Lwów School of Mathematics
Encyclopedia
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
s who worked between the two World War
World war
A world war is a war affecting the majority of the world's most powerful and populous nations. World wars span multiple countries on multiple continents, with battles fought in multiple theaters....
s in Lviv
Lviv
Lviv is a city in western Ukraine. The city is regarded as one of the main cultural centres of today's Ukraine and historically has also been a major Polish and Jewish cultural center, as Poles and Jews were the two main ethnicities of the city until the outbreak of World War II and the following...
, then known as Lwów and located in Poland
Poland
Poland , officially the Republic of Poland , is a country in Central Europe bordered by Germany to the west; the Czech Republic and Slovakia to the south; Ukraine, Belarus and Lithuania to the east; and the Baltic Sea and Kaliningrad Oblast, a Russian exclave, to the north...
, but now located in western Ukraine
Ukraine
Ukraine is a country in Eastern Europe. It has an area of 603,628 km², making it the second largest contiguous country on the European continent, after Russia...
. The mathematicians often met at the famous Scottish Café
Scottish Café
The Scottish Café was the café in Lwów where, in the 1930s and 1940s, mathematicians from the Lwów School collaboratively discussed research problems, particularly in functional analysis and topology....
to discuss mathematical problems, and published in the journal Studia Mathematica
Studia Mathematica
Studia Mathematica is a Polish mathematics journal published since 1929. It was founded by Stefan Banach and Hugo Steinhaus. It accepts papers written in English, French, German, or Russian, primarily in functional analysis and related areas such as probability theory.- External links :* *...
, founded in 1929. The school was renowned for its productivity and its extensive contributions to subjects such as point-set topology, set theory
Set theory
Set theory is the branch of mathematics that studies sets, which are collections of objects. Although any type of object can be collected into a set, set theory is applied most often to objects that are relevant to mathematics...
and functional analysis
Functional analysis
Functional analysis is a branch of mathematical analysis, the core of which is formed by the study of vector spaces endowed with some kind of limit-related structure and the linear operators acting upon these spaces and respecting these structures in a suitable sense...
. The biographies and contributions of these mathematicians were documented in 1980 by their contemporary Kazimierz Kuratowski
Kazimierz Kuratowski
Kazimierz Kuratowski was a Polish mathematician and logician. He was one of the leading representatives of the Warsaw School of Mathematics.-Biography and studies:...
in his book A Half Century of Polish Mathematics: Remembrances and Reflections.
Many of the mathematicians, especially those of Jewish background, fled this southeastern part of Poland in 1941 when it became clear that it would be invaded by Germany
Germany
Germany , officially the Federal Republic of Germany , is a federal parliamentary republic in Europe. The country consists of 16 states while the capital and largest city is Berlin. Germany covers an area of 357,021 km2 and has a largely temperate seasonal climate...
. Few of the mathematicians survived World War II
World War II
World War II, or the Second World War , was a global conflict lasting from 1939 to 1945, involving most of the world's nations—including all of the great powers—eventually forming two opposing military alliances: the Allies and the Axis...
, but after the war a group including some of the original community carried on their work in western Poland's Wrocław, the successor city to prewar Lwów; see Polish population transfers (1944–1946). A number of the prewar mathematicians, prominent among them Stanisław Ulam, became famous for work done in the West.
Notable members of the Lwów School of Mathematics included:
- Stefan BanachStefan BanachStefan Banach was a Polish mathematician who worked in interwar Poland and in Soviet Ukraine. He is generally considered to have been one of the 20th century's most important and influential mathematicians....
- Feliks BarańskiFeliks BaranskiFeliks Barański was a Polish mathematician and an active member of the so-called Lwow School of Mathematics. Born May 1915 in Lwow, Austria-Hungary , he joined the circle of young, talented mathematicians formed around Stefan Banach and Hugo Steinhaus...
- Władysław Orlicz
- Stanisław Saks
- Hugo SteinhausHugo SteinhausWładysław Hugo Dionizy Steinhaus was a Polish mathematician and educator. Steinhaus obtained his PhD under David Hilbert at Göttingen University in 1911 and later became a professor at the University of Lwów, where he helped establish what later became known as the Lwów School of Mathematics...
- Stanisław Mazur
- Stanisław Ulam
- Juliusz SchauderJuliusz SchauderJuliusz Paweł Schauder was a Polish mathematician of Jewish origin, known for his work in functional analysis, partial differential equation and mathematical physics.Born on September 21, 1899 in Lemberg, he had to fight in World War I right after his graduation from school...
- Mark KacMark KacMark Kac was a Polish mathematician. His main interest was probability theory. His question, "Can one hear the shape of a drum?" set off research into spectral theory, with the idea of understanding the extent to which the spectrum allows one to read back the geometry. Kac completed his Ph.D...
- Antoni Łomnicki
- Stefan KaczmarzStefan KaczmarzStefan Kaczmarz was a Polish mathematician. His Kaczmarz method provided the basis for many modern imaging technologies, including the CAT scan....
- Herman AuerbachHerman AuerbachHerman Auerbach was a Polish mathematician and member of the Lwów School of Mathematics.Auerbach was professor at Lwów University. During the Second World War because of his Jewish descent he was imprisoned by the Germans in the Lwów ghetto. In 1942 he was murdered at Bełżec extermination...
- Włodzimierz Stożek
- Stanisław Ruziewicz
See also
- Polish School of MathematicsPolish School of MathematicsThe Polish School of Mathematics refers to the mathematics community that flourished in Poland in the 20th century, particularly during the Interbellum between World Wars I and II.- Overview :The Polish School of Mathematics subsumed:...
- Kraków School of MathematicsKraków School of MathematicsKraków School of Mathematics was a sub-group of Polish School of Mathematics represented by mathematicians from the Kraków universities—Jagiellonian University and the AGH University of Science and Technology, active during the interwar period...
- Warsaw School of MathematicsWarsaw School of Mathematics"Warsaw School of Mathematics" is the name given to a group of mathematicians who worked at Warsaw, Poland, in the two decades between the World Wars, especially in the fields of logic, set theory, point-set topology and real analysis. They published in the journal Fundamenta Mathematicae, founded...