Home Page of Stefan Banach

A Remarkable Life of Stefan Banach

by Emilia Jakimowicz

(translated by John Greczek)

This article was published in Stefan Banach. Remarkable life, Brilliant mathematics,

ed. by Emilia Jakimowicz and Adam Miranowicz

(Gdańsk University Press, 2011).

1  The Early Years

,,Wilkosz transferred together with me to the Sobieski Grammar School, for reasons unknown to me. Banach remained in Grammar School IV until he took and passed his final examinations there in 1910.

After I left the Goetz school my ties with Banach were not as strong as before although Wilkosz continued to maintain a close relationship with him and, as Wilkosz and I were still friends, I often saw them together.

As I remember him, Stefan Banach was mild mannered but not without a gentle sense of humor and he was a good friend at school, although a little reserved. He always wore a clean and decent school uniform, like the rest of us, and he did not look pale, sickly, or hungry, although forced through meager material circumstances to tutor younger schoolmates for money, as well as those in the wider population; his own classmates he would help freely and without payment.

From their earliest school years Banach and Wilkosz bonded together through their mutual love of mathematics. During the so-called school "breaks" I often saw them solving math problems, which seemed to me, a student of humanities, to be quite incomprehensible.

Banach's friendship with Wilkosz was not limited to only the school grounds. They would meet after class in Wilkosz's home on Zwierzyniecka Street or in the school buildings as well as in the Krakow Planty Gardens. Later on, when they were older, walking home with them through the streets of Krakow might take half the night when in a very excited state and oblivious to time they would be discussing some question or other that challenged their minds.

I took no part in these math discussions but often argued some other issues at length with Wilkosz, with whom I had a closer relationship. We were drawn together during our time at school, and even later, by a common interest in literature and a penchant for some of the same girls at the school."

,,There is documentary evidence that Banach was a very diligent student, which is an uncommon characteristic of geniuses. And it should be remembered that the school curricula of that time stressed Latin, Greek and modern languages, and put little importance on the exact sciences. Banach attended school when it taught precisely in such a classical tradition. Consequently, its teaching programme coincided little with Banach's abilities or interests. Those teaching mathematics were not always fully competent in that discipline and Banach in his reminiscences was quite critical of the lowly level and manner in which his favorite subject was taught at school.

A large number of documents have survived relating to Banach's second year at Grammar School IV. It is interesting to look at the syllabus for that year, and perhaps even useful to those involved with school reform:

Religion, 2 hours per week. The Old Testament.

Latin, 8 hours per week. Supplementing the knowledge acquired in the first year about regular forms and indeclinable parts of speech. The most important irregular forms. Syntax of common subordinate clauses. Verbal and memory exercises as during the first year. Every month 3 classroom assignments, 1 home assignment.

Polish, 3 hours per week. Grammar: Review of subjects covered during the first year. Complex sentences, types of subordinate clauses. Further study of punctuation and correct spelling. Reading of abstracts from literature and recitation. Essays 3 times per month alternating between home and classroom.

German, 5 hours per week. Speech in the form of questions and answers to read passages, memorizing words, phrases and whole passages. Review of regular declension and the main principles of syntax. A weekly assignment, including one per month as homework.

History and Geography, 4 hours per week. Ancient history especially of Greece and Rome employing a biographical approach. Geographical and political maps of Asia and Africa. Latitudinal and longitudinal divisions of Europe. Detailed geography of South Europe and of Great Britain. Cartographic drawing exercises.

Mathematics, 3 hours per week. Review and further study of highest common divisor and least common multiple. Systematic study of common fractions. Conversion of common fractions into decimals and vice versa. Ratios, proportions. The rule of three and use of simple proportions. Inference. Calculation of percentage.

Geometry: Axial and central symmetry, congruent triangles and their application. The most important properties of circles, quadrilaterals and polygon. Training and work assignments as in the first year.

Natural History, 2 hours per week. During the first 6 months zoology: birds, reptiles, amphibians, fish, crustaceans and worms, mollusks, protozoa. Starting in March the world of plants.

The school also offered a choice of other subjects that were not compulsory: history of the homeland, French (which according to school records no second year student selected), singing, art, calligraphy, gymnastics and stenography."

2  First Great Adventure with Mathematics

,,In 1916, during a summer evening while I was taking a walk in the Planty Gardens I overheard a conversation, or rather only a few words; it was so unexpected for me to hear the term Lebesgue integral that I approached the bench on which those speaking were sitting and made their acquaintance: they were Stefan Banach and Otto Nikodym. They told me their small group also included a third friend, Wilkosz."

3  Road to Fame

,,Not only had Banach not graduated from a university but he also obtained his PhD degree in a most unconventional way. When he took up his position in Lvov he had already written several mathematics papers with important results and was constantly coming up with new ideas. However, in response to advice that he ought to soon submit his PhD thesis, he would say that he had time to do so and would be able to come up with something even better compared to what he had produced so far. Finally his superiors became impatient. They had someone compile the results of Banach's latest work. It was considered to be outstanding PhD material. Nonetheless, the regulations required that an official review and external examination were necessary. One day Banach was stopped in a corridor of the Jan Kazimierz University and asked: "Would you come to the Dean's office? There are some people there with questions about certain mathematical propositions that you should definitely be able to help them with". Banach went and readily answered all the questions that were put to him, all the time completely unaware that he was in front of a specially convened commission which had arrived from Warsaw for his PhD examination. Most likely today it would not be possible to obtain a PhD degree in this manner."

,,The decision in 1931 to start publishing the Mathematical Monographs should be considered a particularly important event for Polish mathematics. It marked a new stage in the development of the Polish School of Mathematics. The earliest stage, which could be called the pioneering stage, was characterized by the publication, almost always, of short articles containing new results (appearing mainly in Fundamenta Mathematicae and Studia Mathematica). A time came, however, for a synthesis of all of the achievements of Polish mathematicians, or even for a synthesis of all the mathematics disciplines in which Poles had made especially significant contributions. The initial plan was to publish monographs on the subject of functional analysis: Volume I Operations lineares (Theory of Linear Operations) by Banach, Volume II Théorie de l'integrale (Theory of Integral) by Saks, Volume III Topology by Kuratowski, Volume IV Continuum hypothesis by Sierpiński and Volume V Theory of Trigonometric Series by Steinhaus and Kaczmarz. In a very short time the Mathematical Monographs achieved a position as one of the most important scientific periodicals."

,,He was always able to work under any conditions, and in all circumstances, and was unaccustomed to ease and comfort. His professor's salary of about 1000 zlotys per month should have been quite adequate. However, his fondness for frequenting coffee-houses, utter disregard of any bourgeois concern for material interests, and an absence of regularity in daily affairs, finally plunged him into debt and very trying times. In an attempt to change his situation he began writing textbooks."

4  The Scottish Café

,,One session lasted 17 hours and resulted in the successful proof of an important postulate concerning Banach spaces. No permanent record of it was made, however, and no one since 9 has been able to reproduce it because it was probably completely erased from the tabletop by the cleaners. Unfortunately, many other proofs derived by Banach and his students suffered the same fate.

The many hours spent in discussion of mathematics problems resulted in an atmosphere of perseverance, excitement and concentration and made it possible to forge intellectual common ground."

,,These long sessions in the cafes with Banach, or more often with Banach and Mazur, 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."

,,For Polish mathematicians the Scottish Book became an almost holy relic. Copies of it have been circulated worldwide but the original is exhibited only rarely. At the urging of Steinhaus a new notebook was purchased in Wrocław and was named the New Scottish Book. It was in use between 1946 and 1948 and fulfilled a role similar to that of the original Scottish Book in Lvov. It was in the care of Professors Marczewski and Steinhaus. The tradition of the Scottish Book was thus continued. However, the new version lacked the mythical and legendary qualities that have characterized the original, the unique and inimitable only one."

5  The Dark Years

,,My father was invited to a conference in Kiev, two days before the war broke out between Germany and the Soviet Union. He went there and when he came back the war had started. He had immediately taken the last train to Lvov and arrived just before the Germans took over the city. I dared to ask him in private why he did not stay (in Kiev). He looked at me for a while and then he shrugged and told me that he loved us and that was the way every Banach behaved."

,,It was the highly complicated situation the academic staff found itself in July 1941, that motivated Weigl to continue to run the Institute. He saw, thereby, an opportunity to help the large 13 group of professors and their assistants who had been left deprived of work and position. He successfully extorted the Germans to allow him to take full responsibility for and decide alone whom to choose to be on his staff. The Institute thus grew quickly in size. An unusual and unique group was formed to produce the vaccine for epidemic typhus. It consisted of not just the academics but also of the youth conspiring against the occupiers and threatened with deportation to Germany, and fighters in the underground resistance. Their only common link with the Institute was the work permit they each received."

,,During that time my father came and visited me in Krakow in 1944. He spent a couple of days there and looked better (...). He told me that he was "switching" to study physics problems and had some ideas that should win him the Nobel Prize. Our parting was sad and tinged with a sense of hopelessness. Reality dealt us a blow worse than we could have imagined because that was the last time I saw him."

,,For several months Nikliborc nursed my father and my grieving mother and was a guardian and messenger boy for them. I do not know how within this little person there could be so much heart and courage."

6  Epilogue

,,Banach was the unquestioned superstar of Polish mathematics and his name is known wherever mathematics is taught. In the short fifty-three years of his life (...) he succeeded in combining an overwhelming flow of brilliant ideas with a style of high living that few men could sustain."

,,Banach gave to Polish science, and particularly to Polish mathematics, more than anyone else. (...) He combined within himself a spark of genius with an astonishing internal urge, which addressed him incessantly in the words of the poet: "there is only one thing: the ardent glory of one's craft" ["Il n'y a que la gloire ardente du métier" (Verlaine)] - and mathematicians well know that their craft consists of the same secret as the poets' craft."

References

Acknowledgements