An overheard phrase on a park bench launched Stefan Banach's mathematical career
Strolling through Kraków's Planty park in 1916, the mathematician Hugo Steinhaus was startled to hear two young men on a bench discussing the Lebesgue integral, then a fairly new idea. He walked over, met a self-taught Stefan Banach, and began a partnership that helped create a whole branch of mathematics.
Banach's start had been anything but privileged. Born in Kraków on 30 March 1892, he took his mother's surname because his father, a private in the Austro-Hungarian army, was not permitted to marry. He was raised by a grandmother and then by a foster family. At school he and his friend Witold Wiłkosz spent breaks solving maths problems, though he failed Greek in his first term.
He then drifted. Believing there was nothing left to discover in mathematics, he enrolled in engineering at the Lwów Polytechnic, and during the First World War, excused from service by left-handedness and weak eyesight, he tutored, worked in a bookshop and ran a road-building crew. Steinhaus changed that trajectory, setting him problems and opening academic doors. After Poland regained independence in 1918, Banach got an assistant's post, and he was granted a doctorate without ever finishing a university degree.
That 1920 thesis defined what are now called Banach spaces and laid the foundations of functional analysis. He named them class E spaces; his 1932 book, the first monograph on the general theory, called them spaces of type B, which probably helped attach his name. The thesis also contained his fixed-point theorem. Around him grew the Lwów School of Mathematics, whose members famously met at the Scottish Café, and in 1929 they launched the journal Studia Mathematica. Other ideas bearing his name include the Banach–Tarski paradox and the Hahn–Banach theorem.
The Second World War brought Soviet and then German occupation of Lwów. When the Red Army returned in 1944 Banach helped reopen the university and prepared to move to Kraków, where a chair awaited him, but he died on 31 August 1945. The Polish Mathematical Society created a prize in his name in 1946, and a minor planet has carried his name since 2001.
Source: Stefan Banach
