Stefan Banach

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Stefan Banach
Born	March 30, 1892(1892-03-30)
Died	August 31, 1945
Citizenship	Austro-Hungarian, Polish, Soviet Union[1]
Nationality	Polish
Fields	mathematics
Institutions	Lwów (Lviv) University
Alma mater	Lwów (Lviv) Polytechnic
Notable awards	Memberships: Academy of Sciences of the Ukrainian SSR, Polish Academy of Learning

Stefan Banach [ˈstɛfan ˈbanax] ( listen) (Ukrainian: Степан Степанович Банах; 1892–1945) was a Polish mathematician who worked in interwar Poland and in Soviet Ukraine. A self-taught mathematics prodigy, Banach was the founder of modern functional analysis and a founder of the Lwów 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 concepts named after Banach include the Banach–Tarski paradox, Hahn–Banach theorem, Banach–Steinhaus theorem, and Banach space.

Contents 1 Life 2 Works 3 Quotes 4 See also 5 References 6 External links

Life

Stefan Banach was born March 30, 1892, in Cracow, 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.^[2]. 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 Cracow laundry.^[2] Stefan Greczek paid for his son's education and would be the only relative whom Banach would personally know.^[2]

Already as a student at Cracow'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.^[3] 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.^[4]

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 Cracow, 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 the Jagiellonian University, but little is known of that period in his life.^[5]

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 Cracow'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,^[6] 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.

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,^[7] the following year it was also translated into French and gained wider recognition in European academic circles.^[8] 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 the Soviet Union, Lwów came under the control of the Soviet Union. Banach, from 1939 a corresponding member of the Academy of Sciences of Ukraine, and on good terms with Soviet mathematicians,^{[citation needed]} had to promise to learn Ukrainian to be allowed to keep his chair and continue his academic activities.[3] 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 lice with his blood at Professor Rudolf Weigl's Typhus Research Institute.

After the Red Army captured 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, Poland, where he had been promised a chair at the Jagiellonian University.^[9] He was also considered a candidate for Minister of Education of Poland[4]. In January 1945, however, he was diagnosed with lung cancer and was allowed to stay in Lviv. 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^[10].

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 of functional analysis. He was also one of the founders and editors of the journal, Studia Mathematica.

Besides being one of the founders of functional analysis, Banach also made important contributions to measure theory, set theory, and other branches of mathematics.

Quotes

Stanisław Marcin Ulam, another mathematician of the Lwów School of Mathematics, in his autobiography, attributes this to Banach:

"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."

Hugo Steinhaus:

"Banach was my greatest scientific discovery."

See also

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

References

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