Stefan Banach

From Wikipedia, the free encyclopedia

Stefan Banach ([,stɛfan 'banaɣ] (help·info); 1892-1945) was an eminent Polish mathematician and university professor. A self-taught mathematical prodigy, Banach was a founder of functional analysis and of the Lwów School of Mathematics. 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.

Notable mathematical concepts named after Banach include the Banach–Tarski paradox, Hahn–Banach theorem, Banach-Steinhaus theorem, and Banach space.

Contents 1 Life 2 Work 3 Quotes 4 Notes and references 5 See also 6 External links

[edit] Life

Stefan Banach was born March 30, 1892, in 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 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]

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 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]

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, spending 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]

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.

Steinhaus introduced Banach to academic circles and significantly accelerated his career. After Poland regained independence, in 1920 Banach was given assistantship at the Jagiellonian University. Steinhaus' protection also allowed him to receive a doctorate without actually graduating from any university. The doctorate's thesis, accepted by the Jan Kazimierz University of Lwów and published in 1922,^[5] included the basic ideas of the functional analysis, that was soon to become an entirely new branch of mathematics. The thesis was widely discussed in academic circles and allowed him to become a professor at the Lwów University of Science and Technology in 1922. Initially an assistant to Prof. Antoni Łomnicki, in 1927 Banach received his own chair. In 1924 he was also accepted as a member of the Polish Academy of Skills. At the same time, since 1922, Banach also headed the second Chair of Mathematics at the Jan Kazimierz 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 so-called Lwów School of Mathematics. The group in 1929 started publishing its own journal, the Studia Mathematica, devoted primarily to Banach's field of study - the functional analysis. Around that time Banach also started 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 to French and gained wider recognition in the academic circles of Europe.^[7] The book was also the first in a large series of monographs on mathematics, edited by Banach and his circle.

Following the Invasion of Poland by Nazi Germany and Soviet Union, Lwów was occupied by the latter state. Being a corresponding member of the Academy of Sciences of the Ukrainian SSR, and otherwise on good terms with Soviet mathematicians, he was allowed to keep his chair and continue his academic activities. Following the German take-over of the city in 1941, all universities were definitively closed and Banach, along with many of his colleagues and his son, was forced to make his living by feeding lice with his blood at Professor Rudolf Weigl's Typhus Research Institute. After the second Soviet occupation of Lwów commenced in 1944, Banach returned to the university and helped re-establish it after the war years. However, as it was decided to expel all Poles^{[citation needed]} of the territories that were alredy annexed by the Soviets, Banach started preparing to leave the city and settle in Kraków^{[citation needed]}. He was promised a chair at the Jagiellonian University. However, in January of 1945 he was diagnosed a lung cancer and was allowed to stay. He died August 31, 1945, at the age of 53. His funeral at the Łyczaków Cemetery turned into a patriotic demonstration of the Poles who were still in the city.

[edit] 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 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.

[edit] 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."

[edit] Notes and references

[edit] See also

• Banach space
• Banach algebra
• Banach-Steinhaus theorem
• Banach–Tarski paradox
• Hahn-Banach theorem
• Banach fixed point theorem
• Banach-Schauder theorem
• Banach-Alaoglu theorem

[edit] 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