During my stay in Princeton I felt that there was some hesitation on Johnny's part about his own work. He was immersed in his new work on continuous geometries and in the theory of classes of operators in Hilbert spaces. I myself was not so interested in problems concerning properties of Hilbert spaces. Johnny, I could feel, was not completely certain of the importance of this work, either. Only when he found, from time to time, some ingenious, technically elegant trick or a new approach did he seem visibly stimulated or relieved of his own internal doubts.
It was at that time that he began to think of problems away from pure mathematics, although this was not the first time in his life. (He had written his famous book on the mathematical foundations of quantum theory in 1929.) He was thinking now more about classical problems in physics. For example, he studied problems of turbulence in hydrodynamics. In his continuous geometries, their elements do not play the role of what we normally consider as "points" in Euclidean space; it is a creation of a "pointless" geometry, a name which lent itself to many an easy joke.
He came back again and again to the possibilities of reformulating the logic of quantum theory, the substance of the talk he gave at the Warsaw seminar. In Princeton he frequently worked on this topic. Listening to his conversation, I saw or felt his own hesitation, and I suffered from doubt, too, because there was no definite experimental possibility of verifying this — it seemed purely a question of logic. Purely "grammatical" approaches never interested me much. When something is merely convenient or typographically useful, it seems less interesting to me than when there is a more real physical base, or if abstract, still somehow palpable. I have to admit that there are cases where formalism by itself has great value — for example, the technique, or rather the notation of Feynman graphs in physics. It is a purely typographical idea, it does not bring in itself any tangible input into a physical picture, nevertheless, by being a good notation it can push thoughts in directions that may prove useful or even novel and decisive. Beyond this (and extremely important), there is the magic of "algorithms," or symbolism in mathematics. Calculus itself shows the wonder of it. Various transforms, generating functions, and the like perform almost miraculously in mathematical applications.
Von Neumann was the master of, but also a little bit the slave to, his own technique. When he saw that something could be done, he let himself be carried away on tangents. My own feeling is that some of his mathematical work on classes of operators or on quasi-periodic functions, for example, is very interesting technically, but to my taste not terribly important; he could not resist doing it because of his facility.
How terribly important habit is. It may largely determine the characteristics or the nature of the brain itself. Habits influence or perhaps can largely determine the choice of trains of thought in one's work. Once these are established (and in my opinion they may be established very quickly — sometimes after just a few trials), the "connections" or "programs" or "subroutines" become fixed. Von Neumann had this habit of considering the line of least resistance. Of course, with his powerful brain he could quickly vanquish all small obstacles or difficulties and then go on. But if the difficulty was great right from the start, he would not knock his head against the wall, nor would he — as I once expressed it to Schreier — walk around the fortress and knock here and there to find the weakest spots and try to break through. He would switch to another problem. On the whole in his work habits I would call Johnny more realistic than optimistic.
Johnny was always a hard worker; he had a great energy and toughness behind a physical appearance that was somewhat on the soft side. Each day he would start writing before breakfast. Even at parties in his house, he would occasionally leave the guests to go to his study for half an hour or so to record something that was on his mind.
He may not have been an easy person to live with — in the sense that he did not devote enough time to ordinary family affairs.
Some people, especially women, found him lacking in curiosity about subjective or personal feelings and perhaps deficient in emotional development. But in his conversations with me, I felt that only a certain shyness prevented him from having more explicit discussions along these lines. Such seeming diffidence is not uncommon among mathematicians. Non-mathematicians often reproach us for this and may resent this apparent emotional insensitivity and excessive quantitative and rational bent, especially in attitudes towards mundane matters outside science. Von Neumann was so busy with mathematics, physics, and with academic affairs, not to mention increasingly innumerable activities later on as a consultant to many projects and Government advisory work, he probably could not be a very attentive, "normal" husband. This might account in part for his not-too-smooth home life.
To be sure, he was interested in women, outwardly, in a peculiar way. He would always look at legs and the figure of a woman. Whenever a skirt passed by he would turn and stare — so much so that it was noticed by everyone. Yet this was absentmindedly mechanical and almost automatic. About women in general he once said to me, "They don't do anything very much." He meant, of course, nothing much of importance outside of their biological and physiological activities.
He did not show social prejudice and never concealed his Jewish origins (even though I think he had actually been baptized a Christian in his childhood). In fact, he was very proud of the birth of the state of Israel in 1948 and was pleased by the Jewish victories over the surrounding Arab countries — a sort of misplaced nationalism.
His father, a banker, had been titled "von." In the Austro-Hungarian Empire people were rewarded with titles but these could also be obtained by gifts of money to the government. Johnny never used the full title (neither did von Kárman who was also of Jewish origin). He was ill at ease with people who were self-made or came from modest backgrounds. He felt most comfortable with third- or fourth-generation wealthy Jews. With someone like me, he would then often use Jewish expressions or jokes as a spice to conversation. He was a man of the world, not exactly snobbish but quite conscious of his position, who felt more at ease with people with the same background.
He was broadly educated and well versed in history, especially of the Roman Empire — its power and organization fascinated him. Perhaps part of this interest stemmed from a mathematician's appreciation of the difference between variables involving individual points, or persons, and groups of such, or classes of things. He was given to finding analogies between political problems of the present and of the past. Sometimes, the analogy was genuinely there, but there were so many other different factors that I don't think his conclusions were always justified.
In general, he tended not to disagree with people. He would not contradict or dissuade when asked for advice about things they were inclined to do. In matters of ordinary human affairs, his tendency was to go along, even to anticipate what people wanted to hear. He also had the innocent little trick of suggesting that things he wanted done originated with the persons he wanted to do them! I started using this ploy myself after I learned it from him. However, in scientific matters, he did defend the principles he believed in.
When it came to other scientists, the person for whom he had a deep admiration was Kurt Gödel. This was mingled with a feeling of disappointment at not having himself thought of ''undecidability." For years Gödel was not a professor at Princeton, merely a visiting fellow, I think it was called. Apparently there was someone on the faculty who was against him and managed to prevent his promotion to a professorship. Johnny would say to me, "How can any of us be called professor when Gödel is not?" When I asked him who it was who was unfriendly to Gödel, he would not tell me, even though we were close friends. I admired his discretion.