Conversation at the Whiteheads' was extremely varied. Besides the war, one discussed philosophy, science, literature, and people. The subject of Bertrand Russell came up once. He was having great troubles in this country. He had quarreled with Barnes, the Philadelphia millionaire who employed him at the time, and he was in difficulty at City College because of his views on sex and lectures on free love. Harvard tried to get him, but the invitation did not go through because of a wave of protests from proper Bostonians. I remember Whitehead talking about all this and Mrs. Whitehead exclaiming, "Oh, poor Bertie!" There was also talk of mathematics. Once someone asked, "Professor Whitehead, which is more important: ideas or things?" "Why, I would say ideas about things," was his instant reply.
I spent much of my time with the other Poles who had found their way to Cambridge — Tarski, Stefan Bergman and Alexander Wundheiler. They were all terribly unhappy, Wundheiler most of all. He always had some kind of "Weltschmerz." We would sit in front of my little radio which I left on all day long, and listen to the war news. He would stay for hours in my room, and we drank brandy from toothbrush glasses. He was a talented mathematician, an extremely nice, pleasant, and intelligent person, with a mind rather hard to describe — that of an intelligent critic, but somewhat lacking the "it" of mathematical invention. Genius is not the word I mean. It is hard to describe the talent for innovation, even on a modest scale; besides, it exists in a continuous spectrum and is largely influenced by "luck." There may be such a thing as habitual luck. People who are said to be lucky at cards probably have certain hidden talents for those games in which skill plays a role. It is like hidden parameters in physics, this ability that does not surface and that I like to call ''habitual luck." It is often remarked that in science there are people who have so much luck that one begins to feel it is something else. Wundheiler lacked this special spark.
I don't remember when and how he first appeared in the States. He had a temporary job at Tufts College in Boston. He had the usual impressions, complaints, appreciation and admiration for the United States; we talked about that at great length. Attitudes of students amused and shocked him. Being used to the more formal Polish manners, he was quite put out when in class one day a student called out to him, "Psst! The window is open. Can you close it?" One did not talk to professors that way in Poland.
He was interested in the geometry of the Dutch mathematician Schouten, which to me was too formal and symbolic. The notations were so complicated, I made fun of the formulae saying that they considered a geometric object a mere symbol, a letter around which indices were hung right, left, up, and down — like decorations on a Christmas tree.
We gradually lost contact after I left Cambridge. I learned later that he had committed suicide. I had a premonition of this because of a poem he would recite about a man who hanged himself with his tie. He was lonely, and many times he had told me of his unhappiness because of his looks. He was a very short man with an intelligent face, but not one that was considered appealing to women. He thought of himself as ugly, which bothered him.
In many cases, mathematics is an escape from reality. The mathematician finds his own monastic niche and happiness in pursuits that are disconnected from external affairs. Some practice it as if using a drug. Chess sometimes plays a similar role. In their unhappiness over the events of this world, some immerse themselves in a kind of self-sufficiency in mathematics. (Some have engaged in it for this reason alone.) Yet one cannot be sure that this is the sole reason; for others, mathematics is what they can do better than anything else.
Toward the end of the 1940 academic year Birkhoff intimated to me that there might be a vacancy at the University of Wisconsin. He added, "You should not be like the other European refugees who try at all costs to stay on the East Coast. Do as I have done, try to get a job in Madison. It is a good university; I was there as a young man." Taking his advice, I went to a meeting of the American Mathematical Society at Dartmouth to meet Professor Mark Ingraham, who was chairman of the mathematics department in Madison. In those days, mathematics meetings were job fairs at which one could see the department chairmen — almost like hereditary caciques, each surrounded by supplicants, groups of younger men looking for jobs. The situation was completely reversed in the late 1950s and early 1960s, when a lone young man fresh from school, with a brand-new Ph.D., would be surrounded by chairmen looking for young professors.
At the Dartmouth meeting I had a comical adventure. Late in the evening I walked into my dormitory room. It was dark, and I tried to get into bed without putting the light on. As I sat down, I heard a squeak and a groan. My bed had another occupant. I groped for the other bed. The occupant of my bed said, "Dr. Ulam?" I answered, "Yes." Immediately he said, "Given a group which is such and such, does it have this and that property?" I thought a moment and answered, ''Yes," proceeding to outline a reason. "If it is compact, then it is true." "But if it isn't compact," he tried to continue. It was late, I was tired, and felt like saying, "If it isn't compact, to hell with it." I let the conversation drop and fell asleep.
G. D. Birkhoff seemed to like and appreciate my work. I think I know a possible reason. He liked my self-confidence and my near impudence in defending the point of view of modern mathematics based on set theory against his more classical approach. He admired the so-to-speak hormonal, emotional side of mathematical creativity. I probably reminded him of the way he felt when he was young. He liked the way I got almost furious when — in order to draw me out — he attacked his son Garrett's research on generalized algebras and more formal abstract studies of structures. I defended it violently. His smile told me that he was pleased that the worth and originality of his son's work was appreciated.
In discussing the general job situation, he would often make skeptical remarks about foreigners. I think he was afraid that his position as the unquestioned leader of American mathematics would be weakened by the presence of such luminaries as Hermann Weyl, Jacques Hadamard, and others. He was also afraid that the explosion of refugees from Europe would fill the important academic positions, at least on the Eastern seaboard. He was quoted as having said, "If American mathematicians don't watch out, they may become hewers of wood and carriers of water." He never said that to me, but he did often make slighting remarks about the originality of some foreigners. He also maintained that they ought to be content with more modest positions; objectively speaking, this was understandable and even fair. Just the same, I would sometimes get angry. Perhaps because my family had been so well off and that until 1940 I never had to give much thought to my financial situation, I could be independent and said what I thought openly. Once I countered one of his attacks on foreigners with, "What pleasure do you find in playing a game where the outcome does not depend on the skill of the opponent but on some external circumstance? What pleasure is there in winning a game of chess from a player who is forced to make poor moves because he needs help from his opponent?" He was quite taken back by this remark.
But Birkhoff helped me to secure the job in Madison. He spoke to Ingraham on my behalf; after the Dartmouth meeting, I received an offer of an instructorship in Madison. At thirty, and with a certain reputation among mathematicians in Poland and America, I felt I could have been offered at least an assistant professorship. But the circumstances were so far from normal, and with someone like Jacques Hadamard, the most celebrated French mathematician, having been offered a lectureship in New York, or Tarski having been taken on as an instructor in Berkeley, I swallowed my pride and accepted the offer. Financially, it was not bad — something like twenty-three hundred dollars a year. Nevertheless, I felt sad at leaving Harvard and the "cultural East" for what I believed to be a more primitive and intellectually barren Middle West. On the East Coast it was implied that Harvard and perhaps Yale and Princeton were the only places with "culture." I was sure that Madison, about which I knew nothing, would be like Siberia and that I was being exiled. But since there were no alternatives, I prepared to leave Cambridge at the end of the summer, grimly determined to live through the years of exile and to await the outcome of the war.