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Oppenheimer's opposition to the development of the H-bomb were not exclusively on moral, philosophical, or humanitarian grounds. I might say cynically that he struck me as someone who, having been instrumental in starting a revolution (and the advent of nuclear energy does merit this appellation), does not contemplate with pleasure still bigger revolutions to come...

It seems to me this was the tragedy of Oppenheimer. He was more intelligent, receptive, and brilliantly critical than deeply original. Also he was caught in his own web, a web not of politics but of phrasing. Perhaps he exaggerated his role when he saw himself as "Prince of Darkness, the destroyer of Universes." Johnny used to say, "Some people profess guilt to claim credit for the sin."

Computers were brand-new; in fact the Los Alamos MANIAC was barely finished. The Princeton von Neumann machine had met with technical and engineering difficulties that had prolonged its perfection.

As soon as the machines were finished, Fermi, with his great common sense and intuition, recognized immediately their importance for the study of problems in theoretical physics, astrophysics, and classical physics. We discussed this at length... After deliberating about possible problems, we found a typical one requiring long-range prediction and long-time behavior of a dynamical system. It was the consideration of an elastic string with two fixed ends, subject not only to the usual elastic force but having, in addition, a physically correct small non-linear term.

Our problem turned out to have been felicitously chosen. The results were entirely different qualitatively from what even Fermi, with his great knowledge of wave motions, had expected. The original objective had been to see at what rate the energy of the string, initially put into a single sine wave (the note was struck as one tone), would gradually develop higher tones with the harmonics, and how the shape would finally become "a mess" both in the form of the string and in the way the energy was distributed among higher and higher modes. Nothing of the sort happened. To our surprise the string started playing a game of musical chairs, only between several low notes, and perhaps even more amazingly, after what would have been several hundred ordinary up and down vibrations, it came back almost exactly to its original... shape.

I know that Fermi considered this to be, as he said, "a minor discovery." And when he was invited a year later to give the Gibbs Lecture, he intended to talk about this. He became ill before the meeting.

These were the days of defense research contracts. Even mathematicians frequently were recipients. Johnny and I commented on how in some of their proposals scientists sometimes described how useful their intended research was for the national interest, whereas in reality they were motivated by bonafide scientific curiosity and an urge to write a few papers. Sometimes the utilitarian goal was mainly a pretext. This reminded us of the story of the Jew who wanted to enter a synagogue on Yom Kippur. In order to sit in a pew he had to pay for his seat, so he tried to sneak in by telling the guard he only wanted to tell Mr. Blum inside that his grandfather was very ill. But the guard refused, telling him: "Ganev, Sie wollen beten" ["You thief! You really want to pray"]. This, we liked to think, was a nice abstract illustration of the point.

Vita

Just after Johnny was offered the post of AEC Commissioner and before he accepted and became one in 1954 we had a long conversation. He had profound reservations about his acceptance because of the ramifications of the Oppenheimer Affair... In a two-hour visit to Frijoles Canyon one afternoon he bared his doubts and asked me how I felt about it. He joked, "I'll become a commissionnaire." (In French the term is used to mean errand boy.) But he was flattered and proud that although foreign born he would be entrusted with a high governmental position of great potental influence in directing large areas of technology and science.

Our usual conversations were either about mathematics or about his new interest in a theory of automata. These conversations had started in a sporadic and superficial way before the war at a time when such subjects hardly existed. After the war and before his illness we held many discussions on these problems. I proposed to him some of my own ideas about automata consisting of cells in a crystal-like arrangement.

It is evident that Johnny's ideas on a future theory of automata and organisms had roots that went back in time, but his more concrete ideas developed after his involvement with electronic machines. I think that one of his motives for pressing for the development of electronic computers was his facination with the working of the nervous system and the organization of the brain itself. After his death some of his collaborators collected his writings on the outlines of the theory of automata.

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Von Neumann's reputation and fame as a mathematician and as a scientist have grown steadily since his death. More than his direct influence on mathematical research, the breadth of his interests and of his scientific undertakings, his personality and his fantastic brain are becoming almost legendary.

Now Banach, Fermi, von Neumann were dead -the three great men whose intellects had impressed me the most. These were sad times indeed.

Vita

LOS ALAMOS

BOULDER

1957 February 8: Von Neumann dies in Walter Reed Hospital

1957-67 Research advisor, with John Manley, to Norris Bradbury, Director of Los Alamos

1960 Publication of A Collection of Mathematical Problems

1961-62 Fall semester: Visiting Professor at University of Colorado

1963 Winter quarter: Visiting Professor at University of California, San Diego

1965-77 Visiting Professor of Mathematics, and later Chairman of Mathematics Department, at University of Colorado. Spends vacations in Santa Fe

1967 Retires from Los Alamos but main

tains loose connection with the Laboratory as a dollar-a-year consultant

1968-75 Professor of Biomathematics at University of Colorado Medical School

1972-73 Sabbatical year at Massachusetts Institute of Technology, University of Paris, and Los Alamos

As a result of my work on the hydrogen bomb, I became drawn into a maze of involvements. These had to do precisely with government science and with work as a member of various Space and Air Force committees. Also, in some circles I became regarded as Teller's opponent, and I suspect I was consulted as a sort of counterweight. Some of these political activities included my stand on the Test Ban Treaty ... The cartoonist Herblock drew in the Washington Post a picture of the respective positions of Teller and me in which I fortunately appeared as the "good guy."

The idea of nuclear propulsion of space vehicles was born as soon as nuclear energy became a reality... I think Feynman was the first in Los Alamos during the war to talk about using an atomic reactor which would heat hydrogen and expel the gas at high velocity. A simple calculation shows that this would be more efficient than expelling the products of chemical reactions.

I became involved with two such projects... The first was Project Rover, a nuclear-reactor rocket which was being designed in Los Alamos already quite a few years before the Russian Sputnik, but with very limited funds. The second was a space vehicle, later named Orion. Around 1955 Everett and I wrote a paper about a space vehicle propelled by successive explosions of small nuclear charges..

When it was decided to do something in earnest about Project Rover, Wiesner named a Presidential Committee to look into the matter. I was one of its members... The committee wrote a report which by faint praise, essentially condemned Project Rover to a de facto death by proposing to make it a purely theoretical study without funds for experimental work or any investment in construction. The physicist Bernd Matthias was the only member of the committee who joined me in writing a dissenting opinion.

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At the same time, I was continuing my own work. After Fermi's death Pasta and I decided to continue exploratory heuristic experimental work on electronic computers in mathematical and physical problems ...

The problem of clusters of stars was I think the first study of this nature using computers. We took a great number of mass points representing stars in a cluster. The idea was to see what would happen in the long-range time scale of thousands of years to the spherical-looking cluster whose initial conditions imitated the actual motions of such stars.

Edward Lasker

(International Chess Master) and Stan, late sixties

While such astrophysical calculations were going on, I began in an amateurish way to work on some questions of biology. After reading about the new discoveries in molecular biology which were coming fast, I became curious about a conceptual role which mathematical ideas could play in biology.

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During the Los Alamos years I frequently took time off to return to academic life and around 1965 I started visiting the University of Colorado on a more regular basis... In 1967 I decided to retire from Los Alamos and accept a professorship in Boulder ... The University of Colorado was flourishing ... and the mathematics department experienced an explosive growth in size and quality. Besides Boulder was sufficiently close to Los Alamos ... so I could continue as a consultant and visit frequently... The mathematics department was acquiring excellent researchers... [among them] a younger, brilliant Pole, Jan Mycielski, a student of Steinhaus, whom I invited to accept a professorship.

In 1967 ... Mark Kac and I were invited to write a long article [for Britannica Perspectives,]... a semi-popular presentation of modern ideas and perspectives of... the great concepts of mathematics ... Since then it has appeared separately under the title Mathematics and Logic.

Lae Alamos Science Special Issue 1987

Mark Kac had also studied in Lwów, but since he was several years younger than I (and I had left when only twenty-six myself), I knew him then only slightly... After the war he visited Los Alamos, and we developed our scientific collaboration and friendship ... Mark is one of the very few mathematicians who possess a tremendous sense of what the real applications of pure mathematics are and can be ... He was one of Steinhaus's best students.

[After I retired from the University of Colorado, we] sold our Boulder house and bought another one in Santa Fe, which has become our base. From Santa Fe I commute three or four times a week to the Los Alamos Laboratory. Its superb scientific library and computing facilities allow me to continue working ... Dan Mauldin, a professor at North Texas State University [and I] are now collaborating on a collection of new unsolved problems. This book will have a different emphasis from that of my Collection of Mathematical Problems. The new collection will deal more with mathematical ideas connected to theoretical physics and biological schemata.

In the short span of my life great changes have taken place in the sciences... Sometimes I feel that a more rational explanation for all that has happened during my lifetime is that I am still only thirteen years old, reading Jules Verne or H. G. Wells, and have fallen asleep.

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It is still an unending source of surprise for me to see how a few scribbles on a blackboard or on a sheet of paper could change the course of human affairs. I became involved in the work on the atomic bomb, then in the work on the hydrogen bomb, but most of my life has been spent in more theoretical realms.

21

Vita

BOULDER
SANTA FE

1974-84 Winter trimesters: Graduate Research Professor, University of Florida

1975 Retires from University of Colorado

1979-84 Visiting Professor of Biomathematics, University of Colorado Medical School

1980-84 Visiting Professor at Neurosciences Institute of Rockefeller University

1982-83 Fall semester: Visiting Professor at University of California, Davis

1984 Dies in Santa Fe on May 13

At the time of his death, Stanislaw M. Ulam was an elected Fellow of the American Academy of Arts and Sciences and an elected member of the National Academy of Sciences and the American Philosophical Society. He sat on the Board of Governors and the Scientific Advisory Committee of the Weizmann Institute of Science (Rehovot, Israel) and the Board of the Jurzykowski Foundation (New York, New York). He belonged to the Polish Mathematical Society, the American Mathematical Society, the American Physical Society, and the American Association for the Advancement of Science.

He held honorary degrees from the University of New Mexico, the University of Pittsburgh, and the University of Wisconsin and was recipient of the Sierpinski Medal, the Heritage Award, and the Polish Millenium Prize.

He had been a member and/or chairman of the Committee on Innovations of the National Academy of Sciences, the Committee on Applications of Mathematics of the National Research Council, the Visiting Commmittee for Mathematics and the Visiting Committee for Applied Mathematics of Harvard University, the Gibbs Lecture Committee of the American Mathematical Society, and the Mathematics Research Committee of the Mathematical Association of America.

He had served as consultant to President Kennedy's Science Advisory Committee, Air Force General Twining's Space Research Committee, IBM Corporation, General Atomic Corporation, North American Aviation Corporation, Hycon Corporation, and other organizations.

Building in Lwów in which the Ulam family resided, photographed after the war

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O

ne morning in 1946 in Los Angeles, Stan Ulam, a newly appointed professor at the University of Southern California, awoke to find himself unable to speak. A few hours later he underwent an emergency operation. His skull was sawed open and his brain tissue sprayed with newly discovered antibiotics. The diagnosis-encephalitis, an inflammation. of the brain. After a short convalescence he managed to recover, apparently unscathed.

In time, however, some changes in his personality became obvious to those who knew him. Paul Stein, one of his collaborators at Los Alamos, remarked that, while before his operation Stan had been a meticulous dresser, a dandy of sorts, afterwards he became visibly

by Gian-Carlo Rota

careless in the details of his attire, even
though his clothing was still expensively
chosen.

When I met him, many years after
the event, I could not help noticing that
his trains of thought were unusual, even
for a mathematician. In conversation he
was livelier and wittier than anyone I
had ever met, and his ideas, which he
spouted out at odd intervals, were fasci-
nating beyond anything I have witnessed
before or since. However, he seemed to
studiously avoid going into any details.
He would dwell on a given subject no
longer than a few minutes, then impa-
tiently move on to something entirely
unrelated.

Out of curiosity I asked Oxtoby,
Stan's collaborator in the thirties, about
their working habits before his oper-
ation. Surprisingly, Oxtoby described

how at Harvard they would sit for hours
on end, day after day, in front of the
blackboard. Since I met him, Stan never
did anything of the sort. He would per-
form a calculation, even the simplest,
only when he had absolutely no other
way out. I remember once watching
him at the blackboard trying to solve
a quadratic equation. He furrowed his
brow in rapt absorption, while scribbling
formulas in his tiny handwriting. When
he finally got the answer, he turned
around and said with relief, “I feel I
have done my work for the day."

The Germans have aptly called Sitzfleisch the ability to spend endless hours at a desk doing gruesome work. Sitzfleisch is considered by mathematicians to be a better gauge of success than any of the attractive definitions of tal

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