Ulam's obituary of Kuratowski

Stanisław Ulam wrote an obituary of Kazimierz Kuratowski (1896-1980) which was published in The Polish Review 26 (1) (1981), 62-66. It is a very personal account consisting largely of Ulam's interactions with Kuratowski. We present a version below.

Kazimierz Kuratowski (1896-1980).

Kazimierz Kuratowski died in Warsaw, June 18, 1980 at the age of 84. A great mathematician, one of the creators of modern topology, he had an enormous influence in research and in education, not only in Poland but throughout the world. One of the founders of the famous Polish mathematics periodical Fundamenta Mathematicae, he was responsible for the development of the new spirit of modern mathematics. After the end of World War II his great merit was the reestablishment and reorganisation of numerous mathematical activities in Poland. His influence also spread to the United States through his many students.

In what follows I shall try to reminisce about my early contacts with him before World War II in Poland, and later, and will attempt to sketch some traits of his personality and his activities.

I was his first doctoral student and received my Doctorate of Science at the Polytechnic Institute in Lwów in the General Faculty in 1933. Through out high school and partly thanks to a teacher, Professor Zawirski, who was also a docent at the University, I was interested in mathematics. In the fall of 1927 I entered the Polytechnic Institute in the division of electrical engineering and as a freshman took a course in Set Theory (a general abstract foundation of mathematics) taught by a new young professor freshly arrived from Warsaw, named Kuratowski. At that time he was slim, rather short in stature, lively in speech but slow and measured in his movements, a quality he retained throughout his life. The course was attended by some fifteen students and the lectures were, in contrast to my high school experiences, monuments of logic, clarity, systematic presentation, and preparation.

That same year, just before the Christmas recess, Kuratowski mentioned a still unresolved problem about a property of transformations in Set Theory. I thought for hours about this problem, and at the end of a week believed I had found a solution. When classes resumed I communicated it to Kuratowski with great excitement. It proved to be correct!

From that time on I visited him in his office every morning after classes, amazed at his accessibility and at the obvious interest he took in me. I began to think about switching from engineering to mathematics, but the decision was a hard one. There were few, if any, university positions vacant for graduates in mathematics, and my family was initially doubtful about the practical outlook of undertaking such studies in the General Faculty. So I postponed the decision until, I told myself, I could solve another open problem of mathematics. In the spring of 1928 I was fortunate enough to succeed in solving a second problem which had come up in Kuratowski's course, and he decided that these two results should be published as two papers in Fundamenta.

I should add here that Kuratowski was a bachelor at the time and lived in a pension where he returned for lunch after classes. I used to accompany him home and we walked the mile or so between the Institute and his domicile conversing almost exclusively about mathematics. These conversations are still vivid in my mind, and it is only many years later that I have come to appreciate the patience and the interest this thirty-one-year-old professor was showing in an eighteen-year-old very eager student. After lunch at home with my parents, I frequently returned to the Institute not only for other classes, but for more discussions with some of the other professors of mathematics such as Banach, and some of the younger ones like Mazur and Auerbach who also became my friends. At the time Banach was a professor at the University but he occasionally taught additional courses at the Polytechnic Institute.

In 1929 Kuratowski married. I remember that he sometimes took a plane, a rare occurrence in those days, from Lwów to Warsaw to visit his fiancée. He and his wife later settled in Lwów and instead of our daily walks, I remember being invited to their house once or twice a week for mathematical discussions.

In 1930 I managed to solve another problem which Kuratowski had mentioned. It was a problem of his and Banach's concerning possible generalisation and strengthening of their joint result.

During these years of studies I was very remiss in writing up original work and, worse yet, could not bring myself to take the exams in the regular courses. It was at Kuratowski's insistence that my early papers were written up and published, and thanks to this original work I was, exceptionally, allowed to take the examinations all at once. In 1932, I received my M.A. and in 1933 obtained my doctorate, under Kuratowski.

I should note here that the Lwów mathematicians had the habit of gathering in coffee houses and tea-rooms. Banach, Stozek and others spent hours between lectures sipping coffee and discussing mathematics at the Cafe Roma, then at the Szkocka, almost daily. Steinhaus and Kuratowski on the whole preferred the more genteel atmosphere of Zaleski's tea room some two hundred yards away.

The Mathematical Society met at the University almost every Saturday evening and invariably some people repaired afterwards to the coffee houses to continue the discussions, Kuratowski attracted to Lwów mathematicians from Warsaw. Sierpinski, Mazukiewicz, Tarski, and Knaster paid us frequent visits. Karol Borsuk, who was just a few years older than I, came to stay for several months to work with him and also with me. We became close friends and collaborators from that time on. I am mentioning all this to indicate how active and widespread the mathematical life was in Lwów.

Shortly after I received my doctorate, Kuratowski abruptly left Lwów and returned to Warsaw to become a professor at the University. A chair was especially created for him by the then minister of education, W Jedrzejewicz, now living in the United States. The reason for his departure was this: The General Faculty of the Polytechnic Institute was abolished by decree from Warsaw, I suppose for economic reasons. It had awarded only two doctoral degrees, mine and Jan Blaton's, a young physicist who worked under Rubinowicz. Kuratowski and several other professors lost their positions. (Among them, Jan de Rosen, a famous painter and architect who later came to the United States and created the celebrated mosaics of the Washington D.C. Cathedral.)

I came to the United States in December 1935 on an invitation from the mathematician John von Neumann for a few months' visit to the Institute for Advanced Studies in Princeton. Great was my surprise when, the following March, Kuratowski appeared at the Institute while on a lecture tour of American universities. This was his first visit to the United States. There were many more to come after World War II. While he was in Princeton I received an offer of a position at Harvard. His testimonial on my behalf may have played a role. When I asked him whether I ought to accept the position, he encouraged me to do so in view of the scarcity of openings in Poland.

Every summer, including 1939, I returned to Poland to visit my family and friends, and continued to collaborate actively with the Polish mathematicians. Kuratowski and Borsuk invited me several times to stop off in Warsaw on the way to Lwów and give some lectures at the University. He asked me once to visit him at his summer villa outside Warsaw. To my great surprise I found him playing a fair game of tennis. It had not occurred to me that he could be interested in things other than mathematics!

Two weeks after I had returned to Harvard in 1939 the German invasion of Poland took place and all contacts with Kuratowski and other Polish colleagues ceased.

I learned in a round-about way of the tragedies that befell the Lwów professors. Stozek, Lomnicki, Bartel, and many others were gathered by the Nazis shortly after their entry into Lwów and executed, some with members of their families. Kuratowski was in Warsaw when the Germans occupied the city. I had no news about him or any of the other Warsaw mathematicians until after the war. Only then did I learn of the horrors they lived through.

Kuratowski's "Notes for an Autobiography" appeared in Kultura in 1979. After his death, his daughter, Sofja Kuratowska, a medical doctor and research biologist, found on his desk a manuscript of reminiscences. Fragments were published last summer in Kultura (Aug. 3 and ff.). They are supposed to appear soon in book form in Poland, published separately by "Czytelnik."

It is impossible for me to give even only a bare idea of the moving account of his Odyssey during the occupation: his narrow escapes from arrest by the Gestapo, the gruesome happenings which befell his friends and colleagues, all the while his being very active in the underground work of the secret university! His equanimity and courage come through every page. Perhaps this helped him escape the terrible fate shared by so many others.

His detailed account continues with the period after the liberation. It describes his decisive, really Herculean work to re-establish not only mathematics but other sciences as well in post-war Poland. He was named director of the Mathematics Institute of the Polish Academy of Sciences. As he said, this became the very core of his life.

It is heart-breaking to read his account of the reopening of the academic year 1945-46 amid the ruins of the city which, he wrote, "was slowly being reborn as a Phoenix from the ashes."

I cannot describe, even in general terms, his titanic organisational and educational efforts. It seems also almost superhuman that he could have continued them alongside original creative scientific work.

In the obituary of Kuratowski which appeared in Kultura, Borsuk summarises his scientific achievements and a former student, Engelkind, paints a portrait of him as his professor.

His creative mathematical research continued unabated to the end of his life. There now exists an English translation of the two volumes of his monumental book on topology, which is a veritable bible of the foundations of the subject. In another book, Half a Century of Polish Mathematics, he describes the development of the Polish School and his role in both its subject matter and its organisation and reorganisation. How mathematical logic, set theory, topology, functional analysis, and other branches of mathematics flourished between 1918 and 1940, and the rebirth of the School after World War II. The book was recently translated into English and published by Pergamon Press in Oxford. He also wrote an excellent textbook on infinitesimal analysis. In this article I cannot give even a selection of his research papers or of his celebrated theorems.

Kuratowski received many academic honours including membership in numerous scientific academies. He was very prominent and active in the International Mathematical Union and was, inter alia, a member of the committee which awarded the Balsan Prize. One of its first recipients was Pope John XXIII.

Our post-war contacts resumed, first by correspondence, then in person during his frequent visits to American universities and my infrequent ones to Poland. In the late forties he was able to stop off in New Mexico and my wife and I drove him to El Paso on his way to other university centres. By then he had become somewhat portly and even slower in his movements than I remembered. My wife was very struck by his measured and smiling ways and his absolute imperturbability when our car broke down in the middle of the desert and it took several hours before we could obtain help. A similar episode happened when we visited him in Poland. He invited us to drive with him to Krakow but his car developed troubles on the outskirts of Warsaw. He remained patiently unruffled while his chauffeur frantically tried to get it repaired. After his war experiences, he said, nothing could ever upset him anymore.

As a host he was unequalled in graciousness and 'savoir faire'. During a brief morning visit at the Mathematics Institute in Warsaw he received us in his large office. We sat with him in deep leather upholstered chairs in a comfortable conversation corner while, in addition to the inevitable tea, a uniformed attendant appeared with mounds of wild strawberries with whipped cream!

As the first of his many students, I bear a great debt of gratitude for his decisive influence on me during my early youth, for the initial choice of my career, and for his having introduced me to the world of mathematics and mathematicians. There are many in America today who have been his students and his students' students. His unceasing work and steadfast character have been examples to follow. His mind was remarkable for its clarity, taste, and moderation and common sense approach to the role of abstraction in the great and varied fields of mathematics.

Last Updated June 2024