- Stefan Banach
Infobox Scientist

name = Stefan Banach

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birth_date = Birth date|1892|3|30

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death_date = Death date|1945|8|31

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nationality = Polish

citizenship = Austro-Hungarian, Polish, Soviet Union [*"new border "realignment" conferred Soviet citizenship on its new Polish inhabitants". [*]*http://www.holocaustforgotten.com/poland.htm*]

field =mathematics

work_institutions = Lwów (Lviv) University

alma_mater = Lwów (Lviv) Polytechnic

doctoral_advisor =Hugo Steinhaus

doctoral_students =Stanisław Mazur Stanisław Ulam

known_for =Banach–Tarski paradox Banach–Steinhaus theorem

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prizes = Memberships:

Academy of Sciences of the Ukrainian SSR,Polish Academy of Learning

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footnotes =**Stefan Banach**Audio-IPA-pl|banach.ogg|'|s|t|e|f|a|n|-|'|b|a|n|a|x (Ukrainian: Степан Степанович Банах; 1892–1945) was a Polishmathematician who worked in interwar Poland and inSoviet Ukraine .A self-taught mathematics prodigy, Banach was the founder of modern

functional analysis and a founder of theLwów School of Mathematics . Among his most prominent achievements was the 1932 book, "Théorie des opérations linéaires" (Theory of Linear Operations), the first monograph on the general theory of linear-metric space .Notable

mathematical concept s named after Banach include theBanach–Tarski paradox ,Hahn–Banach theorem ,Banach–Steinhaus theorem , andBanach space .**Life**Stefan Banach was born

March 30 ,1892 , at St. Lazarus General Hospital inKraków , then part of Austro-Hungarian Galicia. Banach's parents were Stefan Greczek, a young soldier in theAustro-Hungarian Army , and one Katarzyna Banach, natives of thePodhale region.pl icon cite web | author=Monika Waksmundzka-Hajnos | title=Wspomnienie o Stefanie Greczku | publisher=Gdańsk University | year=2006 | work=Wortal Stefana Banacha | url=http://banach.univ.gda.pl/greczek.html#start | accessdate=2007-02-22 ]Unusually, Stefan's surname was that of his mother instead of his father, though he received his father's given name. Since Banach's father 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 be reared by a friend of Banach's father, the owner of a Kraków laundry.

Banach's mother left him after baptizing him when he was four days old. Her name on the birth certificate is Katarzyna Banach. Later in life Banach would ask his father to tell him his mother's actual identity but would only be told that he had taken an oath of secrecy about it. [

*MacTutor Biography|id=Banach|title=Stefan Banach*] Stefan Greczek would go on to marry twice and have a son by his first wife and four children by the second. He would pay for his son's education and be the only relative whom Banach would ever know personally.Already as a student at Kraków's "Gymnasium" no. IV, Banach became known as a prodigy. In 1906, aged 14, he was studying higher mathematics, and two years later he had started in on several languages, western and eastern.en icon cite book | author =Roman Kałuża | translator =Ann Konstant | title =Through a Reporter's Eyes: the life of Stefan Banach | year =1996 | editor = | pages =137 | chapter = | chapterurl = | publisher = | location = | id =ISBN 0817643710

url =http://books.google.com/books?vid=ISBN0817637729&id=i3ZrfMinChkC&printsec=frontcover&dq=Stefan+Banach#PPP1,M1 | format = | accessdate = ] After obtaining his "matura " at age 18 in 1910, Banach went with his friend Witold Wiłkosz to Lviv, then the capital of Galicia, intending to enroll in engineering at theLwów Polytechnic . However, as Banach had to earn money to support his studies, it was not until 1914 that he finally, at age 22, passed hishalf-diploma exams .Roman Kałuża, op.cit., 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 Lviv, Banach left for Kraków, to spend the rest of the war there and in other Galician towns. He made his livingtutor ing at local "gymnasium"s and working in abookshop . He may have attended lectures at theJagiellonian University , but little is known of that period in his life.Roman Kałuża, op.cit., p.16]In 1916, in Cracow's "Planty" gardens, Banach encountered Professor

Hugo Steinhaus , one of the most renowned mathematicians of the age. Steinhaus became fascinated with the self-taught young mathematician. The encounter resulted in a long-lasting collaboration and friendship. It was also through Steinhaus that Banach met his future wife, Łucja Braus.Steinhaus introduced Banach to academic circles and substantially accelerated his career. After Poland regained independence, in 1920 Banach was given an assistantship at Kraków's

Jagiellonian University . Steinhaus' backing also allowed him to receive adoctorate without actually graduating from a university. The doctoral thesis, accepted byLwów University and published in 1922,fr icon pl icon cite journal | author =Stefan Banach | year =1922 | month = | title =Sur les opérations dans les ensembles abstraits et leur application aux équations intégrales | journal =Fundamenta Mathematicae | volume =III | issue = | pages = | id = | url = | format = | accessdate = ] included the basic ideas offunctional 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 theLwów Polytechnic . Initially an assistant to ProfessorAntoni Łomnicki , in 1927 Banach received his own chair. In 1924 he was also accepted as a member of thePolish Academy of Learning . At the same time, from 1922, Banach also headed the second Chair of Mathematics atLwów University . Young and talented, Banach gathered around him a large group of mathematicians. The group, meeting in theScottish 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,Stefan Banach: "Teoria operacji liniowych".] the following year it was also translated into French and gained wider recognition in European academic circles.fr icon Stefan Banach: "Théorie des opérations linéaires" (Theory of Linear Operations).] The book was also the first in a long series of mathematics monographs edited by Banach and his circle.Following the invasion of Poland by

Nazi Germany and theSoviet Union , Lwów came under the control of theSoviet Union . Banach, from 1939 acorresponding member of theAcademy of Sciences of Ukraine , and on good terms with Soviet mathematicians,Fact|date=May 2008 had to promise to learn Ukrainian to be allowed to keep his chair and continue his academic activities. [*[*] Following the German takeover of Lviv in 1941, all universities were closed and Banach, along with many colleagues and his son, was forced to eke out a living feeding*http://www.lwow.com.pl/g8.htm Artyku³y o Lwowie*] at www.lwow.com.pllice with hisblood at ProfessorRudolf Weigl 'sTyphus Research Institute.After the

Red Army capturedLvov in theLvov–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 inKraków ,Poland , where he had been promised a chair at theJagiellonian University . [*[*] He was also considered a candidate for Minister of Education of Poland. [*http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Banach.html*] Banach biography on The MacTutor History of Mathematics archive.*[*] In January 1945, however, he was diagnosed with lung cancer and was allowed to stay in Lviv. He died on*http://banach.univ.gda.pl/zyciorys.html Wortal Stefana Banacha*] at banach.univ.gda.plAugust 31 ,1945 , aged 53. His funeral at theLychakiv Cemetery turned into a patriotic demonstration by the Poles who still remained in the city.Tadeusz Krzyżewski, as cited in: pl icon cite web | author=Stanisław Kosiedowski | title=Stefan Banach | publisher= | year= | work=Mój Lwów | url=http://www.lwow.com.pl/m.htm | accessdate=2008-05-20 ]**Works*** "Rachunek różniczkowy i całkowy, tom I" (Differential and Integral Calculus, vol. 1), Lwów, Zakład Narodowy im. Ossolińskich, 1929, 294 pp.

*"Rachunek różniczkowy i całkowy, tom II" (Differential and Integral Calculus, vol. 2), Lwów, Książnica-Atlas, 1930, 248 pp.

*"Teoria operacji. Tom l. Operacje liniowe" (Theory of operations, vol. 1: Linear operations), Warsaw, Kasa im. Mianowskiego, 1931, viii + 236 pp.

* "Théorie des opérations linéaires, Monografie Matematyczne 1" (Theory of Linear Operations, Mathematical Monographs 1), Warsaw, 1932, vii + 254 pp.

* "Mechanika w zakresie szkół akademickich, Monografie Matematyczne 8" (Mechanics for Academic Schools, Mathematical Monographs 8), Warsaw, Lwów, Wilno, 1938.Banach's most influential work was "Théorie des opérations linéaires" (Theory of Linear Operations, 1932). In it he formulated the concept now known as "

Banach space ," and proved many fundamental theorems offunctional analysis .Besides being one of the founders of functional analysis, Banach also made important contributions to

measure theory ,set theory , and other branches of mathematics.He was also one of the founders and editors of the journal, "

Studia Mathematica ".**Quotes**Stanisław Ulam, another mathematician of the

Lwów School of Mathematics , in his autobiography, quotes Banach as saying: :"Good mathematicians see analogies. Great mathematicians see analogies between analogies."Hugo Steinhaus said of Banach::"An exceptional intellect, exceptional discoveries... he gave Polish science... more than anybody else.":"Banach was my greatest scientific discovery."**ee also***

16856 Banach

*Amenable Banach algebra

*Banach–Alaoglu theorem

*Banach algebra

*Banach bundle

*Banach fixed point theorem

*Banach function algebra

*Banach integral

*Banach limit

*Banach manifold

*Banach's matchbox problem

*Banach measure

*Banach–Mazur game

*Banach–Mazur theorem

*Banach–Schauder theorem

*Banach–Steinhaus theorem

*Banach–Stone theorem

*Banach–Tarski paradox

*Functional analysis

*Hahn–Banach theorem

*Legitimacy

*List of Poles**References**::**In-line:****External links*** [

*http://banach.univ.gda.pl/e-index.html Page devoted to Stefan Banach*]

* [*http://matwbn.icm.edu.pl/kstresc.php?tom=1&wyd=10 Théorie des opérations linéaires*] French translation from 1932

* [*http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Banach.html The MacTutor History of Mathematics archive*] Article on Stefan Banach

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