Banach - Definition and Overview

Stefan Banach (March 30, 1892 in Kraków, Poland–August 31, 1945 in L'viv, Ukraine), was a Polish mathematician, one of the moving spirits of the Lwów School of Mathematics in pre-war Poland. He was largely self-taught in mathematics; his genius was accidentally discovered by Hugo Steinhaus.

When World War II began, Banach was President of the Polish Mathematical Society and a full professor of University of Lwów. Being a corresponding member of Academy of Sciences of the Ukrainian SSR, and otherwise on good terms with Soviet mathematicians, he was allowed to keep his chair despite the Soviet occupation, from 1939, of the city. Banach survived the subsequent brutal German occupation from 1941, earning a living by feeding lice on his blood in typhoid fever research conducted under Prof. Rudolf Weigl. His health declined during the occupation, and he developed lung cancer. After the war Lwów was incorporated into the Soviet Union, and Banach died there before he could be repatriated to Poland. He is buried at the Lychakivskiy Cemetery.

Trivia

Théorie des opérations linéaires (Teoria operacji liniowych, 1932) is regarded as Banach's most influential work. He also initiated and edited the Studia Mathematica series.

Stanisław Marcin Ulam, another mathematician of the Lwów School of Mathematics, in his autobiography, attributes this to Banach:

"Good mathematicians see analogies. Great mathematicians see analogies between analogies."

Banach was the founder of functional analysis; he also made important contributions to the theory of vector spaces, measure theory, set theory and other branches of mathematics.

See also

• Banach space
• Banach algebra
• Banach-Steinhaus theorem
• Banach-Tarski paradox
• Hahn-Banach theorem
• Banach fixed point theorem