Stefan Banach (Polish: [ˈstɛfan ˈbanax] ( listen);
30 March 1892 – 31 August 1945) was a Polish mathematician who is
generally considered one of the world's most important and influential
20th-century mathematicians. He was the founder of modern functional
analysis, and an original member of the
Lwów School of
Mathematics. His major work was the 1932 book, Théorie des
opérations linéaires (Theory of Linear Operations), the first
monograph on the general theory of functional analysis.
Born in Kraków, Banach attended IV Gymnasium, a secondary school, and
worked on mathematics problems with his friend Witold
Wilkosz (pl). After graduating in 1910, Banach moved to Lwów.
World War I
World War I Banach returned to Kraków, where he
befriended Hugo Steinhaus. After Banach solved some mathematics
problems which Steinhaus considered difficult, they published their
first joint work. In 1919, with several other mathematicians, Banach
formed a mathematical society. In 1920 he received an assistantship at
Lwów Polytechnic. He soon became a professor at the Polytechnic,
and a member of the Polish Academy of Learning. He organized the
Lwów School of Mathematics". Around 1929 he began writing his
Théorie des opérations linéaires.
After the outbreak of World War II, in September 1939,
Lwów was taken
over by the Soviet Union. Banach became a member of the Academy of
Ukraine and was dean of
Lwów University's Department of
Mathematics and Physics. In 1941, when the Germans took over Lwów,
all institutions of higher education were closed to Poles. As a
result, Banach was forced to earn a living as a feeder of lice at
Rudolf Weigl's Institute for Study of
Typhus and Virology. While the
job carried the risk of infection with typhus, it protected him from
being sent to slave labor in Germany and from other forms of
repression. When the Soviets recaptured
Lwów in 1944, Banach
reestablished the University. However, because the Soviets were
Poles from Soviet-annexed formerly-Polish territories, Banach
prepared to return to Kraków. Before he could do so, he died in
August 1945, having been diagnosed seven months earlier with lung
Some of the notable mathematical concepts that bear Banach's name
include Banach spaces, Banach algebras, Banach measures, the
Banach–Tarski paradox, the Hahn–Banach theorem, the
Banach–Steinhaus theorem, the Banach–Mazur game, the
Banach–Alaoglu theorem, and the Banach fixed-point theorem.
1.1 Early life
1.2 Discovery by Steinhaus
1.4 World War II
4 See also
7 External links
Stefan Banach was born on 30 March 1892 at St. Lazarus General
Hospital in Kraków, then part of the Austro-Hungarian Empire, into a
Góral Roman Catholic family and was subsequently baptised by his
father, while his mother abandoned him upon this event and her
identity is ambiguous. Banach's parents were Stefan Greczek and
Katarzyna Banach, both natives of the
Podhale region. Greczek
was a soldier in the
Austro-Hungarian Army stationed in Kraków.
Little is known about Banach's mother. According to his baptismal
certificate, she was born in
Borówna and worked as a domestic
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. 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
Płowa and her niece Maria Puchalska in Kraków. Young Stefan would
regard Franciszka as his foster mother and Maria as his older
sister. In his early years Banach was tutored by Juliusz Mien, a
French intellectual and friend of the Płowa family, who had emigrated
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.
In 1902 Banach, aged 10, enrolled in Kraków's IV Gymnasium (also
known as the Goetz Gymnasium). While the school specialized in the
humanities, Banach and his best friend Witold Wiłkosz (also a future
mathematician) spent most of their time working on mathematics
problems during breaks and after school. 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.
After obtaining his matura (high school degree) at age 18 in 1910,
Banach moved to
Lwów with the intention of studying at the Lwów
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
Kraków 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.
World War I
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, 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 Stanisław
Zaremba and Kazimierz Żorawski, but little is known of that period of
Discovery by Steinhaus
Otto Nikodym and
Stefan Banach Memorial Bench in Kraków, Poland
(sculpted by Stefan Dousa)
In 1916, in Kraków'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
Kraków mathematicians (Władysław Ślebodziński, Leon
Chwistek, Alfred Rosenblatt and Włodzimierz Stożek) 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, Łucja Braus.
Scottish Café, meeting place of many famous
Steinhaus introduced Banach to academic circles and substantially
accelerated his career. After
Poland regained independence, in 1920
Banach was given an assistantship at the
Lwów 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
Lwów 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
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
Mathematics at University of 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, 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
World War II
Banach's grave, Lychakiv Cemetery,
Lviv (Lwów, in Polish)
Following the invasion of
Nazi Germany and the Soviet Union,
Lwów 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
Lwów 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
Institute. Employment in Weigl's Institute provided many unemployed
university professors and their associates protection from random
arrest and deportation to Nazi concentration camps.
Red Army recaptured
Lviv 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. 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 Lwów. He died on 31 August 1945, aged 53. His
funeral at the
Lychakiv Cemetery was attended by hundreds of
Decomposition of a ball into two identical balls - the Banach–Tarski
Banach'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,
Théorie des opérations linéaires, 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. 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 "Banach–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 Émile Picard, was included in his dissertation,
and was later extended by his students (for example in the
Banach–Schauder theorem) and other mathematicians (in particular
Brouwer and Poincaré and Birkhoff). The theorem did not require
linearity of the space, and applied to any
Cauchy space (complete
The Hahn–Banach theorem, is one of the fundamental theorems of
Banach monument, Kraków
Stanislaw Ulam, another mathematician of the
Lwów School of
Mathematics, in his autobiography, quotes Banach as saying:
"Good mathematicians see analogies. Great mathematicians see analogies
Hugo Steinhaus said of Banach:
"Banach was my greatest scientific discovery."
List of things named after Stefan Banach
Closed range theorem
List of Poles
^ https://www.britannica.com/biography/Stefan-Banach, “Stefan Banach
^ https://www.britannica.com/biography/Stefan-Banach, “Polish
mathematician who founded modern functional analysis and helped
develop the theory of topological vector spaces.”
^ "Home Page of Stefan Banach". kielich.amu.edu.pl. Retrieved 19
^ "Banach biography". www-history.mcs.st-andrews.ac.uk. Retrieved 19
^ Peter Stachura,
Poland in the Twentieth Century, Springer (1999), p.
^ Waksmundzka-Hajnos 2006, p. 16
^ a b Duda, Roman (2009). "Facts and Myths about Stefan Banach" (PDF).
Newsletter of the European
Mathematical Society. EMS (71): 29.
^ a b c O'Connor and Robertson
^ Kałuża 1996, pp. 2–4
^ Kałuża 1996, pp. 1–3
^ Kałuża 1996, p. 3
^ Kałuża 1996, p. 137
^ Jakimowicz & Miranowicz 2007, p. 4
^ Kałuża 1996, pp. 3–4
^ Jakimowicz & Miranowicz 2007, p.5
^ Kałuża 1996, p. 13
^ Kałuża 1996, p. 16
^ Jakimowicz & Miranowicz 2007, p. 6
^ Kałuża 1996, p. 23
^ a b c d Jahnke 2003, p. 402
Stefan Banach (1922). "Sur les opérations dans les ensembles
abstraits et leur application aux équations integrals (On operations
in the abstract sets and their application to integral equations)".
Fundamenta Mathematicae (in French and Polish). 3.
^ Stefan Banach: Teoria operacji liniowych.
^ Stefan Banach: Théorie des opérations linéaires (in French;
Theory of Linear Operations).
^ a b James 2003, p. 384
^ a b MacCluer 2008, p. 6
^ National Research Council of the National Academies (25 March 2014).
Developing a 21st Century Global Library for
National Academies Press. p. 35. ISBN 9780309298513.
Retrieved 28 March 2018.
^ Strick, Heinz Klaus (2011). "
Stefan Banach (March 30, 1892 –
August 8, 1945)".
Mathematics in Europe. Translated by Kramer, David.
Mathematical Society. Retrieved 28 March 2018.
Jahnke, Hans Niels (2003). A History of Analysis. American
Mathematical Society. ISBN 0821826239.
Jakimowicz, E.; Miranowicz, A., eds. (2007).
Stefan Banach -
Remarkable life, Brilliant mathematics. Gdańsk University Press and
Adam Mickiewicz University Press. ISBN 978-83-7326-451-9.
James, Ioan (2003). Remarkable Mathematicians: From Euler to von
Neumann. Cambridge University Press. ISBN 0521520940.
Kałuża, Roman (1996). Through a Reporter's Eyes: The Life of Stefan
Banach. Translated by Wojbor Andrzej Woyczyński and Ann Kostant.
Birkhäuser. ISBN 0-8176-3772-9.
Kosiedowski, Stanisław. "Stefan Banach". Mój Lwów. Retrieved 20 May
O'Connor, John J.; Robertson, Edmund F. (2000). "Stefan Banach".
Tutor History of
Mathematics archive. University of St. Andrews.
Retrieved 19 August 2012.
Siegmund-Schultze, Reinhard (2003). Jahnke, Hans Niels, ed. A History
of Analysis. American
MacCluer, Barbara (2008). Elementary Functional Analysis. Springer.
Urbanek, Mariusz (April 2002). "Geniusz: gen i już". Polityka. 8
Waksmundzka-Hajnos, Monika (2006). "Wspomnienie o Stefanie Greczku".
Focus. Gdańsk University (11).
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