Stefan Banach

Early life Stefan Banach was born on 30 March 1892 at St. Lazarus General Hospital in Kraków, then part of the Austro-Hungarian Empire, into a Góral Roman Catholic family, Stefan spent the first few years of his life with his grandmother, but when she was taken ill, Greczek arranged for his son to be raised by Franciszka Płowa and her niece Maria Puchalska in Kraków. Young Stefan came to regard Franciszka as his foster mother and Maria as his older sister. In his early years Banach was tutored by Juliusz Mien, a French intellectual and friend of the Płowa family, who had emigrated to Poland and supported himself with photography and translations of Polish literature into French. Mien taught Banach French and most likely encouraged him in his early mathematical pursuits. In 1902, Banach, aged 10, enrolled in Kraków's IV Gymnasium (also known as the Goetz Gymnasium). While the school specialized in the humanities, Banach and his best friend Witold Wiłkosz (also a future mathematician) spent most of their time working on mathematics problems during breaks and after school. Later in life Banach credited Dr. Kamil Kraft, the mathematics and physics teacher at the school, with kindling his interests in mathematics. After obtaining his matura (high school degree) at age 18 in 1910, Banach moved to Lwów (today called Lviv) with the intention of studying at the Lwów Polytechnic. He initially chose engineering as his field of study since at the time he was convinced that there was nothing new to discover in mathematics. When World War I broke out, Banach was excused from military service due to his left-handedness and poor vision. When the Russian Army opened its offensive toward Lwów, Banach left for Kraków, where he spent the rest of the war. He made his living as a tutor at the local schools, worked in a bookstore and as a foreman of a road building crew. He attended some lectures at the Jagiellonian University at that time, including those of the famous Polish mathematicians Stanisław Zaremba and Kazimierz Żorawski, but little is known of that period of his life. Discovery by Steinhaus and Stefan Banach Memorial Bench in Kraków, Poland (sculpted by Stefan Dousa) In 1916, in Kraków's Planty park, Banach encountered Professor Hugo Steinhaus, one of the renowned mathematicians of the time. According to Steinhaus, while he was strolling through the gardens he was surprised to overhear the term "Lebesgue integral" (Lebesgue integration was at the time still a fairly new idea in mathematics) and walked over to investigate. As a result, he met Banach, as well as Otto Nikodym. The thesis was widely discussed in academic circles and allowed him in 1922 to become a professor at the Lwów Polytechnic. Initially an assistant to Professor Antoni Łomnicki, in 1927, Banach received his own chair. In 1924 he was accepted as a member of the Polish Academy of Learning. At the same time, from 1922, Banach also headed the second Chair of Mathematics at University of Lwów. Young and talented, Banach gathered around him a large group of mathematicians. The group, meeting in the Scottish Café, soon gave birth to the "Lwów School of Mathematics". In 1929 the group began publishing its own journal, Studia Mathematica, devoted primarily to Banach's field of study—functional analysis. Around that time, Banach also began working on his best-known work, the first monograph on the general theory of linear-metric space. First published in Polish in 1931, ==Contributions==

Banach's dissertation, completed in 1920 and published in 1922, formally axiomatized the concept of a complete normed vector space and laid the foundations for the area of functional analysis. In this work Banach called such spaces "class E-spaces", but in his 1932 book, Théorie des opérations linéaires, he changed terminology and referred to them as "spaces of type B", which most likely contributed to the subsequent eponymous naming of these spaces after him. The theory of what came to be known as Banach spaces had antecedents in the work of the Hungarian mathematician Frigyes Riesz (published in 1916) and contemporaneous contributions from Hans Hahn and Norbert Wiener. For a brief period in fact, complete normed linear spaces were referred to as "Banach–Wiener" spaces in mathematical literature, based on terminology introduced by Wiener himself. However, because Wiener's work on the topic was limited, the established name became just Banach spaces. Likewise, Banach's fixed point theorem, based on earlier methods developed by Charles Émile Picard, was included in his dissertation, and was later extended by his students (for example in the Banach–Schauder theorem) and other mathematicians (in particular Brouwer and Poincaré and Birkhoff). The theorem did not require linearity of the space, and applied to any complete Cauchy space (in particular to any complete metric space). The Hahn–Banach theorem is one of the fundamental theorems of functional analysis. Further theorems related to Banach are: • Banach–Tarski paradox • Banach–Steinhaus theorem • Banach–Alaoglu theorem • Banach–Stone theorem ==Recognition==

In 1946, the Stefan Banach Prize (Polish: Nagroda im. Stefana Banacha) was established by the Polish Mathematical Society. In 1992, the Institute of Mathematics of the Polish Academy of Sciences established a special Stefan Banach Medal for outstanding achievements in mathematical sciences. Since 2009, the International Stefan Banach Prize has been conferred by the Polish Mathematical Society to mathematicians for best doctoral dissertations in the mathematical sciences with the objective to "promote and financially support the most promising young researchers". Stefan Banach is the patron of a number of schools and streets including in Warsaw, Lviv, Świdnica, Toruń and Jarosław. In 2001, a minor planet 16856 Banach, discovered by Paul Comba in 1997, was named after him. In 2012, the National Bank of Poland celebrated the mathematician's achievements by issuing a series of commemorative coins designed by Robert Kotowicz (golden 200-zloty coin, silver 10-zloty coin and Nordic Gold 2-zloty coin). In 2016, a commemorative bench featuring Banach and Otto Nikodym was unveiled in Kraków's Planty Park on the 100th anniversary of the conversation the two mathematicians held when they first met Hugo Steinhaus, which proved instrumental in the development of his scientific career. In 2019, Polish entomologist Marcin Kamiński named a newly discovered species of South African darkling beetle, Machleida banachi, in honor of the mathematician Stefan Banach and his contributions to science. In 2021, one of the episodes of Polish documentary TV series Geniusze i marzyciele (Geniuses and Dreamers) aired on TVP1 and TVP Dokument channels was devoted to Stefan Banach. In 2022, Google Doodle commemorated the 100th anniversary of Banach receiving his title of professor. ==Quotes==

Stanislaw Ulam, another mathematician of the Lwów School of Mathematics, in his autobiography, quotes Banach as saying: Hugo Steinhaus said of Banach: == See also ==