Ulam, the man and the mathematician

First of all a few words of introduction . Ulam was a friend and collaborator of mine for about 50 years . We had innumerable mathematical and political discussions and have several joint papers . While discussing mostly our joint work I will neglect his work in physics, biology, computers and computer science . Ulam wrote a very successful autobiography [71 and I will mention only a few incidents which as far as I remember are not mentioned in his autobiography and which I hope are accurate . I first met Ulam in Cambridge, England in 1935 and then again in 1938-39 in Cambridge, Massachusetts at Harvard University where he was a member of the Society of Fellows . But our real mathematical contact started when I visited him twice at the University of Wisconsin between 1941 and 1943 and where we obtained our first joint results . Then I met him in Santa Fe and Los Angeles in 1946. He had a serious illness there (almost his only illness, he enjoyed very good health up to his fatal heart attack), probably encephalitis . He completely recovered and while he was recuperating I visited him on an island south of Los Angeles (all this is described in his autobiography) . I visited him several times in Los Alamos, the last time was in 1952 . In 1963 there was a meeting on number theory in Boulder ; we met there and also visited Aspen together . I was at his house when he got a call from the White House asking his advice about the test ban-Ulam was strongly in favor of it . Then in 1968 and 1970 I was Visiting Professor at the University of Colorado and there we wrote our first joint papers on additive number theory and set theory . In 1970 my mother, then 90 years old, was also with me, and Frangoise (Mrs. Ulam) wrote a little article about her . Later in the 70's we often were together at the University of Florida. I had planned to continue our work when I learned that he suddenly died of a coronary attack in May 1984 . Ulam was clearly both a prodigy and a "dotigy" . The word úotigy cannot be found in any dictionary and is due to Ulam himself . I gave a talk on child prodigies and Ulam remarked that we were both "dotigies", i .e., we really should be in our dotage but can still "prove and conjecture" . Perhaps it is a sad commentary on human fate that the best wish we can make for a baby is "May you be a prodigy and then later a dotigy" . Ulam was certainly a prodigy, for he proved before he was 20 that in every infinite set there is a 2-valued measure where the whole set has measure 1, points have measure 0, and the measure is finitely additive . Tarski discovered this independently a few months later. Recently I found out that F . Riesz antici-