Summing Up a Life in Numbers

...To a person in the field, this information clearly indicates the author's precocity, but it can have little import to the general reader...

...This attempt to take excessive credit for what was basically a group achievement reminds Ulam of a story about a pension in Berlin before the War...

...he was involved on a day-to-day basis with Hans Bethe, Enrico Fermi, Robert J. Oppenheimer, and other outstanding physicists...

...The first thing that struck me about him were his eyes—brown, large, vivacious, and full of expression...

...The faculty of neighboring MIT included Witold Hurewicz and Norman Levinson, while Harvard boasted Marshall Stone, Hassler Whitney and G. D. Birkhoff, the leading American mathematician of the time, who was instrumental in having Ulam appointed a Junior Fellow from 1936-39...

...Unfortunately, this kind of encyclopedic approach leaves little room for any explanation of the mathematics, or detailed portraits of personalities, not to mention dramatization of events...

...By his own assertion, Ulam liked to boast (in contrast to von Neumann), "Especially some of my trivial accomplishments like athletics or winning at games...

...Ulam's discussion of the events surrounding the dropping of the bomb on Hiroshima demonstrates both his concern for scientific recognition and his strong sense of Jewishness...

...To the end, Ulam remains the competitive scientist, his thoughts gliding across the nature of mathematics, its relation to physics and the biological advances that lie ahead...

...Johnny was always a hard worker...

...His habit of intermingling funny remarks, jokes, and paradoxical anecdotes made him far from remote or forbidding...

...He seems to be saying: "See all the important theorems I have proved and all the famous mathematicians and physicists I have known and collaborated with...

...Tamarkin was Russian, not of Jewish origin exactly, but a Karaite...

...Soon it becomes apparent that Ulam's primary objectives are to record the major problems (both pure and applied) that interested him during 50 years of creative research, and at the same time to describe in at least some detail the many mathematicians and physicists he has known...

...Of his initial arrival in New Mexico, he writes: "We stopped for lunch at the Hotel La Fonda fin Santa Fe...

...Although our research has been in totally different fields (mine in abstract algebra...

...Consequently, although the book reads easily enough, the tone of the writing is flat, the characters are viewed from the outside and events are often inadequately described...

...He remembered enough to correct an occasional mistake or mispronunciation on my part...

...In his interview he was asked whether he was for or against Jews in the academic profession and also whether he was liberal...

...And why were the names of so many mathematicians and physicists marching in what seemed a continuous procession across its pages...

...I have had some contact with almost all those mentioned in the book (including Ulam himself), and a few are even good friends...

...His vanity comes through in many other ways, too: "Perhaps I liked it [E...

...Ulam seemed an ideal person to convey the richness and variety of mathematics and its applicability to the "real" world...

...Steinhaus was one of the few Polish professors of Jewish descent...

...He begins by telling how Ernest Lawrence and Oppenheimer each took credit for the accomplishments...

...As students, we used to joke that the Society of Fellows was Harvard's way of making an award "higher" than a PhD...

...Anyone entering it—especially at Harvard, where I studied —was bound to meet most of the "celebrities...

...Whereupon another man stood up shyly and said, 'Excuse me, Mr...

...In a newspaper interview, "Lawrence modestly admitted that he more than anyone else was responsible for the atomic bomb...

...There is more satisfaction in being mentioned in a short history than in one which has 10.000 pages...

...As the dishes were passed at dinner from boarder to boarder, "one man was taking most of the asparagus on the platter...

...T. Bell's Development of Mathematics] because my work is mentioned there even though the book was written when I was only 28 and it is a rather small volume...

...The only exception is the picture of von Neumann...

...and the boy answers, 'I wrote: Nebech, Nebech, Nebeck.' 'That is correct, so why did you receive an F?' 'I spelled Nebech with two b's'" A less pleasant aspect of the book is its uncovering of Ulam's ego and need for recognition...

...He was working at Los Alamos the day the first atomic bomb was dropped...

...I told Banach of a remark of von Neumann: 'Die Goim haben der folgenden Satzbeweisen (The goys have proved the following theorem...

...His researches had cut across a broad canvas of mathematics and physics, from the purest abstract fields to the awesome frontiers of the development of the hydrogen bomb to the first uses of high speed electronic computers...

...Ulam leaves the reader with strong impressions of the central role Jews played in mathematics (far out of proportion to their numbers), the attitude of American universities before World War II toward hiring Jews, and a lively feeling for Jewish humor...

...Later he [Dean Montgomery] told me stories about the atmosphere at Yale, which at that time [1941] was ultraconservative...

...Each day he would start writing before breakfast...

...Julius Schauder was murdered by the Nazis...

...This is not as surprising as it may appear, for between 1935 (the year Ulam came to the United States from Poland) and 1957 (the year his closest friend, the great "Johnny" von Neumann, died prematurely of cancer)—the main period covered here—the world of mathematics was quite circumscribed...

...So what did you write?* asks the father...

...What particularly piqued my interest, though, was the prospect of having a mathematician of Ulam's caliber bring to life some of the important discoveries in which he had been involved, of his dramatizing for the ordinary reader the excitement every scientist feels at those moments when the flash of insight reveals some hitherto unknown truth...

...After an interesting New Mexico-style meal, we walked...

...later, he served on various high-level committees that advised the government on scientific affairs...

...At once I found him congenial...

...He sent back a letter which I treasure for all the things it said," Ulam tells us, without offering the slightest hint of what they might be...

...For the layman cannot be expected to know that in the late 19th century George Cantor had revolutionized set theory, the foundation of all mathematics...

...James D. Watson had done this for me in The Double Helix, his narrative of the breaking of the genetic code, complete with the tensions and rivalries between the participants in that pioneering effort...

...Goldberg, we also like asparagus!'" The final chapter of Adventures of a Mathematician is entitled "Random Reflections...

...Ulam's affection for his colleague is especially apparent when he tells of the days before von Neumann's death: "By then he was very, very ill...

...his in the theory of sets, topology, analysis, applied mathematics, mathematical physics, mathematical biology) and we are of different mathematical "generations" (I am 14 years his junior), the individuals Ulam has worked with have been part of my own background as well...

...And Oppenheimer is reported quoting the Bhagavad-Gita: "It flashed to my mind that I had become the Prince of Darkness, the destroyer of Universes...

...What audience was the book addressing...

...His head was impressively large...

...I would sit with him and try to distract him...

...I was reading to him in Greek from a work copy of Thucydides...

...Even at parties in his house, he would occasionally leave the guests to go to his study for half an hour...

...He had a sort of waddling walk...

...As I began to read Adventures of a Mathematician, however, anticipation quickly turned to puzzlement...

...During World War II, for example, Ulam wanted to become involved in the Canadian war effort and wrote to Alfred North Whitehead to request the influential philosopher's assistance...

...Throughout the book there is a deep sense of Jewishness, too...

...he was there during the conflict over Edward Teller's approach to the design of the "Super" bomb, and his own efforts were crucial to its ultimate development...

...Reviewed by Daniel Gorenstein Professor of Mathematics, Rutgers University As a professional mathematician, I looked forward to reading S. M. Ulam's memoirs...

...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...

...Describing himself at 16, Ulam writes with no further amplification, "I was working on some problems on transfinite numbers and on the problem of the continuum hypothesis...

...Nor is the nonmathematician likely to make very much out of the following quote from the author's famous teacher in Warsaw, Stefan Banach: "It was characteristic of certain Jews always to try to change the established scheme of things—Jesus, Marx, Freud, Cantor...

...Even though he answered both questions 'wrongly,' he nevertheless received an offer [from Yale...

...I will never forget the scene a few days before he died...

...Johnny told the classic story of a boy who had received a failing grade on an essay describing the past, present and future of the Hungarian empire...

...Ulam's close relationship with "Johnny" over many years is depicted with considerable feeling and depth...

...During recovery from a brain operation that almost killed him, Ulam played chess with Paul Erdos (a leading mathematician and friend) and is quite pleased that his opponent became tired before he did...