The Congress in Zürich was an enormous affair compared to any I had previously attended, but quite small in comparison to those after World War II. I still have a photograph of all the members standing in front of the Technische Hochschule. There for the first time I saw and met many foreign mathematicians.
The meeting was interesting, and I found it stimulating to hear about many types or fields of mathematics other than the ones cultivated in Poland. The diversity of mathematical fields opened new vistas and suggested new ideas to me. In those days I went to almost every available general talk.
Many of the German and West European mathematicians appeared to me nervous; some had facial twitches. On the whole compared to the Poles I knew they seemed less at ease. And even though in Poland there was great admiration for the Göttingen school of mathematics, I again felt, perhaps not justifiably, my own sense of self-confidence.
I gave my own little talk feeling only moderately nervous. The reason for this comparative lack of nervousness, I think, in retrospect, was due to my attitude, compounded of a certain drunkenness with mathematics and a constant preoccupation with it.
Somebody pointed out a short old man. It was Hilbert. I met the old Polish mathematician Dickstein, who was in his nineties and walking around looking for his contemporaries. Dickstein's teacher had been a student of Cauchy in the early nineteenth century, and he still considered Poincaré, who died in 1912, a bright young man. To me this was like going into the prehistory of mathematics and it filled me with a kind of philosophical awe. I met my first American mathematician, Norbert Wiener. Von Neumann was not there, and this was a disappointment. I had heard so much about his visit to Lwów in 1929.
At the hotel swimming pool I met the famous physicist Pauli with Professor Wavre and Ada Halpern. Wavre, Ada's professor, was a Swiss mathematician, known for his studies of the celebrated classical problem of figures of equilibrium of rotating planetary and stellar bodies, among other things. Ada came from Lwów. She was a very good-looking girl who was studying mathematics at the University of Geneva. For a few years I had an off-and-on romance with her. In front of all this company, I turned to Pauli and tried a pun, saying: "This is a Pauli Verbot" (a Paulian physical principle which asserts that two particles with the same characteristics cannot occupy the same place), referring to Wavre and me who were both there in the company of this pretty young lady.
Another interesting encounter occurred one afternoon in the woods around the famous Dolder Hotel. Having lost my way, I ran into Paul Alexandroff and Emmy Noether walking together and discussing mathematics. Alexandroff knew about some of my work for I had sent him reprints and we had had some previous mathematical correspondence. In fact one of the great joys of my life had been to receive a letter from him addressed to Professor S. Ulam. During this encounter he suddenly said to me: "Ulam, would you like to come to Russia? I could arrange everything and would like very much to have you." As a Pole, and with my rather capitalistic family background, his invitation flattered me, but such a trip appeared quite unthinkable.
The Congress over, after a little excursion to Montreux with Kuratowski and Knaster I returned to Poland in time to take my Master's degree.
I had an almost pathological aversion to examinations. For over two years I had neglected to take the examinations which were usually necessary to progress from one year to the next. My professors had been tolerant, knowing that I was writing original papers. Finally, I had to take them — all at once.
I studied for a few months, took a kind of comprehensive examination and wrote my Master's thesis on a subject which I thought up myself. I worked for a week on the thesis, then wrote it up in one night, from about ten in the evening until four in the morning, on my father's long sheets of legal paper. I still have the original manuscript. (It is unpublished to this day.) The paper contains general ideas on the operations of products of sets, and some of it outlines what is now called Category Theory. It also contains some individual results treating very abstractly the idea of a general theory of many variables in diverse parts of mathematics. All this was in the fall of 1932 upon my return from Zürich.
In 1933 I took my Doctor's examination. The thesis was published by Ossolineum, an establishment which printed the Lwów periodical Studia Mathematica. It combined several of my earlier papers, theorems, and generalizations in measure theory.
My degree was the first doctorate awarded at the Polytechnic Institute in Lwów from the new Department of General Studies which had been established in 1927. It was the only department that gave Master's and Doctor's degrees, all the others being engineering degrees.
The ceremony was a rather formal affair. It took place in a large Institute hall with family and friends attending. I had to wear a white tie and gloves. My sponsors Stozek and Kuratowski each gave a little speech describing my work and the papers I had written. After a few words about the thesis, they handed me a parchment document.
The ''aula" — the large hall in which the ceremony took place — was decorated with traditional frescoes. These were very much like some I saw twenty years later on the walls of the MIT cafeteria. The MIT frescoes depict scantily dressed women in postures of flight, symbolizing sciences and arts, and a large female figure of a goddess hovering over a recoiling old man. I used to joke that it represented the Air Force giving a contract to physicists and mathematicians. In Fuld Hall, the Institute Building in Princeton, there is also an old painting in the tea room where people assemble for conversation in the afternoon. There again one sees an old man who seems to be shying away from an angel coming down from the clouds. When I was told that nobody knew what it was supposed to represent, I suggested that it might be a representation of Minna Ries, the lady mathematician who directed the Office of Naval Research at the time, proposing a Navy contract to Einstein, who is recoiling in horror.
After the examinations and ceremonies I published a few more papers and then had to take it easy for the rest of 1933, for a bad paratyphoid infection left me weak for several months — one of the rare times in my life when I was seriously ill.
But not all was serious work and no play. In the early 1930s, a high school teacher of science by the name of Hirniak, a wizened, small man, came to our coffee house. He would sit a few tables away from us, sipping vodka and coffee in turn, and busily scribbling on a pad of paper. Every once in a while he would get up and join our table to gossip or kibitz when Nikliborc and Stozek played chess. Nikliborc would repeat with glee: "Gehirn [brain in German], Gehirniak!"
Hirniak, who taught mathematics, physics, and chemistry, was trying to solve Fermat's famous problem. This is one of the best-known unsolved problems in mathematics, and for a long time has attracted cranks as well as amateurs, who regularly produce false or very incomplete proofs of Fermat's conjecture.
Hirniak was a fixture at the coffee house, and his conversation was delightfully picturesque and full of unconsciously humorous statements. We would collect and repeat them to each other; I used to paste some of them on the walls of my room at home.
It turned out that my father knew Hirniak, whose wife owned a large soda-water factory and whose legal affairs were handled by my father's firm. My father considered Hirniak a humorously foolish person. When he saw my collection of Hirniak maxims, I believe he was surprised and perhaps even wondered about my sanity. I had to explain to him the subtlety of the humor and its special appeal to mathematicians.