Stefan Banach

Stefan Banach
Born	(1892-03-30)30 March 1892 Kraków, Austria-Hungary (today Poland)
Died	31 August 1945(1945-08-31) (aged 53) Lviv, Ukrainian SSR, Soviet Union (today Ukraine)
Alma mater	Technical University of Lwów
Known for	Banach space Functional analysis Banach algebra Banach measure Banach–Tarski paradox Banach fixed-point theorem Banach–Steinhaus theorem Banach–Mazur theorem Banach–Schauder theorem Hahn–Banach theorem Banach–Alaoglu theorem Banach–Stone theorem Banach manifold Banach bundle Surjection of Fréchet spaces
Awards	Membership: Polish Academy of Learning
Scientific career
Fields	Mathematics
Institutions	University of Lwów
Doctoral advisors	Hugo Steinhaus Kazimierz Twardowski
Doctoral students	Stanisław Mazur
Other notable students	Józef Schreier Stanislaw Ulam

Stefan Banach (Polish: [ˈstɛfan ˈbanax] ^ⓘ; 30 March 1892 – 31 August 1945) was a Polish mathematician^[1] who is generally considered one of the 20th century's most important and influential mathematicians.^[2] He was the founder of modern functional analysis,^[1] and an original member of the Lwów 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]

Born in Kraków to a family of Goral descent, Banach showed a keen interest in mathematics and engaged in solving mathematical problems during school recess. After completing his secondary education, he befriended Hugo Steinhaus, with whom he established the Polish Mathematical Society in 1919 and later published the scientific journal Studia Mathematica. In 1920, he received an assistantship at the Lwów Polytechnic, subsequently becoming a professor in 1922 and a member of the Polish Academy of Learning in 1924. Banach was also a co-founder of the Lwów School of Mathematics, a school of thought comprising some of the most renowned Polish mathematicians of the interwar period (1918–1939).

Some of the notable mathematical concepts that bear Banach's name include Banach spaces, Banach algebras, Banach measures, the Banach–Tarski paradox, the Hahn–Banach theorem, the Banach–Steinhaus theorem, the Banach–Mazur game, the Banach–Alaoglu theorem, and the Banach fixed-point theorem.