The Lwów section of the Polish Mathematical Society held its meetings at the University most Saturday evenings. Usually three or four short papers were given during an hour or so, after which many of the participants repaired to the coffee house to continue the debates. Several times I announced beforehand that I had some results to communicate at one of these sessions when my proof was not complete. I felt confident, but I was also lucky, because I finished the proofs before I had to speak.
I was nineteen or twenty when Stozek asked me to become secretary of the Lwów Section, a job which mainly required sending announcements of meetings and writing up short abstracts of talks for the Society's Bulletin. There was, of course, much correspondence between our section and the other sections in Cracow, Poznan, and Wilno. Important problems arose about transferring the administrative seat of the Society from Cracow, the ancient Polish royal city, to Warsaw, the capital, where the headquarters of the Society were eventually located. Needless to say this took a great deal of maneuvering and politicking.
One day a letter came from the Cracow center soliciting the support of the Lwów section. I told Stozek, who was the president of our section, ''An important letter just arrived this morning." His reply—"Hide it so no human eye will ever see it again" — was a great shock to my youthful innocence.
The second big congress I attended was held in Wilno in 1931. I went to Wilno by train via Warsaw with Stozek, Nikliborc, and one or two other mathematicians. They kept fortifying themselves with snacks and drinks, but when I pulled out a flask of brandy from my pocket, Stozek burst into laughter and said, "His mama gave it to him in case he should feel faint." This made me acutely aware of how young I was in the eyes of others. For many years I was the youngest among my mathematical friends. It makes me melancholy to realize that I now have become the oldest in most groups of scientists.
Wilno was a marvelous city. Quite different from the cities of the Austrian part of Poland, it gave a definitely oriental impression. The whole city appeared exotic to me and much more primitive than my part of Poland. The streets were still paved with cobblestones. When I prepared to take a bath in my hotel room, the gigantic bathtub had no running water. When I rang the bell a sturdy fellow in Russian boots appeared with three large buckets of hot water to pour into the tub.
I visited the church of St. Ann, the one which Napoleon admired so much on his way to Moscow that he wanted to move it to France.
This was the first and last time I ever visited Wilno. I should mention here that one of the most prominent Polish mathematicians, Antoni Zygmund, was a professor there until World War II. He left via Sweden in 1940 to come to the United States and is now a professor at the University of Chicago.
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? I don't know. It especially affected Banach, Mazur, and myself, but not Kuratowski, for example.
Much of the historical development of mathematics has taken place in specific centers. These centers, large or small, have formed around a single person or a few individuals, and sometimes as a result of the work of a number of people — a group in which mathematical activity flourished. Such a group possesses more than just a community of interests; it has a definite mood and character in both the choice of interests and the method of thought. Epistemologically this may appear strange, since mathematical achievement, whether a new definition or an involved proof of a problem, may seem to be an entirely individual effort, almost like a musical composition. However, the choice of certain areas of interest is frequently the result of a community of interests. Such choices are often influenced by the interplay of questions and answers, which evolves much more naturally from the interplay of several minds. The great nineteenth-century centers such as Göttingen, Paris, and Cambridge (England) all exercised their own peculiar influence on the development of mathematics.
The accomplishments of the mathematicians in Poland between the two world wars constitute an important element in mathematical activity throughout the world and have set the tone of mathematical research in many areas.
This is due in part to the influence of Janiszewski, one of the organizers of Polish mathematics and a writer on mathematical education, who unfortunately died young. Janiszewski advocated that the new state of Poland specialize in well-defined areas rather than try to work in too many fields. His arguments were, first, that there were not many persons in Poland who could become involved, and second, that it was better to have a number of persons working in the same domain so they could have common interests and could stimulate each other in discussions. On the other hand, this reduced somewhat the scope and breadth of the investigations.
Although Lwów was a remarkable center for mathematics, the number of professors both at the Institute and at the University was extremely limited and their salaries were very small. People like Schauder had to teach in high school in order to supplement a meager income as lecturer or assistant. (Schauder was murdered by the Germans in 1943.) Zbigniew Lomnicki worked as an expert in probability theory in a government institute of statistics and insurance. If I had to name one quality which characterized the development of this school, made up of the mathematicians from the University and the Polytechnic Institute, I would say that it was their preoccupation with the heart of the matter that forms mathematics. By this I mean that if one considers mathematics as resembling a tree, the Lwów group was intent on the study of the roots and the trunk rather than the branches, twigs, and leaves. 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 retrospect it seems somewhat curious that the ideas of algebra were not considered in a similar general setting. It is equally curious that studies of the foundations of physics — in particular a study of space-time — have not been undertaken in such a spirit anywhere to this day.
Lwów had frequent and lively interaction with other mathematical centers, especially Warsaw. From Warsaw Sierpinski would come occasionally, so would Mazurkiewicz, Knaster, and Tarski. In Lwów they would give short talks at the meetings of the mathematical society on Saturday evenings. Sierpinski especially liked the informal Lwów atmosphere, the excursions to inns and taverns, and the gay drinking with Banach, Ruziewicz, and others. (Ruziewicz was murdered by the Germans on July 4, 1941.)
Mazurkiewicz once spent a semester lecturing in Lwów. Like Knaster in topology, he was a master at finding counter examples in analysis, examples showing that a conjecture is not true. His counter examples were sometimes very complicated, but always ingenious and elegant.
Sierpinski, with his steady stream of results in abstract set theory or in set theoretical topology, was always eager to listen to new problems — even minor ones — and to think about them seriously. Often he would send solutions back from Warsaw.
Bronislaw Knaster was tall, bald, very slim, with flashing dark eyes. He and Kuratowski published many papers together. He was really an amateur mathematician, very ingenious at the construction of sets of points and continua with pathological properties. He had studied medicine in Paris during the first World War. Being extremely witty, he used to entertain us with descriptions of the polyglot international group of students and the indescribable language they spoke. He quoted one student he had overheard in a restaurant as having said: "Kolego, pozaluite mnia ein stückele von diesem faschierten poisson," an amalgam of Polish, Russian, Yiddish, German, and French!