, isn't it? " And I said, "Yes. " And he said, "Well, if you now go and be interviewed by Instructor Commander Gascoyne, he'll tell you a bit more about what you are expected to do. " Instructor Commander Gascoyne said, "Well now, I gather that you've done some mathematics but my job is to This content downloaded from 40.77. 167.15 on Sun, 28 Aug 2016 04:49:22 UTC All use subject to http://about.jstor. org/terms CONVERSATION WITH GEORGE A. BARNARD 199 make it clear to you that your prime function aboard ship is to answer questions about bets. You're in the Officers' Mess and people will ask you about poker. How are you at it? " So I said that I didn't know that I was very good at it. Anyway, we all passed through this process in which the real function was to see how you would get on, and we went through color blindness tests and so on. I subsequently met most of the rest of the group from my year during the war, and learned that none of us had been appointed as instructor lieutenants. [Laughs] "THAT WAS THE MOST FANTASTIC LUCK