Stefan Banach
Born	March 30, 1892(1892-03-30)
Died	August 31, 1945
Citizenship	Austro-Hungarian, Polish
Fields	mathematics
Institutions	Lwów (Lviv) University
Alma mater	Lwów (Lviv) Polytechnic
Notable awards	Memberships: National Academy of Sciences of Ukraine, Polish Academy of Learning

Stefan Banach [ˈstɛfan ˈbanax] ( listen) (Ukrainian: Степан Степанович Банах, 1892-1945) was an eminent Polish mathematician who worked in interwar Poland and briefly in Soviet Ukraine. A self-taught mathematical prodigy, Banach was the founder of modern functional analysis and a founder of the Lwów School of Mathematics at Lwów University (now Lviv Ivan Franko National Ukrainian University). Among his most prominent achievements was a 1932 book, Théorie des opérations linéaires (Theory of Linear Operations), the first monograph on the general theory of linear-metric space. Stefan Banach User:Stako 08:59, 10 Feb 2005 (UTC)~ File links The following pages link to this file: Stefan Banach Categories: GFDL images ... is the 89th day of the year (90th in leap years) in the Gregorian calendar. ... Year 1892 (MDCCCXCII) was a leap year starting on Friday (link will display the full calendar) of the Gregorian Calendar (or a leap year starting on Wednesday of the 12-day slower Julian calendar). ... is the 243rd day of the year (244th in leap years) in the Gregorian calendar. ... Year 1945 (MCMXLV) was a common year starting on Monday (link will display the full calendar). ... For other meanings of mathematics or uses of math and maths, see Mathematics (disambiguation) and Math (disambiguation). ... The building of the University. ... Alma mater is Latin for nourishing mother. It was used in ancient Rome as a title for the mother goddess, and in Medieval Christianity for the Virgin Mary. ... Lviv Polytechnic (full name Lviv Polytechnic National University, Ukrainian Національний університет Львівська політехніка, Polish Politechnika Lwowska) is the biggest scientifical university in Lviv. ... The National Academy of Sciences of Ukraine is the highest state research organization of Ukraine. ... The Polish Academy of Skills (Polish: Polska Akademia Umiejętności, PAU), till 1919 just The Academy of Skills (Akademia Umiejętności, AU) founded in 1872 in Kraków as continuation of the Kraków Scientific Society (Towarzystwo Naukowe Krakowskie, est. ... The purpose of this page is to lay out our policies for handling sounds, and give people some useful information for handling sound files. ... Leonhard Euler, considered one of the greatest mathematicians of all time A mathematician is a person whose primary area of study and research is the field of mathematics. ... Anthem: Mazurek DÄ…browskiego Capital Warsaw Language(s) Polish Government Republic President List Prime minister List Legislature Sejm Historical era Interwar period  - World War I November 11, 1918  - Invasion November 2, 1939 Area  - 1939 388,600 km2 150,039 sq mi Population  - 1939 est. ... State motto: Пролетарі всіх країн, єднайтеся! Official language None. ... Wunderkind redirects here. ... Functional analysis is the branch of mathematics, and specifically of analysis, concerned with the study of spaces of functions. ... The Lwów School of Mathematics was a group of mathematicians who worked between the World Wars in Lwów, Poland (now Lviv, Ukraine). ... The building of the University. ... The fundamental concept in linear algebra is that of a vector space or linear space. ... In mathematics, a metric space is a set where a notion of distance between elements of the set is defined. ...

Notable mathematical concepts named after Banach include the Banach–Tarski paradox, Hahn–Banach theorem, Banach–Steinhaus theorem, and Banach space. Mathematics is commonly defined as the study of patterns of structure, change, and space; more informally, one might say it is the study of figures and numbers. Mathematical knowledge is constantly growing, through research and application, but mathematics itself is not usually considered a natural science. ... For other uses, see Concept (disambiguation). ... A ball can be decomposed into a finite number of pieces and reassembled into two balls identical to the original. ... In mathematics, the Hahn–Banach theorem is a central tool in functional analysis. ... In mathematics, Banach spaces (pronounced ), named after Stefan Banach who studied them, are one of the central objects of study in functional analysis. ...

Life

Stefan Banach was born March 30, 1892, in Krakau (Kraków), then part of Austro-Hungarian Galicia. Banach's parents were Stefan Greczek, a young soldier in the Austro-Hungarian Army, and Katarzyna Banach, both natives of the Podhale region.^[1]. Since Banach's father was a private and was prevented by military regulations from marrying, and the child's mother was too poor to support young Stefan, the couple decided that the child should be reared by a friend of Banach's father, the owner of a Kraków laundry.^[1] Stefan Greczek paid for his son's education and would be the only relative whom Banach would personally know.^[1] is the 89th day of the year (90th in leap years) in the Gregorian calendar. ... Year 1892 (MDCCCXCII) was a leap year starting on Friday (link will display the full calendar) of the Gregorian Calendar (or a leap year starting on Wednesday of the 12-day slower Julian calendar). ... For other uses, see Krakow (disambiguation). ... Austria-Hungary, also known as the Dual monarchy (or: the k. ... For other uses, see Galicia. ... The Austro-Hungarian Army was the ground force of the Austro-Hungarian Empire. ... Podhale The Podhale (literally Mountain meadows) is Polands most southern region, sometimes referred to as the Polish highlands. The Podhale is located in the foothills of the Tatra range of the Carpathian mountains, and is characterized by a rich tradition of folklore that is much romanticized in the Polish... A Private is a soldier of the lowest military rank (equivalent to Nato Rank Grades OR-1 to OR-3 depending on the force served in). ... Matrimony redirects here. ...

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.^[2] After obtaining his matura at age 18 (1910), Banach went with his friend Witold Wiłkosz to Lemberg (Polish Lwów; now Lviv, Ukraine; then the capital of Galicia), intending to enroll in engineering at the Lwów Polytechnic. However, as Banach had to earn money to support his studies, it was not until 1914 that he finally, at age 22, passed his half-diploma exams.^[3] A gymnasium (pronounced with or, in Swedish, as opposed to ) is a type of school providing secondary education in some parts of Europe, comparable to English Grammar Schools and U.S. High Schools. ... Wunderkind redirects here. ... Matura (Matur, Maturità, Maturität) is the word commonly used in Austria, Albania, Bosnia and Herzegovina, Bulgaria, Croatia, Italy, Liechtenstein, Macedonia, Montenegro, Poland, Serbia, Slovenia, Switzerland and Ukraine for the final exams young adults (aged 18 or 19) take at the end of their secondary education. ... Lviv ( Львів in Ukrainian; Львов, Lvov in Russian; Lwów in Polish; Leopolis in Latin; Lemberg in German—see also cities alternative names) is a city in western Ukraine with 830,000 inhabitants (an additional 200,000 commute daily from suburbs). ... For other uses, see Galicia. ... Lviv Polytechnic (full name Lviv Polytechnic National University, Ukrainian Національний університет Львівська політехніка, Polish Politechnika Lwowska) is the biggest scientifical university in Lviv. ...

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, to spend the rest of the war there and in other Galician towns. He made his living tutoring at local gymnasiums and working in a bookshop. He may have attended lectures at Kraków University, but little is known of that period in his life.^[4] “The Great War ” redirects here. ... In British, Australian, New Zealand, and some Canadian universities, a tutor is often but not always a postgraduate student or a lecturer assigned to conduct a seminar for undergraduate students, often known as a tutorial. ... A gymnasium (pronounced with or, in Swedish, as opposed to ) is a type of school providing secondary education in some parts of Europe, comparable to English Grammar Schools and U.S. High Schools. ... Categories: Bookstores | Stub ... For several academies alternatively called Krakow Academy, see Education in Kraków The Jagiellonian University (Polish: , often shortened to UJ) is located in Kraków, Poland. ...

In 1916, in Kraków'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. Hugo Dyonizy Steinhaus (January 14, 1887 - February 25, 1972) was a Polish mathematician, educator, and humanist. ...

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 a doctorate without actually graduating from a university. The doctoral thesis, accepted by Lwów University and published in 1922,^[5] 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 Lwów Polytechnic. Initially an assistant to Professor Antoni Łomnicki, 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 Lwów University. For other uses, see Krakow (disambiguation). ... For several academies alternatively called Krakow Academy, see Education in Kraków The Jagiellonian University (Polish: , often shortened to UJ) is located in Kraków, Poland. ... The building of the University. ... Functional analysis is the branch of mathematics, and specifically of analysis, concerned with the study of spaces of functions. ... Lviv Polytechnic (full name Lviv Polytechnic National University, Ukrainian Національний університет Львівська політехніка, Polish Politechnika Lwowska) is the biggest scientifical university in Lviv. ... Antoni Marian Łomnicki (b. ... The Polish Academy of Skills (Polish: Polska Akademia Umiejętności, PAU), till 1919 just The Academy of Skills (Akademia Umiejętności, AU) founded in 1872 in Kraków as continuation of the Kraków Scientific Society (Towarzystwo Naukowe Krakowskie, est. ... The building of the University. ...

Scottish Café, 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,^[6] the following year it was also translated into French and gained wider recognition in European academic circles.^[7] The book was also the first in a long series of mathematics monographs edited by Banach and his circle. Kawiarnia Szkocka This image has been released into the public domain by the copyright holder, its copyright has expired, or it is ineligible for copyright. ... Kawiarnia Szkocka This image has been released into the public domain by the copyright holder, its copyright has expired, or it is ineligible for copyright. ... Kawiarnia Szkocka in Lwów The Kawiarnia Szkocka (Scottish Café) was the café where Polish mathematicians from the Lwów School of Mathematics spent their afternoons, discussing mathematical problems. ... Motto: Semper fidelis Oblast Lviv Oblast Municipal government City council (Львівська міська рада) Mayor City chairman Lyubomyr Bunyak Area 171,01 km² Population  - city  - urban  - density 808,900 ? 4786/km² Founded City rights 13th century 1353 Latitude Longitude 49°51′ N 24°01′ E Area code +0322 Car plates  ? Twin towns Corning, Freiburg... Kawiarnia Szkocka in Lwów The Kawiarnia Szkocka (Scottish Café) was the café where Polish mathematicians from the Lwów School of Mathematics spent their afternoons, discussing mathematical problems. ... The Lwów School of Mathematics was a group of mathematicians who worked between the World Wars in Lwów, Poland (now Lviv, Ukraine). ... Studia Mathematica was a Polish mathematics journal published from 1929 to 1982. ... The fundamental concept in linear algebra is that of a vector space or linear space. ... In mathematics, a metric space is a set where a notion of distance between elements of the set is defined. ...

Banach's grave, Łyczaków Cemetery, Lviv

Following the invasion of Poland by Nazi Germany and the Soviet Union, Lwów came under the control of the Soviet Union. Banach, being a corresponding member of the Academy of Sciences of Ukraine, and otherwise on good terms with Soviet mathematicians, was allowed to keep his chair and continue his academic activities. Following the German takeover of Lwów in 1941, all universities were closed and Banach, along with many colleagues and his son, was forced to eke out a living feeding lice with his blood at Professor Rudolf Weigl's Typhus Research Institute. User:Stako 08:52, 10 Feb 2005 (UTC)~ File links The following pages link to this file: Stefan Banach Categories: Pre-1994 Poland images ... User:Stako 08:52, 10 Feb 2005 (UTC)~ File links The following pages link to this file: Stefan Banach Categories: Pre-1994 Poland images ... Cemetery in 2003 Lychakivskiy Cemetery (Polish Cmentarz Łyczakowski Ukrainian Личаківський цвинтар) is a famous cemetery in Lviv. ... “Lvov” redirects here. ... For the Soviet Unions military action against Poland under the same alliance, see Soviet invasion of Poland (1939). ... Nazi Germany, or the Third Reich, commonly refers to Germany in the years 1933–1945, when it was under the firm control of the totalitarian and fascist ideology of the Nazi Party, with the Führer Adolf Hitler as dictator. ... CCCP redirects here. ... Suborders Anoplura (sucking lice) Rhyncophthirina Ischnocera (avian lice) Amblycera (chewing lice) Lice (singular: louse) (order Phthiraptera) are an order of over 3000 species of wingless parasitic insects. ... For other uses, see Blood (disambiguation). ... Rudolf Weigl Professor Rudolf Stefan Weigl (1883 - 1957) was a famous Czech-Polish biologist and inventor of the first effective vaccine for epidemic typhus. ... For the unrelated disease caused by Salmonella typhi, see Typhoid fever. ...

After the Red Army retook Lwów (Lvov) 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 removing Poles from annexed formerly-Polish territories, Banach began preparing to leave the city and settle in Kraków, where he had been promised a chair at the Jagiellonian University.^[8] In January 1945, however, he was diagnosed with lung cancer and was allowed to stay in Lvov. He died on August 31, 1945, aged 53. His funeral at the Lychakiv Cemetery turned into a patriotic demonstration by the Poles who still remained in the city. For other organizations known as the Red Army, see Red Army (disambiguation). ... Lviv ( Львів in Ukrainian; Львов, Lvov in Russian; Lwów in Polish; Leopolis in Latin; Lemberg in German—see also cities alternative names) is a city in western Ukraine with 830,000 inhabitants (an additional 200,000 commute daily from suburbs). ... Combatants Germany Soviet Union Commanders Josef Harpe (Heeresgruppe Nordukraine) Ivan Koniev (1st Ukrainian Front) Strength 370,000 men 340 AFVs 4,800 guns 1,200,000 men 1,979 AFVs 11,265 guns Casualties 350,000 men 520 AFVs 198,000 men 1,285 AFVs The Lvov-Sandomierz Offensive[1... For other uses, see Krakow (disambiguation). ... For several academies alternatively called Krakow Academy, see Education in Kraków The Jagiellonian University (Polish: , often shortened to UJ) is located in Kraków, Poland. ... is the 243rd day of the year (244th in leap years) in the Gregorian calendar. ... Year 1945 (MCMXLV) was a common year starting on Monday (link will display the full calendar). ...

Work

Théorie des opérations linéaires (Teoria operacji liniowych, 1932) is regarded as Banach's most influential work. In it he formulated the concept now known as Banach space, and proved many fundamental theorems of functional analysis. He was also one of the founders and editors of the journal Studia Mathematica. In mathematics, Banach spaces (pronounced ), named after Stefan Banach who studied them, are one of the central objects of study in functional analysis. ... Functional analysis is the branch of mathematics, and specifically of analysis, concerned with the study of spaces of functions. ... Studia Mathematica was a Polish mathematics journal published from 1929 to 1982. ...

Besides being one of the founders of functional analysis, Banach also made important contributions to measure theory, set theory, and other branches of mathematics. In mathematics, a measure is a function that assigns a number, e. ... Set theory is the mathematical theory of sets, which represent collections of abstract objects. ...

Quotes

Banach on a 1982 Polish postage stamp

Stanisław Marcin Ulam, another mathematician of the Lwów School of Mathematics, in his autobiography, attributes this to Banach: A selection of Hong Kong postage stamps A postage stamp is evidence of pre-paying a fee for postal services. ... StanisÅ‚aw Ulam in the 1950s. ... The Lwów School of Mathematics was a group of mathematicians who worked between the World Wars in Lwów, Poland (now Lviv, Ukraine). ...

"Good mathematicians see analogies. Great mathematicians see analogies between analogies."

Hugo Steinhaus said of Banach: Hugo Dyonizy Steinhaus (January 14, 1887 - February 25, 1972) was a Polish mathematician, educator, and humanist. ...

"An exceptional intellect, exceptional discoveries...he gave Polish science...more than anybody else."

Hugo Steinhaus: Hugo Dyonizy Steinhaus (January 14, 1887 - February 25, 1972) was a Polish mathematician, educator, and humanist. ...

"Banach was my greatest scientific discovery."

Stefan Banach:

"A mathematician is a person who can find analogies between theorems; a better mathematician is one who can see analogies between proofs and the best mathematician can notice analogies between theories. One can imagine that the ultimate mathematician is one who can see analogies between analogies."

See also

• Banach algebra
• Hahn-Banach theorem
• Banach fixed point theorem
• Banach-Schauder theorem
• Banach-Alaoglu theorem

In functional analysis, a Banach algebra, named after Stefan Banach, is an associative algebra A over the real or complex numbers which at the same time is also a Banach space. ... In mathematics, the Hahn-Banach theorem is a central tool in functional analysis. ... The Banach fixed point theorem (also known as the contraction mapping theorem or contraction mapping principle) is an important tool in the theory of metric spaces; it guarantees the existence and uniqueness of fixed points of certain self maps of metric spaces, and provides a constructive method to find those... In mathematics, there are two theorems with the name open mapping theorem. Functional analysis In functional analysis, the open mapping theorem, also known as the Banach-Schauder theorem, is a fundamental result which states: if A : X → Y is a surjective continuous linear operator between Banach spaces X and Y... The Banach-Alaoglu theorem (also known as Alaoglus theorem) states that the closed unit ball of the dual space of a normed vector space is compact in the weak* topology. ...

References

Year 2007 (MMVII) was a common year starting on Monday of the Gregorian calendar in the 21st century. ... is the 53rd day of the year in the Gregorian calendar. ...

External links

• Page devoted to Stefan Banach
• Théorie des opérations linéaires French translation from 1932
• The MacTutor History of Mathematics archive Article on Stefan Banach
• Stefan Banach at the Mathematics Genealogy Project