Still, my interests in science did not take all of my time. I avidly read Polish literature, as well as writers as diverse as Tolstoy, Jules Verne, Karl May, H. G. Wells, and Anatole France. As a boy I preferred biographies and adventure stories.
Besides these more cerebral activities, I engaged actively in sports. Beginning at about fourteen I played various positions in soccer with my classmates: goalie, right forward and others. I started playing tennis, too, and was active in track and field.
After school I played cards with my classmates. We played bridge and a simple variety of poker for small stakes. In poker the older boys won most of the time. One of the abilities that apparently does not decrease but rather improves with age is a primitive type of elementary shrewdness. I played chess also, two or three times a week. Although I don't think I ever had too much talent for the game, I certainly had a more than average feeling for positions, and I probably was one of the best players in my group. Like mathematics, chess is one of the things where constant practice, constant thinking, and imagining, and studying are necessary to achieve a mastery of the game.
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. Besides, there was no shortage of lawyers in Lwów. The thought of a university career was attractive, but professorial positions were rare and hard to obtain, especially for people with Jewish backgrounds like myself. Consequently, I looked for a course of studies which would lead to something practical and at the same time would be connected with science. 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.
Chapter 2. Student Years
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.
As I knew many of the subjects in mathematics from my studies, I began to attend a second-year course as an auditor. It was in set theory and given by a young professor fresh from Warsaw, Kazimir Kuratowski, a student of Sierpinski, Mazurkiewicz, and Janiszewski. He was a freshman professor, so to speak, and I a freshman student. From the very first lecture I was enchanted by the clarity, logic, and polish of his exposition and the material he presented. From the beginning I participated more actively than most of the older students in discussions with Kuratowski, since I knew something of the subject from having read Sierpinski's book. I think he quickly noticed that I was one of the better students; after class he would give me individual attention. This is how I started on my career as a mathematician, stimulated by Kuratowski.
Soon I could answer some of the more difficult questions in the 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. Years later, Kuratowski told me that the questions were sometimes significant, often original, and interesting to him.
My courses included mathematical analysis, calculus, classical mechanics, descriptive geometry, and physics. 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.
It was there that I first met Stanislaw Mazur, who was a young assistant at the University. He came to the Polytechnic Institute to work with Orlics, Nikliborc and Kaczmarz, who were a few years his senior.
In conversations with Mazur I began to learn about problems in analysis. I remember long hours of sitting at a desk and thinking about the questions which he broached to me and discussed with the other mathematicians. Mazur introduced me to advanced ideas of real variable function theory and the new functional analysis. We discussed some of the more recent problems of Banach, who had developed a new approach to this theory.
Banach himself would appear occasionally, even though his main work was at the University. I met him during this first year, but our acquaintance began in a more meaningful, intimate, and intellectual sense a year or two later.
Several other mathematicians could frequently be seen in these offices. Stozek, cheerful, rotund, short, and completely bald, was Chairman of the Department of General Studies. The word stozek means ''a cone" in Polish; he looked more like a sphere. Always in good humor and joking incessantly, he loved to consume frankfurters liberally smeared with horseradish, a dish which he maintained cured melancholy. (Stozek was one of the professors murdered by the Germans in 1941.)
Antoni Lomnicki, a mathematician of aristocratic features who specialized in probability theory and its applications to cartography, had office hours in these rooms. (He too was murdered by the Germans in Lwów in 1941.) His nephew, Zbigniew Lomnicki, later became my good friend and mathematical collaborator.
Kaczmarz, tall and thin (who later was killed in military service in 1940), and Nikliborc, short and rotund, managed the exercise sections of the large calculus and differential equations courses. They were often seen together and reminded me of Pat and Patachon, two contemporary comic film actors.
I did not feel I was a regular student in the sense that one may have to study subjects one is not especially interested in. On the other hand, after all these years, I still do not feel much like an accomplished professional mathematician. I like to try new approaches and, being an optimist by nature, hope they will succeed. It has never occurred to me to question whether a mental effort will be wasted or whether to "husband" my mental capital.
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.
I wrote my first paper on this in English, which I knew better than German or French. Kuratowski checked it and the short paper appeared in 1928 in Fundamenta Mathematicae, the leading Polish mathematical journal which he edited. This gave me self-confidence.
I still was not certain what career or course of work I should pursue. The practical chances of becoming a professor of mathematics in Poland were almost nil — there were few vacancies at the University. My family wanted me to learn a profession, and so I intended to transfer to the Department of Electrical Engineering for my second year. In this field the chance of making a living seemed much better.