Stefan Banach (Polish:[ˈstɛfan ˈbanax]ⓘ; 30 March 1892 – 31 August 1945) was a Polishmathematician[1] who is generally considered one of the 20th century's most important and influential mathematicians.[2] He was the founder of modernfunctional analysis,[1] and an original member of theLwów School of Mathematics. His major work was the 1932 book,Théorie des opérations linéaires (Theory of Linear Operations), the first monograph on the general theory of functional analysis.[3]
Unusually, Stefan's surname was his mother's instead of his father's, though he received his father's given name, Stefan. Military regulations did not permit soldiers of Stefan Greczek's rank tomarry; he was aprivate and as the mother was too poor to support the child, the couple decided that he should be reared by family and friends.[9] Stefan spent the first few years of his life with his grandmother, but when she was taken ill, Greczek arranged for his son to be raised by Franciszka Płowa and her niece Maria Puchalska in Kraków. Young Stefan came to regard Franciszka as his foster mother and Maria as his older sister.[10] In his early years Banach was tutored by Juliusz Mien, a French intellectual and friend of the Płowa family, who had emigrated to Poland and supported himself with photography and translations of Polish literature into French. Mien taught Banach French and most likely encouraged him in his early mathematical pursuits.[11]
In 1902, Banach, aged 10, enrolled in Kraków'sIV Gymnasium (also known as theGoetz Gymnasium). While the school specialized in thehumanities, Banach and his best friendWitold Wiłkosz (also a future mathematician) spent most of their time working on mathematics problems during breaks and after school.[12] Later in life Banach credited Dr. Kamil Kraft, the mathematics and physics teacher at the school, with kindling his interests in mathematics.[13] While Banach was a diligent student he did, on occasion, receive low grades (he failed Greek during his first semester at the school) and later spoke critically of the school's math teachers.[14]
After obtaining hismatura (high school degree) at age 18 in 1910, Banach moved toLwów (today calledLviv) with the intention of studying at theLwów Polytechnic. He initially chose engineering as his field of study since at the time he was convinced that there was nothing new to discover in mathematics.[15] At some point he also attendedJagiellonian University in Kraków on a part-time basis. As Banach had to earn money to support his studies it was not until 1914 that he finally, at age 22, passed his high school graduation exams.[16]
WhenWorld War I broke out, Banach was excused from military service due to his left-handedness and poor vision. When theRussian Army opened its offensive toward Lwów, Banach left for Kraków, where he spent the rest of the war. He made his living as atutor at the local schools, worked in a bookstore and as a foreman of a road building crew. He attended some lectures at theJagiellonian University at that time, including those of the famous Polish mathematiciansStanisław Zaremba andKazimierz Żorawski, but little is known of that period of his life.[17]
In 1916, in Kraków'sPlanty park, Banach encountered ProfessorHugo 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 asOtto Nikodym.[18] 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[19] andWłodzimierz Stożek) also established a mathematical society, which eventually became thePolish Mathematical Society.[20] The society was officially founded on 2 April 1919. It was also through Steinhaus that Banach met his future wife, Łucja Braus.
Scottish Café, meeting place of many famous Lwów mathematicians
Steinhaus introduced Banach to academic circles and substantially accelerated his career. AfterPoland regained independence in 1918, Banach was given an assistantship at the Lwów Polytechnic. Steinhaus' backing also allowed him to receive adoctorate without actually graduating from a university. The doctoral thesis, accepted byKing John II Casimir University of Lwów in 1920[21] and published in 1922,[22] included the basic ideas of functional analysis, which was soon to become an entirely new branch of mathematics. In his dissertation, written in 1920, he axiomatically defined what is today called a Banach space.[23] The thesis was widely discussed in academic circles and allowed him in 1922 to become a professor at the Lwów Polytechnic. Initially an assistant to ProfessorAntoni Łomnicki, in 1927, Banach received his own chair. In 1924 he was accepted as a member of thePolish Academy of Learning. At the same time, from 1922, Banach also headed the second Chair of Mathematics atUniversity of Lwów.
Young and talented, Banach gathered around him a large group of mathematicians. The group, meeting in theScottish Café, soon gave birth to the "Lwów School of Mathematics". In 1929 the group began publishing its own journal,Studia Mathematica, devoted primarily to Banach's field of study—functional analysis. Around that time, Banach also began working on his best-known work, the first monograph on the general theory oflinear-metric space. First published in Polish in 1931,[24] the next year it was also translated into French and gained wider recognition in European academic circles.[25] The book was also the first in a long series of mathematics monographs edited by Banach and his circle. On 17 June 1924, Banach become acorrespondence member of thePolish Academy of Sciences and Fine Arts in Kraków.
After theinvasion of Poland byNazi Germany and theSoviet Union, Lwów came under the control of theSoviet Union for almost two years. Banach, from 1939 acorresponding member of theAcademy of Sciences of Ukraine, and on good terms withSoviet mathematicians,[5] had to promise to learn Ukrainian to be allowed to keep his chair and continue his academic activities.[26] After the German takeover of Lwów in 1941 duringOperation Barbarossa, all universities were closed and Banach, along with many colleagues and his son, was employed as alice feeder at ProfessorRudolf Weigl'sTyphus Research Institute. Employment in Weigl's Institute provided many unemployed university professors and their associates protection from random arrest and deportation toNazi concentration camps.
After the SovietRed Army recapturedLviv in theLvov–Sandomierz Offensive of 1944, Banach returned to the university and helped re-establish it after the war years. However, because the Soviets weredeporting Poles from annexed formerly Polisheastern territories, Banach began preparing to leave the city and settle inKraków, Poland, where he had been promised a chair at theJagiellonian University.[5] He was also considered a candidate for Minister of Education of Poland.[27] In January 1945, he was diagnosed withlung cancer and was permitted to stay in Lwów. He died on 31 August 1945, aged 53. His funeral at theLychakiv Cemetery (Cmentarz Łyczakowski) was attended by hundreds of people.[27]
Banach's dissertation, completed in 1920 and published in 1922, formally axiomatized the concept of acompletenormed vector space and laid the foundations for the area offunctional analysis. In this work Banach called such spaces"class E-spaces", but in his 1932 book,Théorie des opérations linéaires, he changed terminology and referred to them as "spaces of type B", which most likely contributed to the subsequenteponymous naming of these spaces after him.[28] The theory of what came to be known asBanach spaces had antecedents in the work of the Hungarian mathematicianFrigyes Riesz (published in 1916) and contemporaneous contributions fromHans Hahn andNorbert Wiener.[21] For a brief period in fact, complete normed linear spaces were referred to as "Banach–Wiener" spaces in mathematical literature, based on terminology introduced by Wiener himself. However, because Wiener's work on the topic was limited, the established name became justBanach spaces.[28]
In 2012, theNational Bank of Poland celebrated the mathematician's achievements by issuing a series of commemorative coins designed by Robert Kotowicz (golden 200-zloty coin, silver 10-zloty coin andNordic Gold 2-zloty coin).[32]
In 2016, a commemorative bench featuring Banach andOtto Nikodym was unveiled in Kraków'sPlanty Park on the 100th anniversary of the conversation the two mathematicians held when they first metHugo Steinhaus, which proved instrumental in the development of his scientific career.[33]
In 2021, one of the episodes of Polish documentary TV seriesGeniusze i marzyciele (Geniuses and Dreamers) aired onTVP1 and TVP Dokument channels was devoted to Stefan Banach.[34]
In 2022,Google Doodle commemorated the 100th anniversary of Banach receiving his title of professor.[35]
^Stefan Banach (1922). "Sur les opérations dans les ensembles abstraits et leur application aux équations integrals (On operations in the abstract sets and their application to integral equations)".Fundamenta Mathematicae (in French and Polish).3.
Chemla, Karine; Chorla, Renaud; Rabouin, David (2016).The Oxford Handbook of Generality in Mathematics and the Sciences. Oxford: University Press.ISBN9780198777267.
