30 March 2024

Today is the birthday of Stefan Banach, one of the most important and influential mathematicians of the 20th century. In the reference database “Zentralblatt für Mathematik”, covering mathematical works published worldwide in the last 150 years, Banach’s name appears most frequently in the titles – over 27 thousand times.

Stefan Banach was born on March 30, 1892, in the small town of Krakow, Poland. From an early age, Banach displayed a remarkable aptitude for mathematics, and it was clear that he possessed an extraordinary analytical mind. Born into a poor family, Banach faced numerous numerous challenges and obstacles, but his passion for mathematics propelled him forward. Even before passing his matriculation exam, he was giving private lessons to suppurt himself. After passing the exam, he worked in a bookshop, but he devoted every free moment to mathematics.

Banach’s brilliance was recognized by a professor at the Jagiellonian University, where he began his formal studies in mathematics. It happend by accident in 1916, in Kraków’s Planty park, Banach encountered Professor Hugo Steinhaus, one of the renowned mathematicians of the time. According to Steinhaus, while he was strolling through the gardens he was surprised to overhear the term “Lebesgue integral” (Lebesgue integration was at the time still a fairly new idea in mathematics) and walked over to investigate. As a result, he met Banach, as well as Otto Nikodym. Steinhaus became fascinated with the self-taught young mathematician. The encounter resulted in a long-lasting collaboration and friendship. In fact, soon after the encounter Steinhaus invited Banach to solve some problems he had been working on but which had proven difficult. Banach solved them within a week and the two soon published their first joint work (On the Mean Convergence of Fourier Series). Steinhaus, Banach and Nikodym, along with several other Kraków mathematicians (Władysław Ślebodziński, Leon Chwistek, Alfred Rosenblatt and Włodzimierz Stożek) also established a mathematical society, which eventually became the Polish Mathematical Society.

In 1920, Professor Antoni Łomnicki appointed Banach to be his assistant at the Lviv Polytechnic. He did so despite the fact that Banach had not completed his university studies. This proved to be the start of Banach’s brilliant career which then progressed quickly.

According to his words, not only had Banach not graduated from a university but he also obtained his PhD degree in the 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.

Stefan Banach quickly became an influential figure in the Polish mathematical community and co-founded the “Lwow School of Mathematics” in 1920. This school played a significant role in the development of functional analysis, a field Banach became best-known for.