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Stefan Banach
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Life
Early life
Stefan Banach was born on 30 March 1892 at St. Lazarus General Hospital in KrakÃ³w, then part of the Austro-Hungarian Empire, into a GÃ³ral Roman Catholic familyWEB,weblink Home Page of Stefan Banach, kielich.amu.edu.pl, 19 August 2017, and was subsequently baptised by his father, while his mother abandoned him upon this event and her identity is ambiguous.WEB,weblink Banach biography, www-history.mcs.st-andrews.ac.uk, 19 August 2017, Peter Stachura, Poland in the Twentieth Century, Springer (1999), p. 51 Banach's parents were Stefan Greczek and Katarzyna Banach, both natives of the Podhale region.JOURNAL, Duda, Roman, Facts and Myths about Stefan Banach, Newsletter of the European Mathematical Society, 2009, 71, 29,weblink EMS, Greczek was a soldier in the Austro-Hungarian Army stationed in KrakÃ³w. Little is known about Banach's mother. According to his baptismal certificate, she was born in BorÃ³wna and worked as a domestic help.Unusually, Stefan's surname was his mother's instead of his father's, though he received his father's given name, Stefan. Since Stefan Greczek was a private and was prevented by military regulations from marrying, and the mother was too poor to support the child, the couple decided that he should be reared by family and friends.{{Harvnb|KaÅ‚uÅ¼a|1996|pp=2â€“4}} Stefan spent the first few years of his life with his grandmother, but when she took ill Greczek arranged for his son to be raised by Franciszka PÅ‚owa and her niece Maria Puchalska in KrakÃ³w. Young Stefan would regard Franciszka as his foster mother and Maria as his older sister.{{Harvnb|KaÅ‚uÅ¼a|1996|pp=1â€“3}} In his early years Banach was tutored by Juliusz Mien, a French intellectual and friend of the PÅ‚owa 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.{{Harvnb|KaÅ‚uÅ¼a|1996|p=3}}In 1902 Banach, aged 10, enrolled in KrakÃ³w's IV Gymnasium (also known as the Goetz Gymnasium). While the school specialized in the humanities, Banach and his best friend Witold WiÅ‚kosz (also a future mathematician) spent most of their time working on mathematics problems during breaks and after school.{{Harvnb|KaÅ‚uÅ¼a|1996|p=137}} Later in life Banach would credit Dr. Kamil Kraft, the mathematics and physics teacher at the gymnasium with kindling his interests in mathematics. While generally Banach was a diligent student he did on occasion receive low grades (he failed Greek during his first semester at the gymnasium) and would later speak critically of the school's math teachers.{{Harvnb|KaÅ‚uÅ¼a|1996|pp=3â€“4}}After obtaining his matura (high school degree) at age 18 in 1910, Banach moved to LwÃ³w with the intention of studying at the LwÃ³w 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. At some point he also attended Jagiellonian University in KrakÃ³w 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.{{Harvnb|KaÅ‚uÅ¼a|1996|p=13}}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 LwÃ³w, Banach left for KrakÃ³w, where he spent the rest of the war. He made his living as a tutor at the local gymnasiums, worked in a bookstore and as a foreman of road building crew. He attended some lectures at the Jagiellonian University at that time, including those of the famous Polish mathematicians StanisÅ‚aw Zaremba and Kazimierz Å»orawski, but little is known of that period of his life.{{Harvnb|KaÅ‚uÅ¼a|1996|p=16}}Discovery by Steinhaus
File:Otto Nikodym Stefan Banach Memorial Bench Krakow Poland.jpg|thumb|Otto Nikodym and Stefan Banach Memorial Bench in KrakÃ³w, PolandPolandIn 1916, in KrakÃ³w's Planty gardens, 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. 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 KrakÃ³w mathematicians (WÅ‚adysÅ‚aw ÅšlebodziÅ„ski, Leon Chwistek, Alfred Rosenblatt and WÅ‚odzimierz StoÅ¼ek) also established a mathematical society, which eventually became the Polish Mathematical Society. The society was officially founded on 2 April 1919. It was also through Steinhaus that Banach met his future wife, Åucja Braus.Interbellum
File:Lwow - Kawiarnia Szkocka.jpg|thumb|200px|Scottish CafÃ©Scottish CafÃ©Steinhaus introduced Banach to academic circles and substantially accelerated his career. After Poland regained independence in 1920, Banach was given an assistantship at the LwÃ³w Polytechnic. Steinhaus' backing also allowed him to receive a doctorate without actually graduating from a university. The doctoral thesis, accepted by King John II Casimir University of LwÃ³w in 1920 and published in 1922, included the basic ideas of functional analysis, which was soon to become an entirely new branch of mathematics. The thesis was widely discussed in academic circles and allowed him in 1922 to become a professor at the LwÃ³w Polytechnic. Initially an assistant to Professor Antoni Åomnicki, in 1927 Banach received his own chair. In 1924 he was also 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 LwÃ³w.Young and talented, Banach gathered around him a large group of mathematicians. The group, meeting in the Scottish CafÃ©, soon gave birth to the "LwÃ³w School of Mathematics". In 1929 the group began publishing its own journal, Studia Mathematica, devoted primarily to Banach's field of study â€” 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, the following year it was also translated into French and gained wider recognition in European academic circles. The book was also the first in a long series of mathematics monographs edited by Banach and his circle. In 17 June 1924 Banach become a correspondence member of the Polish Academy of Sciences and Fine Arts in KrakÃ³w.World War II
File:Cmentarz-Lyczakowski-Grob Banacha.jpg|thumb|left|200px|Banach's grave, Lychakiv Cemetery, Lviv (LwÃ³w, in Polish)]]Following the invasion of Poland by Nazi Germany and the Soviet Union, LwÃ³w 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 mathematicians, had to promise to learn Ukrainian to be allowed to keep his chair and continue his academic activities. Following the German takeover of LwÃ³w in 1941 during Operation Barbarossa, all universities were closed and Banach, along with many colleagues and his son, was employed as 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 Red Army recaptured Lviv in the Lvovâ€“Sandomierz Offensive of 1944, Banach returned to the University and helped re-establish it after the war years. However, because the Soviets were removing Poles from annexed formerly Polish territories, Banach began preparing to leave the city and settle in KrakÃ³w, Poland, where he had been promised a chair at the Jagiellonian University. He was also considered a candidate for Minister of Education of Poland. In January 1945, however, he was diagnosed with lung cancer and was allowed to stay in LwÃ³w. He died on 31 August 1945, aged 53. His funeral at the Lychakiv Cemetery was attended by hundreds of people.Contributions
File:Banach-Tarski Paradox.svg|thumb|center|350px|Decomposition of a ball into two identical balls - the Banachâ€“Tarski paradoxBanachâ€“Tarski paradoxBanach'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, ThÃ©orie des opÃ©rations linÃ©aires, 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.{{Harvnb|MacCluer|2008|p=6}} 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 "Banachâ€“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 Ã‰mile Picard, was included in his dissertation, and was later extended by his students (for example in the Banachâ€“Schauder theorem) and other mathematicians (in particular Brouwer and PoincarÃ© and Birkhoff). The theorem did not require linearity of the space, and applied to any Cauchy space (complete metric space).The Hahnâ€“Banach theorem, is one of the fundamental theorems of functional analysis.Quotes
File:Stefan banach monumento krakow 2007.jpeg|thumb|150px|Banach monument, KrakÃ³wKrakÃ³wStanislaw Ulam, another mathematician of the LwÃ³w School of Mathematics, in his autobiography, quotes Banach as saying:
"Good mathematicians see analogies. Great mathematicians see analogies between analogies."BOOK, Developing a 21st Century Global Library for Mathematics Research,weblink National Research Council of the National Academies, 28 March 2018, 25 March 2014, National Academies Press, 9780309298513, 35, dmy-all,
Hugo Steinhaus said of Banach:
"Banach was my greatest scientific discovery."WEB,weblink Stefan Banach (March 30, 1892 â€“ August 8, 1945), Strick, Heinz Klaus, David, Kramer, 2011, Mathematics in Europe, European Mathematical Society, en-us, 28 March 2018, dmy-all,
See also
Notes
{{Reflist|30em|refs=JOURNAL, Stefan Banach, 1922, Sur les opÃ©rations dans les ensembles abstraits et leur application aux Ã©quations integrals (On operations in the abstract sets and their application to integral equations), Fundamenta Mathematicae, 3, harv, French, Polish, {{Harvnb|Jahnke|2003|p=402}}{{Harvnb|James|2003|p=384}}{{harvnb|KaÅ‚uÅ¼a|1996|p=23}}{{Harvnb|O'Connor and Robertson}}{{harvnb|Jakimowicz|Miranowicz|2007}}, p. 4{{harvnb|Jakimowicz|Miranowicz|2007}}, p.5{{harvnb|Jakimowicz|Miranowicz|2007}}, p. 6Stefan Banach: Teoria operacji liniowych.Stefan Banach: ThÃ©orie des opÃ©rations linÃ©aires (in French; Theory of Linear Operations).{{Harvnb|Urbaniak}}{{Harvnb|Waksmundzka-Hajnos|2006|p=16}}}}References
- BOOK, A History of Analysis, American Mathematical Society, Jahnke, Hans Niels, 2003, 0821826239,
- BOOK, E., Jakimowicz, A., Miranowicz, Stefan Banach - Remarkable life, Brilliant mathematics, GdaÅ„sk University Press and Adam Mickiewicz University Press, 2007, 978-83-7326-451-9,weblink harv,
- BOOK, Remarkable Mathematicians: From Euler to von Neumann, Cambridge University Press, Ioan James, James, Ioan, 2003, 0521520940,
- BOOK, Roman, KaÅ‚uÅ¼a, Through a Reporter's Eyes: The Life of Stefan Banach, BirkhÃ¤user, 1996, 0-8176-3772-9
- WEB, Kosiedowski, StanisÅ‚aw, Stefan Banach, MÃ³j LwÃ³w,weblink 20 May 2008,
- WEB,weblink Stefan Banach, University of St. Andrews, MacTutor History of Mathematics archive, 2000, 19 August 2012, O'Connor, Robertson, John J., Edmund F., harv,
- BOOK, Hans Niels, Jahnke, Reinhard, Siegmund-Schultze, A History of Analysis, American Mathematical Society, 2003, 0-8218-2623-9,weblink harv,
- BOOK, Elementary Functional Analysis, Springer, MacCluer, Barbara, 2008, 0387855289,
- JOURNAL,weblink Geniusz: gen i juÅ¼, Urbanek, Mariusz, Polityka, April 2002, 8, 2348,
- JOURNAL,weblink Wspomnienie o Stefanie Greczku, Waksmundzka-Hajnos, Monika, GdaÅ„sk University, Focus, 2006, 11, harv,
External links
{{Sister project links| wikt=no | commons=no | b=no | n=no | q=Stefan Banach | s=no | v=no | voy=no | species=no | d=no}}- Page devoted to Stefan Banach
- {{MathGenealogy|id=12681}}
- {{worldcat id|id=lccn-n86-118445}}
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