Wiener seemed childish in many ways. Being very ambitious about his place in the history of mathematics, he needed constant reassurance about his creative ability. I was almost stunned a few weeks after our first encounter when he asked me point blank: "Ulam! Do you think I am through in mathematics?" Mathematicians tend to worry about their diminishing power of concentration much as some men do about their sexual potency. Impudently, I felt a strong temptation to say "yes" as a joke, but refrained; he would not have understood. Speaking of that remark, "Am I through," several years later at the first World Congress of Mathematicians held in Cambridge, I was walking on Massachusetts Avenue and saw Wiener in front of a bookstore. His face was glued to the window and when he saw me, he said, "Oh! Ulam! Look! There is my book!" Then he added, "Ulam, the work we two have done in probability theory has not been noticed much before, but see! Now, it is in the center of everything." I found this disarmingly and blessedly naive.
Anecdotes about Wiener abound; every mathematician who knew him has his own collection. I will add my story of what happened when I came to MIT as a visiting professor in the fall of 1957. I was assigned an office across the hall from his. On the second day after my arrival, I met him in the corridor and he stopped me to say, "Ulam! I can't tell you what I am working on now, you are in a position to put a secret stamp on it!" (This presumably because of my position in Los Alamos.) Needless to say, I could do no such thing.
Wiener always had a feeling of insecurity. Before the war he used to talk about his personal problems to J. D. Tamarkin, who was a great friend of his. When he was writing his autobiography, he showed a voluminous manuscript to Tamarkin. Tamarkin, whom I had met in 1936 and with whom I became quite friendly, told me about Wiener's manuscript and how interesting it was. But he also expressed the opinion that Wiener might be sued for libel for many of his outspoken statements. He spoke almost with disbelief about Wiener's text and how he tried to dissuade him from publishing the book in that form. What finally appeared apparently was considerably toned down from the original version.
Another memory I have of Wiener concerns his asking me to go with him to South Station in Boston to meet the English mathematician G. H. Hardy who was coming to the States for a visit. He knew I had met Hardy in England. We collected another mathematician, perhaps it was Norman Levinson, and picked up Hardy at the train. Wiener, who prided himself on his knowledge of the Chinese, their culture and even their language, invited everybody for lunch at a Chinese restaurant. Immediately he started talking Chinese to the waiter, who seemed not to understand a word. Wiener simply remarked, "He must be from the south and does not speak Mandarin." (We were not quite convinced that this was the complete explanation.) It was a very pleasant lunch with much mathematical talk. And after lunch Wiener who had picked up the check discovered that he had no money. Fortunately we found the few necessary dollars in our pockets. Wiener scrupulously reimbursed us later.
It was said that Wiener, although he considered his professorship at MIT quite satisfactory, was very disappointed that Harvard never offered him a post. His father had been a professor at Harvard, and Norbert wanted very much to follow in his footsteps.
Although G. D. Birkhoff was at least ten years his senior, Wiener felt a rivalry with him and wanted to equal or surpass him in mathematical achievement and fame. When Birkhoff's celebrated ergodic theorem proof was published, Wiener tried very hard to go him one better and prove an even stronger theorem. He did manage it, but the strengthening was not as simple or as fundamental as G.D.'s original proof. Here again is an example of the competitive nature of some mathematicians and the sources of their ambition.
I think Wiener had marvelous talents as a mathematician — that is perspicacity and technical genius. He had a supreme general intelligence but, in my opinion, not the spark of originality which does the unusual unrelated to what others have done. In mathematics, as in physics, so much depends on chance, on a propitious moment. Perhaps von Neumann also lacked some of the "irrational," though with his wonderful creativity, he certainly went to and achieved the limits of the "reasonable."
There are several ways in which Wiener and von Neumann intersected in their interests and in their feelings about what was important both in pure mathematics and its applications, but it is difficult to compare their personalities. Norbert Wiener was a true eccentric and von Neumann was, if anything, the opposite — a really solid person. Wiener had a sense of what is worth thinking about, and he understood the possibilities of using mathematics for seemingly more important and more visible applications in theoretical physics. He had a marvelous technique for using Fourier transforms, and it is amazing how much the power of algorithms or symbolism could accomplish. I am always amazed how much a certain facility with a special and apparently narrow technique can accomplish. Wiener was a master at this. I have seen other mathematicians who could do the same in a more modest way. For instance, Steinhaus obtained quite penetrating insights into other fields, and his student, Mark Kac, now at Rockefeller University, surpassed him. Antoni Zygmund in Chicago, another Pole, is a master of the great field of trigonometric series. Several of his students have obtained epoch-making results in other fields — for example, Paul Cohen, who did this in set theory, the most general and abstract part of mathematics.
I don't think Wiener was particularly fond of combinatorial thinking or of working on foundations of mathematicological or set theoretical problems. At the beginning of his career, he may have gone in this direction, but later he applied himself to other fields and to number theory.
Von Neumann was different. He also had several quite independent techniques at his fingertips. (It is rare to have more than two or three.) These included a facility for symbolic manipulation of linear operators. He also had an undefinable "common sense" feeling for logical structure and for both the skeleton and the combinatorial superstructure in new mathematical theories. This stood him in good stead much later, when he became interested in the notion of a possible theory of automata, and when he undertook both the conception and the construction of electronic computing machines. He attempted to define and to pursue some of the formal analogies between the workings of the nervous system in general and of the human brain itself, and the operation of the newly developed electronic computers.
Wiener, somewhat hemmed in by the childishness and naiveté of his personality, was perhaps psychologically handicapped by the fact that, as a child, his father had pushed him as a prodigy. Von Neumann, who also began rather young, had a much wider knowledge of the world and more common sense outside the realm of pure intellect. Furthermore, Wiener was perhaps more in the tradition of talmudistic Judaic scholarship, even though his opinions and beliefs were very libertarian. This was quite conspicuously absent from von Neumann's makeup.
Johnny's overwhelming curiosity included many fields of theoretical physics, beginning with his pioneering work — his attempt to form a rigorous mathematical basis for quantum theory. His book, Die Mathematische Grundlagen der Quantum Mechanik, published over forty years ago, is not only a classic, but still the ''bible" on the subject. He was especially fascinated by the puzzling role of the Reynolds number and the seeming mystery of sudden onsets of turbulence in the motions of fluids. He had discussions with Wiener on the perplexing values of this number which is "dimensionless" — a pure number expressing the ratio of the inertial forces to the viscous forces. It is of the order of two thousand, a large number. Why is this so and not around one, or ten, or fifty? At that time, Johnny and I came to the conclusion that actual detailed numerical computations of many special cases could help throw light on the reasons for the transition from a laminar (regular) to a turbulent flow.