He told me of another discussion he had with Wiener and their different points of view: Johnny advocated, in order to establish models for the working of the human brain, a numerical digital approach through a sequence of time steps, while Wiener imagined continuous or "hormonal" outlines. The dichotomy between these points of view is still of great interest and, of course, by now has been transformed and deepened by the greater knowledge of the anatomy of the brain and by more work in the theory of automata.
The relationship between G. D. Birkhoff and von Neumann was curious. Birkhoff did not really have complete admiration for or appreciation of von Neumann's genius. He probably could not appreciate the many kinds of mathematics von Neumann was pursuing. He admired his technical brilliance, but G.D.'s tastes were more classical, in the tradition of Poincaré and the great French school of analysis. Von Neumann's interests were different. Birkhoff had ambitions to produce something of great importance in physics, and he made a few, technically interesting but not conceptually important contributions to the general theory of relativity. He lectured several times on such subjects in Mexico, stimulating a small school of relativists there. Von Neumann's interests lay in the foundations of the new quantum theory's more recent developments. Theirs were differences of interests, of approaches, and of value systems. Birkhoff appreciated probing in depth more than exploring in breadth. Von Neumann, to some extent, did both. There was, of course, about a quarter-century's difference in age between them, as well as in background and in upbringing. Also, von Neumann never quite forgave G.D. for having "scooped" him in the affair of' the ergodic theorem: Von Neumann had been first in proving what is now called the weak ergodic theorem. By a sheer virtuoso kind of combinatorial thinking, Birkhoff managed to prove a stronger one, and — having more influence with the editors of the Proceedings of the National Academy of Sciences — he published his paper first. This was something Johnny could never forget. He sometimes complained about this to me, but always in a most indirect and oblique way.
In addition to the elementary mathematics courses which I taught during my first year in the Society, I was asked to add advanced courses gradually. I liked this, for the best way to learn a subject is to try to teach it systematically.
Then one gets the real points, the essentials. One was an important undergraduate course in classical mechanics, Math 4 if I remember its former name. Another was Math 9, a course on probability.
At the time I had no precise idea what grades meant: A, B, C, D, or F. But I had rigid standards. I remember an otherwise quite good student, who protested receiving the grade of "C." Some other professors intervened, but I stubbornly, perhaps foolishly, stood my ground. Now I tend to be more lenient, and when I give a "C" or ''D" the students really deserve an "F" or worse!
Tamarkin, who was a professor at Brown University, asked me to teach a graduate course in his place while he took his sabbatical leave for a term. I decided to give the course on the theory of functions of several real variables. It included a lot of new material — much of it my own recent work — and I was rather proud of it. Every Friday I went to Providence by train, taught the course, spent the weekend with Tamarkin at his home, returning to Cambridge on Sunday. When I mentioned the contents of the course to Mazur when I went home to Lwów for the last time during the summer of 1939, he liked it very much. He liked the material, the way it was organized, and said he would love to give such a course himself, all of which pleased me and encouraged me.
Tamarkin was a most interesting person. He was of medium height, very portly — I would say some thirty pounds overweight. He was quite nearsighted, a constant cigar-and-cigarette-smoker, and generally extremely jovial. As I got to know him better, I discovered the wonderful qualities of his mind and character.
Before World War I, he had written some mathematical research papers on the work of G. D. Birkhoff and even improved some of the latter's results a bit, which led to a certain animosity in their relations. Yet when he came to the United States, Birkhoff helped him secure his position at Brown, which had a notable mathematics faculty, including James Richardson, Raymond C. Archibald, and others. Richardson was a gentleman of the old school. Archibald was an eminent historian of mathematics, who established the famous mathematical library of Brown, one of the best in the country.
Tamarkin was interested in Polish-style mathematics and had heard about some of my results in the theory of Banach spaces. He had a quality which perhaps only a small number of mathematicians possess: he was extremely interested in the works of others and less egocentric than most. He was also interested in what was going on in other fields besides his own, whereas most mathematician's — even the best ones — are often deeply immersed in their own work and do not pay much attention to what others around them are doing. Tamarkin befriended me and encouraged me in my work.
He was Russian, not of Jewish origin exactly, but a Karaite. The Karaites were a sect of Semitic people not subject to the usual restrictions on Jews in Russia, the reason being that they claimed they were absent from Palestine when Jesus was condemned to death, and this exempted them. This claim was accepted by the Russian governors. They also had something in common with the ancient Khazars, people of a mysterious sixth- or seventh-century kingdom in southern Russia, a pagan tribe whose king decided to adopt a new religion. He selected Judaism after having asked Christian, Moslem, and Jewish representatives to explain their beliefs. Tamarkin believed he was one of their descendants. He had escaped from Leningrad after the Russian Revolution in a manner not unlike that of George Gamov some ten years later — over the ice of Lake Ladoga to Finland.
While I was at Harvard, Johnny came to see me a few times, and I invited him to dinner at the Society of Fellows. We would also take automobile drives and trips together during which we discussed everything from mathematics to literature and talked without interruption while still paying attention to our surroundings. Johnny liked this kind of travel very much.
Once at Christmas time in 1937, we drove from Princeton to Duke University to a meeting of the American Mathematical Society. On the way, among other things we discussed the effect that the arrival of increasingly large numbers of refugee European scientists would have on the American academic scene. We stopped at an inn where we found a folder describing a local Indian Chief, Tomo-Chee-Chee, who apparently had been unhappy about the arrival of white men. As an illustration of our frequently linguistic and philological jokes, I asked him why it was that the Pilgrims had "landed" while the present European immigrants and scientific refugees merely "arrived." Johnny enjoyed the implied contrast and used this in other contexts as an example of an implied value judgment. We also likened G. D. Birkhoff's increasing qualms about the foreign influence to the Indian Chief's. Continuing our drive, we managed to lose our way a couple of times and joked that it was Chief Tomo-Chee-Chee who had magically assumed the shape of false road signs to lead us astray.
This was the first time I visited the South, and I was much taken by the difference in atmosphere between New York, New England, and the southern states. I remember a feeling of "déjà vu": the more polished manners, the more leisurely pace of life, and the elegant estates. Something seemed familiar, and I wondered what it was. Suddenly I asked myself' if it could be the remnants of the practice of slavery, which reminded me of the traces of feudalism still visible in the country life of Poland. I was also surprised to see so many black people, and their language intrigued me. At a gas station, one of the Negro attendants said, "What would you like now, Captain?" I asked Johnny, "Does he think I might be an officer and calls me Captain as a compliment?" Similarly, the first time I heard myself called "Doc," I wondered how the porter knew that I had a Doctor's degree!