Stefan Banach was born on March 30, 1892 in Krakow, in what was at the time part of Austria-Hungary, but now is Poland. He was the illegitimate son of a tax official. Banach attended the primary school and then the gymnasium in Krakow, showing great talent in mathematics. He then attended the Technical University at Lyvov, receiving a degree in engineering in 1914.
Banach's serious work in mathematics began in 1916 when he met and began collaborating with Hugo Steinhaus. Banach quickly produced a series of important papers and was given an assistantship to the Lyvov Technical University. In spite of the fact that his undergraduate degree was not in mathematics, Banach was awarded the doctoral degree in mathematics in 1920. By 1924 he was a full professor.
Banach's doctoral dissertation is considered the real beginning of functional analysis. In it he defined the abstract spaces that are now known as Banach spaces in his honor (complete, normed vector spaces). Many other fundamental results in functional analysis also bear his name: the Hahn-Banach theorem, the Banach-Steinhaus theorem, the Banach fixed point theorem, and the Banach-Tarski decomposition. Banach and Steinhaus were co-founders of the journal Studia Mathematica, devoted to functional analysis.
Banach was known for his cheerful, sociable manner and his love of the local cafés, where in fact he did much of his mathematical work. During World War II, Lvov was occupied first by Soviet forces, then by German forces, and finally again by Soviet forces. Banach suffered during the German occupation, assigned to a job feeding lice in an institute studying infectious diseases. He died of lung cancer on August 31, 1945 in Lvov.