Stefan Banach at 44 years of age, Lvov 1936 |

[This photograph is from the private collection of the Banach family and used here with the permission of Prof. Alina Filipowicz-Banach.] |

Stefan Banach at 3 years of age at the Krakow Planty Gardens. |

[Photographed by Juliusz Mien. This photograph is from the private collection of the Banach family and used here with the permission of Prof. Alina Filipowicz-Banach.] |

After completing grammar school Wilkosz graduated with a degree in mathematics from the Jagiellonian University in Krakow where he was later to be appointed a professor. Roman Ka³u¿a in an extensive biography [2] of Stefan Banach wrote:,,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."

Many years later Banach said that his interest in mathematics was ultimately aroused and guided by Dr Kamil Kraft (who taught mathematics and physics at Grammar School IV). Perhaps through overwork, or boredom with the classroom material, he lost his enthusiasm for studying. And in 1910, just before his final graduation exams, he confronted a major difficulty. He, the excellent student of former years, was now threatened with a failing grade in eight subjects! Not even the despairing math teacher may have been able to help get him through the exams (even after explaining to the high supervisory commission that they were dealing with an authentic genius in mathematics) were it not for the intervention of the school priest, Father Pawe³ Py³ko, who in those times would have had a deciding voice. The priest, it must be said, showed surprising tolerance in supporting the future mathematician. Banach was a skeptic and had often embarrassed the good priest with some of his comments. Out of a total of 27 final year students 6 achieved a passing grade "with honors". Banach was not among them and had to be satisfied with a grade "with merit" (behind him were only two students who had to retake the exams). After graduation when discussing their future plans Banach and Wilkosz were both convinced that mathematics was already so advanced that nothing new could be achieved in it; and so it would not be worthwhile to go on to study mathematics. Banach chose technology, and Wilkosz oriental languages. Much later, when already deeply involved with mathematics, Banach admitted in a conversation with Prof. Andrzej Turowicz that in their youthful presumption both Wilkosz and he had been wrong about the possibility of advances in mathematics [3]. In 1910, the two friends parted company after they graduated from the grammar 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."

Hugo Steinhaus |

This meeting of Steinhaus and Banach had almost immediate consequences for mathematics. Steinhaus invited both Banach and Nikodym to his house and described to them some problems he had been struggling with for a long time and been unable to solve. Banach came up with a complete solution within a couple of days. It subsequently became the first of Banach's publications, written jointly with Steinhaus, titled "Sur la convergence en moyenne de séries de Fourier" (On the Mean Convergence of Fourier Series), published in a Bulletin of the Krakow Academy of Sciences 2 in 1919. This auspicious beginning brought Banach to the attention of other mathematicians (also in no small measure due to Steinhaus).,,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."

Stefan Banach at 27 years of age, Krakow 1919. |

[This photograph is from the private collection of the Banach family and used here with the permission of Prof. Alina Filipowicz-Banach.] |

Wac³aw Sierpiñski |

£ucja Banach (nee Braus). |

[This photograph is from the private collection of the Banach family and used here with the permission of Prof. Alina Filipowicz-Banach.] |

Stefan Banach Jr. as a student of medicine, 1942. |

The old Jan Kazimierz University at 4, St. Nicolas Street. |

In 1922, after completing postdoctoral work, Banach was appointed a full professor at the university. Two years later he was also elected a Corresponding Member of the Polish Academy of Arts and Sciences. For the 1924/25 academic year he went to Paris on sabbatical leave to lecture and to help with work in his field that had been started there. In addition to his heavy teaching schedule as professor in Lvov, Banach also greatly expanded his research work there. He soon became one of the greatest world experts in functional analysis of which he was one of the founders. About him he gathered several young, illustrious talents. A new institution, the Lvov School of Mathematics, came into existence under the direction of Steinhaus and Banach, and as soon as 1929 began to publish its own periodical dedicated to functional analysis: Studia Mathematica. The world-wide recognition of Banach's results really came only following the publication of his book in 1931, which in the following year was translated into French as Théorie des opérations linéaires (Theory of Linear Operations) [9]. It was the first volume of a series of monographs titled "Mathematical Monographs" ("Monografie Matematyczne" in Polish) of which Banach was one of the founders. This monograph was the first textbook in the field of functional analysis and bestowed fame on both the author and on Polish mathematics.,,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."

1. L. Chwistck, 2. S. Banach, 3. S. Loria, 4. K. Kuratowski, 5. S. Kaczmarz, 6. J. P. Schauder, 7. M. Stark, 8. K. Borsuk, 9. E. Marczewski, 10. S. Ulam, 11. A. Zawadzki, 12. E. Otto, 13. W. Zonn, 14. M. Puchalik, 15. K. Szpunar.

Kazimierz Kuratowski |

Banach also wrote textbooks of advanced mathematics that were associated with and complemented his teaching programme. Thus, volumes I and II of Differential and Integral Calculus [11] appeared in 1929 and 1930, respectively, and volumes I and II of Mechanics - In the Scope of Academic Studies [12] were both published in 1938. These, as well as texts for use in grammar schools, [7], co-authored with Sto¿ek and Sierpiñski, were created during somewhat dramatic circumstances for Banach. Steinhaus wrote [6]:,,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 Sierpiñski 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."

Turowicz mentions [3] that Banach received help at that time from Professor Benedykt Fuliñski (1881-1942), who guaranteed his debts to the creditors. At the same time Fuliñski was instrumental in getting Banach to change his spending habits and set aside some of his income every month. However, it was only his substantial income from his books that helped to pay down the debts, which were only completely liquidated when Banach received a prize from the Polish Academy of Arts and Sciences. By this time it was already 1939. In the meantime there was extensive world-wide interest by mathematicians in Banach's work and results. At the 1936 International Congress of Mathematics in Oslo Banach was entrusted with giving one of the keynote lectures on Die Theorie der Operationen und ihre Bedeutung für die Analysis (The Theory of Operations and its Significance in Analysis), which was undoubtedly a sign of the high regard for and interest in him personally and in his results. In those days guests from all over the world visited Lvov: from Austria - Moses Jacob; from Czechoslovakia - Vaclaw Hlavaty; from Denmark - Axel Andersen; from France - Emil Borel, Maurice Fréchet, Henri Lebesgue, Paul Montel; from Germany - Leon Lichtenstein, Ernst Zermelo; from Great Britain - A. Cyril Offord, A.J. Ward; from Romania - Pierre Segrescu, Simion Stoilov; from Switzerland Rolin Wavre; from the USA - John von Neumann; from the Soviet Union - Pavel S. Alexandrov, Nina Bari, Nikolai N. Bogolyubov, Lazar A. Lusternik, Nikolai Luzin, Dimitrii Menshov, S. Sobolev, and others. In addition to the frequent visits of other Polish mathematicians, e.g., from Warsaw - Karol Borsuk, Stefan Mazurkiewicz, Alfred Tarski, Wac³aw Sierpiñski; from Vilnius - Antoni Zygmund. Functional analysis was the main domain of Banach's scientific work, and his results with it brought him world fame, but he also made significant contributions in other areas of mathematics. These included his work on the theory of real functions, the theory of orthogonal series, and set theory. One of the most spectacular results of set theory was discovered jointly by Banach and Alfred Tarski (Teitelbaum) (1902-1983) and was published in the paper "Sur la décomposition des ensembles de parties respectivement congruentes" (On Dissection of Sets of Points into Equal Parts), in Volume VI of Fundamenta Mathematicae. In this surprising paper, written in French in 1924, the authors discovered that it is possible, by using very original operations, to decompose a ball into parts and reassemble the parts into two balls each identical to the original.,,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."

In this building the "Scottish Café" was located, from a contemporary photograph. |

[Photographed by Nikodem Miranowicz] |

Stanis³aw Mazur and Stanis³aw Ulam |

,,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."

Stanis³aw Mazur |

,,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."

Stanis³aw Ulam |

Formerly the Jan Kazimierz University, now the Ivan Franko University. |

[Photographed by Nikodem Miranowicz] |

Patriae decori civibus educandis (Educated people adorn their country) - Sentencia in frontis almae mater miae). |

[Photographed by Nikodem Miranowicz] |

John von Neumann |

Stanis³aw Mazur i Per Enflö |

[Photographed by Danuta Rago] |

From the left: £ucja Banach, Stefan Banach with son Stefan Jr., Marseilles (France), 1925. |

£ucja Banach with son Stefan Jr., Marseilles (France), 1925. |

At Steinhaus' direction the,,For Polish mathematicians theScottish Bookbecame 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 Wroc³aw and was named theNew Scottish Book. It was in use between 1946 and 1948 and fulfilled a role similar to that of the originalScottish Bookin Lvov. It was in the care of Professors Marczewski and Steinhaus. The tradition of theScottish Bookwas thus continued. However, the new version lacked the mythical and legendary qualities that have characterized the original, the unique and inimitable only one."

German troops entered Lvov during the night of 30 June/1 July 1941, three days after the Soviets had fled the city. Its inhabitants were still under the shock of the monstrous crime perpetrated by the NKGB [People's Commissariat for State Security - the Soviet secret police, intelligence and counterintelligence service] on several thousand prisoners. On 2 July, the Germans arrested Professor Kazimierz Bartel at the Polytechnic. During the night of 3/4 July, SS and Gestapo formations arrested a group of 22 professors of the Jan Kazimierz University, the Lvov Polytechnic and the Veterinary Academy. They shot them all on the Wulka Hills near Lvov at dawn on 4 July [16]. During the time between 1939 and 1945 the Polish School of Mathematics suffered very heavy losses. Many mathematicians were murdered. Among them were: Herman Auerbach (1901-1942); Kazimierz Bartel (1882-1941); Max Eidelheit (1910-1943); Antoni Hoborski (1879-1940); Stefan Kaczmarz (1895-1940); Stefan Jan Kempisty (1892-1940); Micha³ Kerner (1902-1943); Moj¿esz D. Kirszbraun (1903 or 1904-1942); Stanis³aw Marian Ko³odziejczyk (1907-1939); Adolf Lindenbaum (1901-1942); Antoni £omnicki (1881-1941); Józef Marcinkiewicz (1910-1940); Aleksander Rajchman (1890-1940); Stanis³aw Ruziewicz (1889-1941); Stanis³aw Saks (1897-1942); Juliusz Pawe³ Schauder (1899-1943); Józef Schreier (1908-1942); W³odzimierz Sto¿ek (1883-1941); and Zygmunt Zalcwasser (1898-1943). Some died from natural causes and war privations: Leon Chwistek (1884-1944); Samuel Dickstein (1851-1939); Stefan Mazurkiewicz (1888-1945); Witold Wilkosz (1891-1941); Stanis³aw Zaremba (1863-1942), and many others. During the German occupation of Lvov (1941 to 1944) Banach, together with numerous other academicians, various cultural figures, some members of the resistance, as well as school and university students, including his own son (a medical student), was able to secure employment only at the Institute for Typhus Studies. It operated under the direction of Professor Rudolf Weigl and included experiments that required the feeding of lice with human blood. It was a study of importance and urgent interest to the German military and, therefore, provided the participants with an invaluable document that afforded them protection from persecution by the occupiers. At the outbreak of World War II the Biology Faculty at the Jan Kazimierz University in Lvov, working in response to the needs of the Polish Government's Ministry of the Army, was producing large quantities of a vaccine against epidemic typhus. It was for this reason that, following the Soviet occupation of Lvov, on 22 November 1939, the Weigl Institute was incorporated into the newly created Institute of Bacteriology and Sanitary Science, and the Professor was ordered to continue with the production of the vaccine. Thereafter, with the exception of small quantities for civilian use, the rest was being shipped to the Soviet Union to protect the Red Army. In June 1941, the armed forces of the Third Reich attacked the Soviet Union and entered Lvov. The Institute, then called the Institute of Epidemiology and Sanitary Science, was renamed Institut für Fleckfieber und Virusforschung des OKH and, together with the Weigl Institute, came under the control of the Germans. Profesor Weigl was left in charge as Director of the Institute and required to continue, and even to increase, the production of the vaccine. A building on Potocki Street, at one time part of the Queen Jadwiga Grammar School, and more recently used by the Soviets, was provided for this end, and the entire production of the vaccine was earmarked for use by the German land armies. As mentioned by Professor Stefan Kryñski [17]:,,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."

Stefan Banach at 52 years of age, Lvov 1944 |

W³adys³aw Nikliborc (1889-1948) took selfless and very attentive care of the gravely ill Banach during the last few months of his life. Stefan Banach Jr recalled:,,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."

Stefan Banach, Lvov 1944 |

The house of the Riedl family, where Stefan Banach died. |

[This photograph is from the private collection of the Riedl family and used here with the permission of Prof. Tadeusz Riedl.] |

[This photograph is from the private collection of the Riedl family and used here with the permission of Prof. Tadeusz Riedl.] |

Medal of the Polish Academy of Sciences to commemorate the hundredth anniversary of the birth of Stefan Banach. |

Bust of Stefan Banach in the Stefan Banach International Mathematical Center in Warsaw. |

[Photographed by Nikodem Miranowicz] |

Statue of Stefan Banach in front of the Mathematics and Physics Institute of the Jagiellonian University in Krakow. |

Relief of Stefan Banach and stained glass
(Dariusz Jasiewicz's works) at the Stefan Banach High
School (Zespó³ Szkó³ Technicznych i Ogólnokszta³c±cych) in Jaros³aw. |

[Photographed by Adam Tomaszewski] |

Medal and diploma h.c. of the University of the Andes (Venezuela) for Stefan Banacha. |

Postage stamps with the images Polish mathematicians: Zygmunt Janiszewski, Stefan Banach, Stanis³aw Zaremba and Wac³aw Sierpiñski |

[from the collection of W³adys³aw Alexiewicz] |

Poster to commemorate the hundredth anniversary of the birth of Stefan Banach. |

Steinhaus finished his address at the Stefan Banach memorial conference with the words [6]:,,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."

Family mementoes of Stefan Banach at the home of Alina Filipowicz-Banach. |

Alina Filipowicz-Banach |

[Photographed by Adam Miranowicz] |

Stefan Banach Jr. with his wife, Alina Filipowicz-Banach, and their younger daughter Kasia. |

Stefan Banach Jr. and Alina Filipowicz-Banach |

Stefan Banach Jr. and Alina Filipowicz-Banach |

Stefan Banach Jr. |

Iwona Banach-Suchowierska - older daughter of Stefan Banach Jr. and granddaughter of Stefan Banach |

Joachim Stefan Suchowierski - son of Iwa Banach-Suchowierska, great-grandson of Stefan Banach. |

Kasia Banach - younger daughter of Stefan Banach Jr. with her daughters. |

Georgia and Audrey Salas - daughters of Kasa Banach, granddaughter of Stefan Banach |

[These photographs are from the private collection of the Banach family and used here with the permission of Prof. Alina Filipowicz-Banach.] |

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On 23 Jan 2012, 15:47.