Erdös is somewhat below medium height, an extremely nervous and agitated person. At that time he was even more in perpetual motion than now — almost constantly jumping up and down or flapping his arms. His eyes indicated he was always thinking about mathematics, a process interrupted only by his rather pessimistic statements on world affairs, politics, or human affairs in general, which he viewed darkly. If some amusing thought occurred to him, he would jump up, flap his hands, and sit down again. In the intensity of his devotion to mathematics and constant thinking about problems, he was like some of my Polish friends — if possible, even more so. His peculiarities are so numerous it is impossible to describe them all. One of them was (and still is) his own very peculiar language. Such expressions as "epsilon" meaning a child, "slave" and "boss" for husband and wife, "capture" for marriage, "preaching'' for lecturing, and a host of others are now well known throughout the mathematical world. Of all the results we obtained jointly, many have still not been published to this day.
Erdös has not changed much as the years have gone by. He is still completely absorbed by mathematics and mathematicians. Now over sixty, he has more than seven hundred papers to his credit. Among the many sayings about him one goes, "You are not a real mathematician if you don't know Paul Erdös." There is also the well-known Erdös number — the number of steps it takes any mathematician to connect with Erdös in a chain of collaborators. "Number two," for example, is to have a joint paper with someone who has written a paper with Erdös. Most mathematicians can usually find a link with him, if not in one then in two stages.
Erdös continues to write short handwritten letters beginning, "Suppose that x is thus and so…" or "Suppose I have a sequence of numbers…" Toward the end, he adds a few personal remarks, mainly about getting old (this started when he was thirty) or with hypochondriac or pessimistic observations about the fate of our aging friends. His letters are nevertheless charming and always contain new mathematical information. Our correspondence started before the Madison years, containing many discussions of the hardships of young mathematicians who could not find jobs or of how to deal with officials and administrators. He used the expression, "Oh, he is a big shot" about young American assistant professors, and when he called me one, I introduced a subclassification of "big shots, small shots, big fry and small fry''—four orders of status. In 1941, as an assistant professor I told him I was at best a "small shot." This amused him, and he would allot one of these four grades to our friends in conversations or correspondence.
Through thick and thin, Johnny von Neumann and I also continued our correspondence, which included a little mathematics even in those days, and a lot about the tragic happenings in the world. There was much isolationism in the United States, and the obvious and widespread disinclination to enter the war created in me a feeling of despair mixed with resentment. On the whole, Johnny was more optimistic and knew better than I the power of the United States and the long-range goals of U.S. policies. He was already an American citizen engaged (though I did not know it at the time) in the war effort the country was preparing.
The tone of our mathematical correspondence and of our conversations when we met at mathematics meetings changed from the abstract to more applied, physics-related topics. He was now writing about problems of turbulence in hydrodynamics, aerodynamics, shocks, and explosives.
Johnny held discussions with many scientists, among them Norbert Wiener. Although Norbert was a pacifist, he badly wanted to contribute something important to the American war effort. Wiener felt as Russell did that this was a "just war," a necessary war, and the only hope for mankind lay in U.S. intervention and victory. But Norbert was difficult in his dealings with the military, whereas Johnny always got along with them.
Wiener wrote in his autobiography that he had ideas similar to the ones I later proposed as the Monte Carlo method. He says vaguely that he found no response when he talked to someone and so dropped the matter, in the same way that he lost interest in the idea of geometry of vector spaces and function spaces à la Banach. In fact, in one of his books he called these vector spaces (which are associated with Banach's name alone) Banach-Wiener spaces. This nomenclature did not "take" at all.
In the first World War mathematicians had done much work in classical mechanics, calculations of trajectories, and external and internal ballistics. This work was resumed at the beginning of the second World War, although it soon turned out not to be the main thrust of the scientific applications. Hydrodynamic and aerodynamic questions became more detailed and urgent, particularly because they were directly connected with special war problems. Early in 1940 I took from the library a German textbook on ballistics and studied it, but noticed that there was not much in it of importance to the military technology of the forties. At the beginning of the war electronic computing machines did not exist. There were only the beginnings of the mechanical relay machines constructed at Harvard, at IBM, and one or two other places.
As soon as the prescribed time had elapsed I applied for and received American citizenship in Madison in 1941. I hoped that this would make it easier for me to enroll in the war effort. To pass the examination I studied the history of the United States, the essence of the Constitution, the names of Presidents, and the other topics one was likely to be asked about at the examination. I don't remember why, but instead of my having to go to Chicago, an examiner came to Madison to our apartment. After a few words I noticed that he must have been an immigrant himself or the son of an immigrant. His appearance was quite Jewish, and perhaps impudently I asked him about his own origins and background. He did not seem to mind and replied that his parents had come from the Ukraine. Soon I realized with embarrassment that it was I who was examining him.
Immediately after I received the citizenship papers, I tried to volunteer in the Air Force. At thirty I was considered too old to become a combat pilot, but with my mathematical background I thought I could receive training as a navigator, because the University had received a notice that the Air Force was looking for volunteers. I went to a recruiting center not far from Madison for a physical examination. It was given by West Coast Japanese medics who had been relocated in this Middle Western camp. Because the physical tests involved the taking of blood samples, I told myself jokingly that I was losing some blood to the Japanese in defense of my new country. I was disappointed when my application was rejected because of my peculiar eyesight.
Teaching army math courses did not seem sufficiently relevant; I wanted to do something more immediately useful, something that would contribute more directly. I thought of going to Canada to enlist there, and I remembered a conversation in Cambridge in 1940 with Whitehead, who had relatives who were officers in the Royal Canadian Air Force. So I wrote him asking whether he could help me to become involved in the war effort in Canada. He sent back a letter which I treasure for all the things it said. Even though he said that he had written to someone in Canada on my behalf, nothing came of this.