1927 Matriculates from gymnasium. Enters Lwów Polytechnic Institute

Father (left) and uncle Szymon seeing Stan and his young brother, Adam, off for the last time at Gdynia, Poland, 1939

My father, Jozef Ulam, was a lawyer. He was born in Lwów, Poland, in 1877. At the time of his birth the city was the capital of the province of Galicia, part of the Austro-Hungarian Empire. When I was born in 1909 this was still true ... My mother, Anna Auerbach, was born in Stryj, a small town some sixty miles south of Lwów, near the Carpathian Mountains. Her father was an industrialist who dealt in steel and represented factories in Galicia and Hungary.

In November of [1918] the Ukrainians besieged the city... Our house was in a relatively safe part of town, even though occasional artillery shells struck nearby... Many of our relatives came to stay with us... some thirty of them, half being children. There were not nearly enough beds, of course, and I remember people sleeping everywhere on rolled rugs on the floor ... Strangely enough, my memories of these days are of the fun I had playing, hiding, learning card games with the children for the two weeks before the siege was lifted... For children wartime memories are not always traumatic.

At the age of ten in 1919 I passed the entrance examination to the gymnasium. This was a secondary school patterned after the German gymnasia and the French lycées. Instruction usually took eight years. I was an A student, except in penmanship and drawing, but did not study much.

I had mathematical curiosity very early. My father had in his library a wonderful series of German paperback books-Reklam, they were called. One was Euler's Algebra. I looked at it when I was perhaps ten or eleven, and it gave me a mysterious feeling. The symbols looked like magic signs; I wondered whether one day I could understand them.

In high school, I was stimulated by ... the problem of the existence of odd perfect numbers. An integer is perfect if it is equal to the sum of all its divisors including one but not itself. For instance: 61+2+3 is perfect. So is 28 = 1+2+4+7+ 14. You may ask: does there exist a perfect number that is odd? The answer is unknown to this day.

Poincaré molded portions of my scientific thinking. Reading one of his books today demonstrates how many wonderful truths [remain], although everything in mathematics has changed almost beyond recognition and in physics perhaps even more so. I admired Steinhaus's book almost as much, for it gave many examples of actual mathematical problems.

In 1927 I passed my three-day matriculation examinations and a period of indecision began. The choice of a future career was not easy. My father, who had wanted me to become a lawyer so I could take over his large practice, now recognized that my inclinations lay in other directions ... My parents urged me to become an engineer, and so I applied for admission at the Lwów Polytechnic Institute as a student of either mechanical or electrical engineering.

Around [that time] so much was written in newspapers and magazines about the theory of relativity that I decided to find out what it was all about... This interest became known among friends of my father, who remarked that I "understood" the theory of relativity... This gave me a reputation I felt I had to maintain, even though I knew that I did not genuinely understand any of the details. Nevertheless, this was the beginning of my reputation as a "bright child."

Vita

POLISH YEARS

1928 Writes his first paper, published in Fundamenta Mathematicae in 1929

1931 Attends mathematical congress in Wilno

1932 M.A. from Polytechnic Institute

1933 D.Sc. from Polytechnic Institute

In the fall of 1927 I began attending lectures at the Polytechnic Institute in the Department of General Studies, because the quota of Electrical Engineering already was full. The level of the instruction was obviously higher than that at high school, but having read Poincaré and some special mathematical treatises, I naively expected every lecture to be a masterpiece of style and exposition. Of course, I was disappointed.

Soon I could answer some of the more difficult questions in [Kuratowski's] set theory course, and I began to pose other problems. Right from the start I appreciated Kuratowski's patience and generosity in spending so much time with a novice. Several times a week I would accompany him to his apartment at lunch time, a walk of about twenty minutes, during which I asked innumerable mathematical questions ... Between classes, I would sit in the offices of some of the mathematics instructors. At that time I was perhaps more eager than at any other time in my life to do mathematics to the exclusion of almost any other activity.

At the beginning of the second semester of my freshman year, Kuratowski told me about a problem in set theory that involved transformations of sets. It was connected with a well-known theorem of Bernstein: if 2A 2B, then A = B, in the arithmetic sense of infinite cardinals. This was the first problem on which I really spent arduous hours of thinking. I thought about it in a way which now seems mysterious to me, not consciously or explicitly knowing what I was aiming at. So immersed in some aspects was I, that I did not have a conscious overall view. Nevertheless, I managed to show by means of a construction how to solve the problem, devising a method of representing by graphs the decomposition of sets

and the corresponding transformations. Unbelievably, at the time I thought I had invented the very idea of graphs.

Joint mathematics-physics meeting,

Lwów, 1930. Stan is number 10

Kuratowski and

a photo of Banach, circa 1968

It was Mazur (along with Kuratowski and Banach) who introduced me to certain large phases of mathematical thinking and approaches. From him I learned much about the attitudes and psychology of research. Sometimes we would sit for hours in a coffee house. He would write just one symbol or a line like y = f(x) on a piece of paper, or on the marble table top. We would both stare at it as various thoughts were suggested and discussed. These symbols in front of us were like a crystal ball to help us focus our concentration.

Beginning with the third year of studies, most of my mathematical work was really started in conversations with Mazur and Banach. And according to Banach some of my own contributions were characterized by a certain "strangeness" in the formulation of problems and in the outline of possible proofs. As he told me once some years later, he was surprised how often these "strange" approaches really worked.

He [Banach] enjoyed long mathematical discussions with friends and students. I recall a session with Mazur and Banach at the Scottish Café which lasted seventeen hours without interruption except for meals.

These long sessions in the cafés were probably unique. Collaboration was on a scale and with an intensity I have never seen surpassed, equaled or approximated anywhere-except perhaps at Los Alamos during the war years... Needless to say such mathematical discussions were interspersed with a great deal of talk about science in general (especially physics and astronomy), university gossip, politics, the state of affairs in Poland; or to use one of John von Neumann's favorite expressions, the "rest of the universe." The shadow of coming events, of Hitler's rise in Germany and the premonition of a world war loomed ominously.

The second big congress I attended [of mathematicians from the Slavic countries] was held in Wilno in 1931... At the congress I gave a talk about the results obtained with Mazur on geometrical isometric transformations of Banach spaces, demonstrating that they are linear. Some of the additional remarks we made at the time are still unpublished. In general, the Lwów mathematicians were on the whole somewhat reluctant to publish. Was it a sort of pose or a psychological block?

If I had to name one quality which characterized the development of this school, made up of the mathematicians from the University [of Lwów] and the Polytechnic Institute, I would say that it was their preoccupation with the heart of the matter that forms mathematics. On a set theoretical and axiomatic basis we examined the nature of a general space, the general meaning of continuity, general sets of points in Euclidean space, general functions of real variables, a general study of the spaces of functions, a general idea of the notions of length, area and volume, that is to say, the concept of measure and the formulation of what should be called probability.

In 1932 I was invited to give a short communication at the International Mathematical Congress in Zürich. This was the first big international meeting I attended, and I felt very proud to have been invited. In contrast to some of the Polish mathematicians I knew, who were terribly impressed by western science, I had confidence in the equal value of Polish mathematics. Actually this confidence extended to my own work. Von Neumann once told my wife, Françoise, that he had never met anyone with as much selfconfidence adding that perhaps it was somewhat justified.

By 1934 I had become a mathematician rather than an electrical engineer. It was not so much that I was doing mathematics, but rather that mathematics had taken possession of me... At twenty-five, I had established some results in measure theory which soon became well known. These solved certain set theoretical problems attacked earlier by Hausdorff, Banach, Kuratowski, and others. These measure problems again became significant years later in connection with the work of Gödel and more recently with that of Paul Cohen. I was also working in topology, group theory, and probability theory. From the beginning I did not become too specialized. Although I was doing a lot of mathematics, I never really considered myself as only a mathematician. This may be one reason why in later life I became involved in other sciences.

[Nevertheless] ever since I started learning mathematics I would say that I have spentregardless of any other activity-on the average two to three hours a day thinking and two to three hours reading or conversing about mathematics.

Vita

PRINCETON
HARVARD

WISCONSIN

1934 Postdoctoral travels and studies in Vienna, Zürich, Paris, and Cambridge (England)

1935 Scottish Book originates

Returns to Poland. Receives letter of invitation to Institute for Advanced Study in Princeton

December: Sails to America

1936-39 Academic years with Harvard Society of Fellows. Summers at home in Poland

1939 Leaves home for the last time in the fall of 1939, accompanied by his young brother, Adam

1939-40 Lecturer at Harvard

1940-41 Instructor at University of Wisconsin. Meets C. J. Everett. Works with him on ordered groups and projective algebras

Oxtoby and Stan at Harvard, circa 1936

In 1934, the international situation was becoming ominous. Hitler had come to power in Germany. His influence was felt indirectly in Poland. There were increasing displays of inflamed nationalism ... and anti-Semitic demonstrations... For years my uncle Karol Auerbach had been telling me: "Learn foreign languages!" Another uncle, Michael Ulam, an architect, urged me to try a career abroad. For myself, unconscious as I was of the realities of the situation in Europe, I was prompted to arrange a longish trip abroad... to meet other mathematicians... and in my extreme self-confidence, try to impress the world with some new results. My parents were willing to finance the trip.

It was only toward the end of 1934 that I entered into correspondence with von Neumann. He was then in the United States, a very young professor at the Institute for Advanced Study in Princeton. I wrote him about some problems in measure theory. He had heard about me from Bochner, and in his reply he invited me to come to Princeton for a few months, saying that the Insititue could offer me a $300 stipend. I met him [in Warsaw] shortly after my return from England ... Von Neumann appeared quite young to me, although he was ... some five or six years older than I ... At once I found him congenial. His habit of intermingling funny remarks, jokes, and paradoxical anecdotes or observations of people into his conversation, made him far from remote or forbidding.

One of the luckiest accidents of my life happened the day G. D. Birkhoff came to tea at von Neumann's house while I was visiting there ... We talked and, after some discussion of mathematical problems, he turned to me and said, "There is an organization at Harvard called the Society of Fellows. It has a vacancy. There is about one chance in four that if you were interested and applied you might receive this appointment."

I came to the Society of Fellows during its first few years of existence... I was given a tworoom suite in Adams House, next door to another new fellow in mathematics by the name of John Oxtoby... He was interested in some of the same mathematics I was: in set theoretical topology, analysis, and real function theory. Right off, we started to discuss problems concerning the idea of "category" of sets. "Category" is a notion in a way parallel to but less quantitative than the measure of sets We quickly established some new results, and the fruits of our conversations

were published as two notes in Fundamenta. We followed this with an ambitious attack on the problem of the existence of ergodic transformations. The ideas and definitions connected with this had been initiated in the nineteenth century by Boltzmann.

1941 Becomes American citizen. Tries to volunteer in the U.S. Air Force

1941-43 Assistant Professor at University of

Wisconsin

[At the Institute] I went to lectures and seminars, heard Morse, Veblen, Alexander, Einstein, and others, but was surprised how little people talked to each other compared to the endless hours in the coffee houses in Lwów ... There was another way in which the Princeton atmosphere was entirely different from what I expected: it was fast becoming a way station for displaced European scientists. In addition, these were still depression days and the situation in universities in general and in mathematics in particular was very bad.

Birkhoff, in his trail-breaking papers and in his book on dynamical systems, had defined the notion of "transitivity." Oxtoby and I worked on the completion to the existence of limits in the ergodic theorem itself ... We wanted to show that on every manifold (a space representing the possible states of a dynamical system)—the kind used in statistical mechanics-such ergodic behavior is the rule ... It took us more than two years to break through and to finish a long paper, which appeared in The Annals of Mathematics in 1941 and which I consider one of the more important results that I had a part in.

While I was at Harvard, Johnny came to see me a few times, and I invited him to dinner at the Society of Fellows. We would also take automobile drives and trips together during which we discussed everything from mathematics to literature and talked without interruption while still paying attention to our surroundings. Johnny liked this kind of travel very much.

Each summer between 1936 and 1939, I returned to Poland for a full three months. The first time, after only a few months' stay in America, I was surprised that street cars ran, electricity and telephones worked. I had become imbued with the idea of America's absolute technological superiority and unique "know-how." My main emotional reactions were, of course, related to reunion with my family and friends, and the familiar scenes of Lwów, followed by a longing to return to the free and hopeful "open-ended" conditions of life in America.

I had to go to the American consulate in Warsaw each summer I was in Poland to apply for a new visitor's visa in order to return to the United States. Finally, the consul said to me, "Instead of coming here every summer for a new visa, why don't you get an immigration visa?" It was lucky that I did, for just a few months later these became almost impossible to obtain.

[My brother] Adam and I were staying in a hotel on Columbus Circle [in New York] ... It must have been around one or two in the morn

ing when the telephone rang.. my friend the topologist Witold Hurewicz began "Warsaw has been bombed, the war has begun." That is how I learned about the beginning of World War II... Adam was asleep; I did not wake him. There would be time to tell him the news in the morning. Our father and sister were in Poland, so were many other relatives. At that moment, I suddenly felt as if a curtain had fallen on my past life... There has been a different color and meaning to everything ever since.

Birkhoff helped me to secure the job [at the University of Wisconsin] ... Almost at once I met congenial, intelligent people not only in mathematics and science, but also in the humanities and arts ... So I found Madison not at all the intellectual desert I had feared it would be ... I was given a light teaching load... But the very expression ... implied physical effort and fatigue-two things I have always been afraid of, lest they interfere with my own thinking and research.

Something else happened to make Madison most important to me. It was there that I married a French girl, who was an exchange student at Mount Holyoke College and whom I had met in Cambridge, Françoise Aron. Marriage, of course, changed my way of life, greatly influencing my daily mode of work, my outlook on the world, and my plans for the future.

Claire, at 14 months, and Françoise, Los Angeles, 1945

It was in Madison that I met C. J. Everett ... [He] and I hit it off immediately. As a young man he was already eccentric, original, with an exquisite sense of humor, wry, concise, and caustic in his observations. He was totally devoted to mathematics... I found in him much that resembled my friend Mazur in Poland, the same kind of epigrammatic comments and jokes... We collaborated on difficult problems of "order"-the idea of order for elements in a group. In our mathematical conversations, as always, I was the optimist, and had some general, sometimes only vague ideas. He supplied the rigor, the ingenuities in the details of the proof, and the final constructions. Everett exhibited a trait of mind whose effects are, so to speak, non-additive: persistence in thinking. Thinking continuously ... for an hour, is at least for me and I think for many mathematicians-more effective than doing it in two half-hour periods. It is like climbing a slippery slope. If one stops, one tends to slide back. Both Everett and Erdös have this characteristic of long-distance stamina.

I was asked to run the mathematics colloquium, which took place every two weeks ... The colloquium was run differently from what I had known in Poland, where speakers gave tenor twenty-minute informal talks. At Madison they were one-hour lectures. There is quite a difference between short seminar talks like those at our math society in Lwów, and the type of lecture which necessitates talking about major efforts. The latter were better prepared, of course, but their greater formality removed some of the spontaneity and stimulation of the shorter exchanges.