Editing Stefan Banach (section)

==Life==

===Early life===
Stefan Banach was born on 30 March 1892 at St. Lazarus General Hospital in [[Kraków]], then part of the [[Austria-Hungary|Austro-Hungarian Empire]], into a [[Gorals|Góral]] [[Roman Catholic]] family,<ref name=SBHomePage /> and was subsequently baptised by his father.<ref name=MacTutor />{{sfn|Stachura|1999|p=51}} Banach's parents were Stefan Greczek and Katarzyna [[Banach]], both natives of the [[Podhale]] region.{{sfn|Waksmundzka-Hajnos|2006|p=16}}{{sfn|Duda|2009|p=29}} Greczek was a soldier in the [[Austro-Hungarian Army]] stationed in Kraków. Little is known about Banach's mother.<ref name=MacTutor /> According to his [[Baptism|baptismal certificate]], she was born in [[Borówna]] and worked as a domestic helper.{{sfn|Duda|2009|p=29}}

Unusually, Stefan's surname was his mother's instead of his father's, though he received his father's given name, Stefan. Military regulations did not permit soldiers of Stefan Greczek's rank to [[marriage|marry]]; he was a [[private (rank)|private]] and as the mother was too poor to support the child, the couple decided that he should be reared by family and friends.<ref name="Kałuża-2–4">{{Harvnb|Kałuża|1996|pp=2–4}}</ref> 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.<ref name="Kałuża-1-3">{{Harvnb|Kałuża|1996|pp=1–3}}</ref> 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.<ref name="Kałuża-3">{{Harvnb|Kałuża|1996|p=3}}</ref>

In 1902, Banach, aged 10, enrolled in Kraków's ''IV Gymnasium'' (also known as the ''[[Jan Albin Goetz|Goetz Gymnasium]]''). While the school specialized in the [[humanities]], Banach and his best friend [[Witold Wilkosz|Witold Wiłkosz]] (also a future mathematician) spent most of their time working on mathematics problems during breaks and after school.<ref name="Kałuża-137">{{Harvnb|Kałuża|1996|p=137}}</ref> Later in life Banach credited Dr. Kamil Kraft, the mathematics and physics teacher at the school, with kindling his interests in mathematics.<ref name="rem4"/> While Banach was a diligent student he did, on occasion, receive low grades (he failed Greek during his first semester at the school) and later spoke critically of the school's math teachers.<ref name="Kałuża-3-4">{{Harvnb|Kałuża|1996|pp=3–4}}</ref>

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.<ref name="rem5"/> At some point he also attended [[Jagiellonian University]] in Kraków on a part-time basis. As Banach had to earn money to support his studies it was not until 1914 that he finally, at age 22, passed his high school graduation exams.<ref name="Kałuża-13">{{Harvnb|Kałuża|1996|p=13}}</ref>

When [[World War I]] broke out, Banach was excused from military service due to his left-handedness and poor vision. When the [[Imperial Russian Army|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 (mathematician)|Stanisław Zaremba]] and [[Kazimierz Żorawski]], but little is known of that period of his life.<ref name="Kałuża-16">{{Harvnb|Kałuża|1996|p=16}}</ref>

===Discovery by Steinhaus===
[[File:Otto Nikodym Stefan Banach Memorial Bench Krakow Poland.jpg|thumb|200px|[[Otto Nikodym]] and Stefan Banach Memorial Bench in [[Kraków]], [[Poland]] (sculpted by Stefan Dousa)]]
In 1916, in Kraków's ''[[Planty Park|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]].<ref name="rem6" /> Steinhaus became fascinated with the self-taught young mathematician. The encounter resulted in a long-lasting collaboration and friendship. In fact, soon after the encounter Steinhaus invited Banach to solve some problems he had been working on but which had proven difficult. Banach solved them within a week and the two soon published their first joint work (''On the Mean Convergence of Fourier Series''). Steinhaus, Banach and Nikodym, along with several other Kraków mathematicians ([[Władysław Ślebodziński]], [[Leon Chwistek]], Alfred Rosenblatt{{sfn | Ciesielska | Maligranda | 2019 | pp=57–108}} and [[Włodzimierz Stożek]]) also established a mathematical society, which eventually became the [[Polish Mathematical Society]].<ref name="Kaluza-23"/> The society was officially founded on 2 April 1919. It was also through Steinhaus that Banach met his future wife, Łucja Braus.

===Interbellum===
[[File:Lwow - Kawiarnia Szkocka.jpg|thumb|200px|[[Scottish Café]], meeting place of many famous Lwów mathematicians]]
Steinhaus introduced Banach to academic circles and substantially accelerated his career. After [[Second Polish Republic|Poland regained independence]] in 1918, Banach was given an assistantship at the Lwów Polytechnic. Steinhaus' backing also allowed him to receive a [[doctorate]] without actually graduating from a university. The doctoral thesis, accepted by [[Lviv University|King John II Casimir University of Lwów]] in 1920<ref name="Jahnke"/> and published in 1922,<ref name="Fundamenta"/> included the basic ideas of functional analysis, which was soon to become an entirely new branch of mathematics. In his dissertation, written in 1920, he axiomatically defined what is today called a Banach space.<ref>{{cite web | url=https://krakow1.one/uk/eternal/matematychnyj-mist-mizh-krakovom-i-lvovom-yak-stefan-banah-stav-odnym-iz-najvelychnishyh-matematykiv-stolittya-2181 | title=Математичний міст між Краковом і Львовом: як Стефан Банах став одним із найвеличніших математиків століття - krakow1.one | date=16 November 2022 }}</ref> 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 [[Lviv University|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 space|linear]]-[[metric space]]. First published in Polish in 1931,<ref name="Teoria"/> the next year it was also translated into French and gained wider recognition in European academic circles.<ref name="Theorie"/> The book was also the first in a long series of mathematics monographs edited by Banach and his circle. On 17 June 1924, Banach became a [[Corresponding member|correspondence member]] of the [[Polish Academy of Learning|Polish Academy of Sciences and Fine Arts]] in Kraków.

===World War II===
[[File:Cmentarz-Lyczakowski-Grob Banacha.jpg|thumb|left|200px|Banach's grave, [[Lychakiv Cemetery]], [[Lviv]] (''[[Lwów]]'', in [[Polish language|Polish]])]]
After the [[invasion of Poland]] by [[Nazi Germany]] and the [[Soviet Union]], Lwów came under the control of the [[Soviet Union]] for almost two years. Banach, from 1939 a [[corresponding member]] of the [[Academy of Sciences of Ukraine]], and on good terms with [[Soviet Union|Soviet]] mathematicians,<ref name=MacTutor /> had to promise to learn Ukrainian to be allowed to keep his chair and continue his academic activities.<ref name="Urbaniak"/> In 1940 he was appointed by the Soviets as a member of the [[Lviv City Council]]. After the German takeover of Lwów in 1941 during [[Operation Barbarossa]], all universities were closed and Banach, along with many colleagues and his son, was employed as a [[Feeder of lice|lice feeder]] at Professor [[Rudolf Weigl]]'s [[Typhus]] Research Institute. Employment in Weigl's Institute provided many unemployed university professors and their associates protection from random arrest and deportation to [[Nazi concentration camps]].

After the Soviet [[Red Army]] recaptured [[Lwów|Lviv]] in the [[Lvov–Sandomierz Offensive]] of 1944, Banach returned to the university and helped re-establish it after the war years. However, because the Soviets were [[Polish population transfers (1944–1946)|deporting Poles]] from annexed formerly Polish [[Kresy|eastern territories]], Banach began preparing to leave the city and settle in [[Kraków]], Poland, where he had been promised a chair at the [[Jagiellonian University]].<ref name=MacTutor /> He was also considered a candidate for Minister of Education of Poland.<ref name="remark"/> In January 1945, he was diagnosed with [[lung cancer]] and was permitted to stay in Lwów. He died on 31 August 1945, aged 53. His funeral at the [[Lychakiv Cemetery]] (''Cmentarz Łyczakowski'') was attended by hundreds of people.<ref name="remark"/>