Adventures of a Mathematician

Postscript to Adventures by Françoise Ulam

Françoise Ulam

When Scribner’s urged Stan to write his memoirs he agreed to give it a try and in 1972 he took a sabbatical from the University of Colorado to devote himself to the task. For a year, while we traveled to the East and to Paris, he dictated reminiscences which I tape-recorded and transcribed. Back in Boulder, Stan returned to his university duties and I edited and assembled the giant jigsaw puzzle the transcripts had become, until there was a draft for him to look at and add a few connecting sentences here and there. The book appeared in 1976 under the title Adventures of a Mathematician. (Stan wanted to change the title to ’’Misadventures,” but on that he was overruled.)

“Adventures” is Stan, pure Stan, all Stan — even though he hardly wrote a line of it — for I scrupulously refrained from injecting myself into it. It is about his professional life and the scientific times he lived in. Its tone is personal but not intimate, factual more than analytical. In the spirit of the book, I want to complement his story with a few impressions, perceptions, and memories of my own, to weave along a loose thread of time my gradual discovery of the man he was and the life into which he transported me.

Stan and I met in Cambridge at the home of a mutual Polish friend. I was a French exchange student of literature at Mount Holyoke College; he was already a rather well-known young Polish mathematician and a lecturer at Harvard. In the college style of the times, it was “Holyoke graduate student meets Harvard professor.” But the year was 1939 and World War II was engulfing Europe. Castaways from the ruins of the Old World, we were brought together on the shores of the New. I knew at once that he was someone quite out of the ordinary, and he became the focus of my life. In return he gave me a front row seat to his all-absorbing world of science and scientists. And what a world that turned out to be. We were married in 1941 in Wisconsin and we lived in New Mexico the better part of our lives.

What had first attracted me to Stan was that, like all educated Poles, he was a Francophile and spoke a fluent French rolling with Slavic r’s, and that even during these anxious times in the darkest days of the war, he seemed to have absolute self-confidence and unflinching optimism. He was sure the Allies would win, though the question of when remained. I was also dazzled by the breadth of his culture and his encyclopedic memory.

With his unusual looks and magnetic green eyes, he always seemed to stand out in a crowd. I remember a party years later when Georgia O’Keefe pointed an imperious finger in his direction and exclaimed, “Who is that man?”

“That man” was a maverick, a study in contrasts and contradictions, a proud Pole who did not kowtow to anyone and an assimilated, agnostic Jew very conscious of his ethnicity. This translated later into his becoming very involved with a Polish-American cultural organization, the Alfred Jurzykowski Foundation, and with the Israeli Weizmann Institute of Science, the only boards he ever enjoyed actively serving on. And he was also, like many Slavs, improvident and unorganized. He readily left all practical matters to me in the management of our daily life. He loved to be with people and entertain them with his quick wit and inexhaustible fund of Jewish jokes, but he was also insular and insulated, at times sensitive or insensitive, perceptive or imperceptive of others. Someone once jokingly told him that he suffered from “le complexe du roi” with his disregard of the rules of ordinary life. Last but not least, he had the build of an athlete and healthy, earthy appetites. He also claimed he did not know the meaning of the word tired, and although he enjoyed tennis and had played soccer in Poland, he liked to attribute his good health to his disdain for exercise. What he exercised all the time was his mind.

For above all he was a mathematician, and he immediately thrust me among his kind. Early on I noticed that mathematicians live in a world inaccessible to common mortals, and even to each other when they belong to different disciplines. They are a special breed possessed by an intense cerebral life; simultaneously living on two distinct levels of consciousness, they are at once present and able to carry on normally and yet are immersed in the abstractions that form the core of their lives. They are quite different from the community of physicists we were soon to encounter, who seemed much closer to the real world. Stan had a special look in his eyes when pursuing a mathematical-thought. Yet no matter how absorbed he was, he never seemed to mind being interrupted.

Singularly modest about his scientific accomplishments, he was nevertheless keenly aware of his own qualities, which he described as “a blend of memory and imagination, the simple ingredients of mathematical or scientific talent.” (Tempered by a healthy dose of common sense, I might add.) He also seemed to prefer to let his imagination roam than to do elaborate technical calculations. “There are so few of us, and so many of them,” he said. His old professor and friend, Steinhaus, told me “C’est l’homme au monde qui pose le mieux les problèmes.” (He is the man in the world who knows best how to create and formulate problems.) His pretense that he never strained himself with hard work was a pose. His seemingly “effortless luck” and the “brilliant thoughts’’ he was known for did not appear out of the blue. From his dictation which I took in shorthand in the past, I saw how tenaciously he returned to the same points over and over again, each time probing a little further.

He also seemed to prefer to embark on new pursuits whenever they occurred to him than to see anything through, whether it was a movie he enjoyed or a scientific point, I asked him about this once and he replied, “I never like to see or do anything to the end for fear the quality will waver and I will be disappointed.” He turned this into a disdain for putting his work in the more formal and final printed form. For that he relied on collaborators or “thought processors” as I called them, happy to let them help at their various levels of expertise. To David Hawkins it meant “Stan would dramatize a topic, suggest a pathway, and then I would do the work.” Everett said, “Stan tells me what to do and I do it.” At my level, and increasingly after retirement when he no longer had regular secretaries, it meant serving as his “live word processor.’’

Marc Kac, who had known him when they were students in Poland, told me that “there was not a single mathematician who reminded [him] of Stan,” for Stan, besides having an “enormous reservoir of orginality,” also “depended more than anyone else [he] knew on the intellectual stimulation that comes from people, even though in 99.999 % of the cases he was the giver.” He said that “to Stan mathematics was a much wider subject than to most of us,” that he “could see the relevance of mathematical ideas to things which perhaps one would not call mathematics,” and that he was “the first and probably the only one who really experimented with machines to discover interesting facts, to stimulate conjectures.”

He explained that since Stan came from a “culture based on leisure and discourse,” from a “peculiar kind of Polish existence where you were in cafes all hours of the day or night drawing diagrams on small pieces of paper,” he was not very well suited for the American system of “timetables and so many hours of teaching.” And indeed Stan hardly ever conformed to this more structured way of life. He never became a nine-to-five man, not even at Los Alamos. But despite a certain nostalgia for his Polish past, Stan on the whole thrived in this country. He loved its openness, dynamism, and scientific audacity.

When in the fall of 1943 John von Neumann recruited him to join the Manhattan Project, Stan’s life took an abrupt turn. “All at once Stan was connected not only with weapons but with that reservoir of the smartest people in the world. That excited his imagination and he would also excite theirs,” Kac said. At Los Alamos, his friendship with Johnny and the force of his personality soon propelled us among the most interesting physicists. Stan relished the work at the frontiers of physics and the intensity of the exchanges between the members of this isolated community. They reminded him of Lwów. And the symbiosis proved very fortunate, for Stan had never considered himself only a mathematician. From the first he loved New Mexico’s vistas and the quality of its air. He liked to say it was like champagne. In retrospect I think that we were all a little light-headed from it and from the altitude.

As for me, wartime Los Alamos, perched as it was on its forested mesa, was a strange combination of Swiss village, construction site, and army post with PX and commissary where the sun always seemed to shine whatever the season. Clustered around handsome log buildings and built along the contour of the land, it was essentially Oppenheimer’s creation: a sort of Magic Mountain. Life was rustic and egalitarian. The men worked side by side day and night behind fenced areas. The wives mostly kept house and had babies born in P.O. Box 1663, Santa Fe, New Mexico, including our daughter, Claire. These babies were then raised with the help of Hispanic women who spoke little English and Indian maids in native dress silently gliding on deerskin moccassins. The military were present to help the strange, international group of civilians Oppenheimer had gathered there.

When the war ended and it seemed that Los Alamos would fold, we promptly went to the University of Southern California in Los Angeles where Stan suffered the traumatic illness he describes. Convalescing at the beach with his head still swathed in bandages, he soon showed that his brush with death had left him unscathed. Besides working on an obituary of Banach and talking a little mathematics with Erdös, who was visiting, he passed the time standing by a narrow table, lining up solitaire after solitaire (Canfields). This exercise led to the devising of the Monte Carlo method for computing neutron multiplication.

As his strength returned, rather than remain in the backwaters of academe, Stan opted for a prompt return to Los Alamos, which was not closing its doors after all. From the late forties to the early sixties the nucleus of the town expanded to other mesas and Los Alamos slowly evolved into an almost normal community complete with tract houses, stores, and churches. But the countryside and the climate remained, and its scientists were still at the forefront of the world’s efforts to adapt to the new atomic age. It was still a gathering place for the best the country had to offer, who were still blazing trails at the frontiers of science. The cold war and the scientific and political crises that surrounded the development of the H-bomb became part of our daily lives, and we continued to live in a whirl of activity at the lab and at home. Stan had no moral qualms about working on weapons. He was interested in the scientific aspects of the research and did not see anything wrong in that.

In the same sense as the wartime A-Bomb had been Oppenheimer’s doing, the postware H-bomb was essentially Teller’s, except that Stan had to show him how to go about it, and Los Alamos had to build it without him.

And here I have a footnote to add to Stan’s description of the events that led to its building. Stan was acquainted with the fusion proposals, for during the war he had been nominally in Teller’s group. Gradually he developed a hunch that the Super Teller envisaged was not very practical, and when in 1949 Truman ordered the development of that superpowerful weapon, he set out to verify his hunch while the electronic machines were being built. First, he worked just with Everett, then, with an added bevy of young women who had been hastily recruited to grind manually on electric calculators the operations now routinely performed by computers. I became one of them, even though I understood nothing of the mathematics involved. We bore the glamorous name of “data analysts.” This job allowed me inside T-Division, at the time the inner sanctum of the lab, where, as a friend later put, I could “get the smell of the hive.”

I was well placed to watch how personally Teller took the fact that Stan and Everett were the first to blow the whistle with their crude calculations. Every day Stan would come into the office, look at our computations, and come back with new “guestimates,” while Teller objected loudly and cajoled every one around into disbelieving the results. What should have been the common examination of difficult problems became an unpleasant confrontation. More agreeable was the midmorning coffee hour where the great and not so great — including this “data analyst” — gathered to discuss scientific questions that came to their minds, the “state of the universe,” or where to hike on Sunday, one of Fermi’s favorite topics.

The technical and political debates were raging when Stan, mulling over the problems, suddenly came upon a totally new and intriguing approach. Engraved on my memory is the day when I found him at noon staring intensely out of a window in our living room with a very strange expression on his face. Peering unseeing into the garden, he said: “I found a way to make it work.” “What work?” I asked. “The Super” he replied. ’’It is a totally different scheme, and it will change the course of history.”

I, who had rejoiced that the “Super” had not seemed feasible, was appalled by this news, and anxiously asked what he intended to do. He replied that he “would have to tell Edward.” Fearing the Teller might pounce on him again, I ventured that maybe he ought to test his idea on Mark or Bradbury first. He did, but went to Teller the next day just the same.

Teller saw rapidly where the new avenue could lead and they hastened to write their well-known joint report. It is in two parts, Stan told me, because Teller was adding — in Stan’s words — “a parallel scheme” of his own which altered Stan’s original suggestion. My impression is that from then on Teller pushed Stan aside and refused to deal with him any longer. He never met or talked with Stan meaningfully ever again.

Stan was, I felt, more wounded than he knew by this unfriendly rejection, although I never heard him express ill feelings towards Teller. (He rather pitied him instead.) Secure in his own mind that his input had been useful, he withdrew. At that moment in the fall of 1951 when the lab’s collective mind was on carrying out the monumental task of building and testing the weapon (as well as on the struggle against Teller’s attacks), we escaped to Harvard for a few months of well-deserved change. From then on Stan steadfastly continued to avoid being drawn into the political turmoil, except for a brief testimony in Congress in favor of the Test Ban Treaty.

After the Harvard visit we returned once more to Los Alamos where the management, in its wisdom, provided Stan with more freedom than did the academic world. Stan then gradually disengaged himself from weapons to play with the then new, miraculous tool of electornic computing that had been built at the lab, the MANIAC. Johnny’s brainchild, it was the first completely electronic machine with a built-in general operations program. This Model-T of contemporary computers enabled Stan to apply his skills in pure mathematics to other fields of science and experiment, years ahead of the times, with patterns of growth, complexity, nonlinearity, chaos. His research was for the most part written up in obscure Los Alamos reports. Few people were aware of what he was doing outside of their own specialty. Remarkably he did not seem to care. And partly because of the MANIAC’s easy accessibility, for the rest of his life Stan remained connected with the lab. No wonder Seinhaus nicknamed us “Los Ulamos” when he came to visit us in the sixties.

Our life, however, was not all work and no play. We traveled on extended leaves to academic communities east and west, and to France for yearly vacations. We lived simply but comfortably on “bathtub row” (so-called because during the war it had contained the only bathtubs on the post), raising Claire, our child. Stan would show the neighborhood children the craters on the moon with his telescope, or point at Sputnik tracing its orbit through the sky, or play a game of chess with a visiting chess master. We belonged to a group that took visitors to the banks of the Rio Grande for candlelit dinners at Edith Warner’s famed adobe house, which had no electricty or running water. The meals were served by her long-braided Indian companion, Tilano. The contrast of their timeless Indian life with the twentieth-century reality on the Hill offered a great moment of relaxation.

Our house was a continual open house. The parties we gave for the von Neumanns, Gamows, Fermis, Fisk, Rabi, and many others were lively. I had a knack for mixing and matching people, kept a good table, and Stan was always a great catalyst. With frequent trips to congresses and meetings in Russia, Britain, Israel, or Switzerland, our life was that of today’s scientific jet-set.

When I voiced reservations about still living at the heart of thermonuclear work, Stan would reassure me that barring accidents, the H-bomb rendered war impossible. He also agreed, however, that there were too many bombs already, and he “did not believe that Russia would invade Western Europe, one of the supposed reasons for super-rearmament.” (In the light of today’s happenings, he was right as usual.)

This was a time when the question of science and morality was taking on new importance. When asked about the ethics of science, Stan was firm on the necessity of pursuing science for inquiry’s sake, regardless of the consequences. What would Archimedes and Newton have done, he argued, if they had worried about the consequences of their thoughts? Without calculus no modern science could have developed. Admittedly things had changed since the days when Poincaré could say that morality and science were not in conflict, for both aimed at the betterment of mankind. The release of nuclear energy and the possibility of gene manipulation had enormously complicated the problem. But he was quick to point out the useful aspects of nuclear energy and the marvels of biological engineering, if used wisely, and to put the responsibility back in the public’s court for deciding how to use them. He also insisted that it was the scientists’ duty to inform the public of their discoveries.

With the Cold War waning and the Bradbury era ending, the purpose of Los Alamos was becoming dimmer, and the lab was settling into routine. It was also entering periods top-heavy with bureaucratic administrators. Stan, detached from its inner workings, found himself charting a lonelier course, and was outgrowing “government science,” as he called it. He therefore embarked on a renewed involvement with the teaching profession.

He had always been noted for his lecturing style. In the Harvard days the students had named him one of the most stimulating math professors. I watched him once on the lecture circuit give one of his typical Ulamian talks where, hopping from topic to topic, he exposed a group of math majors to a glimpse of the world of science they could not fathom from their more prosaic encounters: a few rods about set theory; anecdotes of his youth when he developed an interest in math; sketches of Los Alamos, of von Neumann; remarks about the bomb at the root of much present-day technology; passing thoughts about Gödel and the importance of his undecidability proofs. He walked about, made a great display of glancing at his watch, always finding the mot juste in an informal stream of consciousness, never saying anything trite, and sowing seeds every so lightly in his listeners’ minds.

With Claire grown and out of the nest, Stan officially retired from Los Alamos in 1967 and launched a retirement career that kept him busier than ever with new university duties, invitations, meetings, lectures, and extended stays in Santa Fe, where we had bought a house.

At the University of Colorado his goal had been to awaken the academic mathematical community to the great potential of the computer age and to “what physics and biology could do for mathematics,” his paraphrase of the famous Kennedy statement. In Boulder he wore three hats: Head of the mathematics department (with an assistant chairman to run the daily departmental affairs); professor in the computing center; and professor in the biology department of the medical school where he lectured occasionally on the speculations and mathematical explorations of neurophysiology and the workings of the brain, which had replaced the attention he had devoted earlier to physics and astrophysics.

In his academic spare time at our Santa Fe pied-à-tierre he continued to use the admirable Los Alamos computing facilities as a dollar-a-year consultant. But he was sorely missing those of his peers who had died before their time, and beginning to feel removed from the younger generation of scientists who arrived during our absences. To counter that, when he retired from Boulder he established a loose connection with the University of Florida as Visiting Graduate Research Professor of Mathematics which remained in effect to the end. In Gainesville he concentrated on giving colloquia and seminars on new mathematical problems he very much wanted to assemble into a new volume of problems. The book was beginning to take shape when he died. Mauldin, his collaborator on the project, has since published an abbreviated version in a mathematical journal.

Invitations to lecture were growing exponentially. If he had accepted them all he would have become like Erdös, an itinerant performer. Claiming he was “nonbiodegradable,” in the first six months of 1978, in addition to extended stays in Santa Fe and Gainesville, Stan gave talks in Paris, Montreal, Vancouver, New York, Washington, Denver, Santa Barbara, Paris again, and Warsaw, priding himself that he never exactly repeated his talks. On the road he experienced a charge of adrenalin. A certain letdown came after the return home: catching up with mail and other obligations, fatigue, increasingly frequent digestive upsets. Towards the very end the strain was beginning to tell.

Then, on May 13, 1984, at the age of 75, while, in Erdös’ words, “still able to prove and conjecture,” on a day he had contentedly returned home from London, Stan had an unexpected seizure, collapsed, and died. This spared him the disintegration he feared, and much as I still miss him, it also spared me the distress of watching him grow old. In his usual way of making light of serious matters to render them more palatable, he used to say “the best way to die is of a sudden heart attack or to be shot by a jealous husband.” He had the good fortune of succombing to the first, though I believe he might have preferred the second.

In a brief memorial eulogy David Hawkins said: “People who do not much live cannot much die. Stan lived very much. Those who live richly have many linkages to the world… Their lives are woven into the world’s fabric, its lattice of associations. When they leave there is a big hole in the lattice, a tear in the fabric. These holes or tears remain… and that simple fact is the human source of all our concerns for immortality.”

Françoise Ulam

Santa Fe, 1990