Stefan Banach: Google Doodle about the Polish mathematician

The great Polish mathematician Stefan Banach (Stefan Banach) is honored by Google with a Google Doodle.

Stefan Banach is considered one of the most important and influential mathematicians of the 20th century in the world. He was the founder of modern functional analysis, and an original member of the Lviv School of Mathematics. His major work was the 1932 book, Théorie des Operations Linéaires (Theory of Linear Functions), the first monograph on the general theory of functional analysis.

Banach was born in Krakow. He attended 4th high school, where he worked on math problems with his friend, Witold Wilkos. After graduating in 1910, he moved to Lvov (now Lviv). However, during World War I, he returned to Krakow, where he befriended Hugo Steinhaus. After Banach solved some mathematical problems that Steinhaus found difficult, they published their first joint paper. In 1919, with several other mathematicians, Banach formed a mathematical society. In 1920 he received a position as an assistant at the Polytechnic of Lvov. He soon became a professor at the Polytechnic and a member of the Polish Academy of Learning. He organized the Lviv School of Mathematics. Around 1929 he began writing Théorie des Operations Lineaires.

After the outbreak of World War II, in September 1939, Lviv was occupied by the Soviet Union. Banach became dean of the Department of Mathematics and Physics at the University of Lviv. In 1941, when the Germans occupied Lwów, all higher education institutions were closed to Poles. As a result, Banach was forced to earn a living as a lice blood feeder at the Rudolf Weigl Institute for Typhoid and Virus Research. While the job involved the risk of contracting typhus, it protected him from being sent to forced labor in Germany and from other forms of repression. When the Soviets recaptured Lviv in 1944, Banach re-founded the University. However, as the Soviets removed Poles from the former Polish territories annexed by the Soviet Union, Banach prepared to return to Krakow. Before he could do so, he died in August 1945, having been diagnosed seven months earlier with lung cancer.

Some of the remarkable mathematical concepts named after Banach include: Banach space, Banach algebra, Banach measure, Banach-Tarski paradox, Hahn-Banach theorem, Banach-Steinhaus theorem, Banach-Mazur game,[20] Banach-Alaoglou theorem and Banach fixed point theorem.

Banach’s thesis, completed in 1920 and published in 1922, formally axiomized the concept of a complete normalized vector space and laid the foundation for the field of functional analysis. In this work, Banach called such spaces “spaces of order E”, but in his 1932 book, Théorie des opérations linéaires, he changed the terminology and referred to them as “spaces of type B”, which probably contributed to the subsequent naming of these spaces from his name.[23] The theory of what became known as a Banach space had earlier work by the Hungarian mathematician Friges Ries (published in 1916) and contemporary contributions by Hans Hahn and Norbert Wiener. In fact, for a short period, complete normal linear spaces were referred to as “Banach-Wiener” spaces in the mathematical literature, based on terminology introduced by Wiener himself. However, because Wiener’s work on the subject was limited, the established name became Banach space only.

Similarly, the Banach fixed point theorem, based on earlier methods developed by Emile Picard, was included in his thesis and later extended by his students (for example in the Banach–Saunder theorem) and other mathematicians (notably Luitzen Ebertus Jan Brauer) . The theorem did not require linearity of the space and applied to any complete Cosy space (in particular any complete metric space).

The Hahn-Banach theorem is one of the fundamental theorems of functional analysis.

In 1992, the Institute of Mathematics of the Polish Academy of Sciences established a special Stefan Banach Medal for outstanding achievements in the mathematical sciences.

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