Stefan Banach (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,
Banach-Mazur game and
Banach space.
Life
Stefan
Banach was born on March 30, 1892, at St. Lazarus General Hospital
in Kraków, then part
of Austro-Hungarian Galicia. Banach's parents
were Stefan Greczek and one Katarzyna Banach, both natives of the
Podhale region.
Stefan Greczek was
born in Ostrowsko near the town of Nowy Targ and at one time was a soldier in the Austro-Hungarian Army stationed in
Kraków. Stefan Greczek's father, Józef, was a farmer and a
village mayor and Józef's wife, Antonina (née Borkowska) bore the
Pomian coat of arms.
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. Stefan Greczek would go on to marry twice and
have a son by his first wife and four children by the second.
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 should be reared by family
and friends. Family legend says that Banach spent his early
childhood in Ostrowsko with his grandmother, to whom he was very
close. When she became ill, his father sent him to Kraków to live
with Franciszka Płowa and her daughter, Maria, although Banach
would continue to visit his grandmother up to her funeral.
Franciszka worked in a branch of the Tęcza laundries while her
husband was the manager of the Krakowski Hotel. Together, they were
able to give Banach what was a relatively comfortable life for the
time. Contacts between Banach and his father were polite and
cordial; though Banach loved his father, he did not show him much
warmth or filial affection.
As a child, Banach was introduced to Juliusz Mien, a French
intellectual who had moved to Kraków in 1870 and who was a guardian
of Maria Płowa. Mien guided Banach by teaching him French and
supervising his education without charge. Mien likely nurtured
Banach's early mathematical skills, and he taught him to speak
French so fluently that later in life Banach was able to impress
foreign colleagues with his knowledge of the language.
In 1902 Banach, aged 10, enrolled in Kraków's
Henryk
Sienkiewicz Gymnasium no. IV
where he became known as a
prodigy.
The school specialized in the humanities, including languages such
as Latin, Greek, and German as well as subjects such as History and
Geography along side some Mathematics. Despite this shortcoming,
Banach and his best friend Witold Wiłkosz, a future mathematician,
would regularly work on mathematics problems during school breaks
and after school. In 1906 Banach, aged 14, was studying higher
mathematics and two years later he had started in on several
languages, both western and eastern, however he was especially fond
of Latin. After obtaining his
matura
at age 18 in 1910, Banach went with Witold Wiłkosz to Lviv, 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.
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 the
Jagiellonian University, but
little is known of that period in his life.
In 1916, in Kraków's
Planty
gardens, Banach encountered Professor
Hugo Steinhaus, one of the 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 a
doctorate without actually graduating from a
university. The doctoral thesis, accepted by
King John II Casimir University of Lwów 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 Chair of 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.
Following
the invasion of Poland by
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 in
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
Typhus
Research Institute. Employment in Weigl's Institute provided many
unemployed university professors and their associates protection
from random arrest and deportation to
Nazi concentration camps.
After the
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 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.
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.
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."
See also
Notes
- Stefan Banach: Teoria operacji liniowych.
- Stefan Banach: Théorie des opérations linéaires
(Theory of Linear Operations).
- Artyku³y o Lwowie at www.lwow.com.pl
- Wortal Stefana Banacha at banach.univ.gda.pl
- Tadeusz Krzyżewski, as cited in:
References
External links