The Lwów school of mathematics ( pl, lwowska szkoła matematyczna) was a group of Polish

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, mathematical structure, structure, space, Mathematica ...

s who worked in the interwar period in

Lwów Lviv ( uk, Львів) is the largest city in western Ukraine, and the seventh-largest in Ukraine, with a population of . It serves as the administrative centre of Lviv Oblast and Lviv Raion, and is one of the main cultural centres of Ukrain ...

Poland Poland, officially the Republic of Poland, , is a country in Central Europe. Poland is divided into Voivodeships of Poland, sixteen voivodeships and is the fifth most populous member state of the European Union (EU), with over 38 mill ...

(since 1945

Lviv Lviv ( uk, Львів) is the largest city in western Ukraine, and the seventh-largest in Ukraine, with a population of . It serves as the administrative centre of Lviv Oblast and Lviv Raion, and is one of the main cultural centres of Ukra ...

Ukraine Ukraine ( uk, Україна, Ukraïna, ) is a country in Eastern Europe. It is the second-largest European country after Russia, which it borders to the east and northeast. Ukraine covers approximately . Prior to the ongoing Russian invas ...

). The mathematicians often met at the famous Scottish Café to discuss mathematical problems, and published in the journal ''

Studia Mathematica ''Studia Mathematica'' is a triannual peer-reviewed scientific journal of mathematics published by the Polish Academy of Sciences. Papers are written in English, French, German, or Russian, primarily covering functional analysis, abstract method ...

'', founded in 1929. The school was renowned for its productivity and its extensive contributions to subjects such as

point-set topology In mathematics, general topology is the branch of topology that deals with the basic set-theoretic definitions and constructions used in topology. It is the foundation of most other branches of topology, including differential topology, geomet ...

set theory Set theory is the branch of mathematical logic that studies sets, which can be informally described as collections of objects. Although objects of any kind can be collected into a set, set theory, as a branch of mathematics, is mostly concer ...

and

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 (e.g. inner product, norm, topology, etc.) and the linear functions defined ...

. The biographies and contributions of these mathematicians were documented in 1980 by their contemporary

Kazimierz Kuratowski Kazimierz Kuratowski (; 2 February 1896 – 18 June 1980) was a Polish mathematician and logician. He was one of the leading representatives of the Warsaw School of Mathematics. Biography and studies Kazimierz Kuratowski was born in Warsaw, ...

in his book ''A Half Century of Polish Mathematics: Remembrances and Reflections''.

Members

Notable members of the Lwów school of mathematics included: *

Stefan Banach Stefan Banach ( ; 30 March 1892 – 31 August 1945) was a Polish mathematician who is generally considered one of the 20th century's most important and influential mathematicians. He was the founder of modern functional analysis, and an origina ...

* Feliks Barański * Władysław Orlicz *

Stanisław Saks Stanisław Saks (30 December 1897 – 23 November 1942) was a Polish mathematician and university tutor, a member of the Lwów School of Mathematics, known primarily for his membership in the Scottish Café circle, an extensive monograph on the th ...

Hugo Steinhaus Hugo Dyonizy Steinhaus ( ; ; January 14, 1887 – February 25, 1972) 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 Jan Kazimierz Un ...

* Stanisław Mazur *

Stanisław Ulam Stanisław Marcin Ulam (; 13 April 1909 – 13 May 1984) was a Polish-American scientist in the fields of mathematics and nuclear physics. He participated in the Manhattan Project, originated the Teller–Ulam design of thermonuclear weapo ...

* Józef Schreier *

Juliusz Schauder Juliusz Paweł Schauder (; 21 September 1899, Lwów, Austria-Hungary – September 1943, Lwów, Occupied Poland) was a Polish mathematician of Jewish origin, known for his work in functional analysis, partial differential equations and m ...

* Mark Kac * Antoni Łomnicki * Stefan Kaczmarz * Herman Auerbach * Włodzimierz Stożek * Stanisław Ruziewicz

The end of the school

Many of the mathematicians, especially those of

Jew Jews ( he, יְהוּדִים, , ) or Jewish people are an ethnoreligious group and nation originating from the Israelites Israelite origins and kingdom: "The first act in the long drama of Jewish history is the age of the Israelites""T ...

ish background, fled this southeastern part of Poland in 1941 when it became clear that it would be invaded by

Germany Germany, officially the Federal Republic of Germany (FRG),, is a country in Central Europe. It is the most populous member state of the European Union. Germany lies between the Baltic and North Sea to the north and the Alps to the sou ...

. Few of the mathematicians survived

World War II World War II or the Second World War, often abbreviated as WWII or WW2, was a world war that lasted from 1939 to 1945. It involved the World War II by country, vast majority of the world's countries—including all of the great power ...

, but after the war a group including some of the original community carried on their work in western Poland's

Wrocław Wrocław (; , . german: Breslau, , also known by other names) is a city in southwestern Poland and the largest city in the historical region of Silesia. It lies on the banks of the Oder in the Silesian Lowlands of Central Europe, roughly ...

, the successor city to prewar Lwów; see

Polish population transfers (1944–1946) The Polish population transfers in 1944–1946 from the eastern half of prewar Poland (also known as the expulsions of Poles from the Kresy macroregion), were the forced migrations of Poles toward the end and in the aftermath of World War I ...

. A number of the prewar mathematicians, prominent among them

, became famous for work done in the

United States The United States of America (U.S.A. or USA), commonly known as the United States (U.S. or US) or America, is a country primarily located in North America. It consists of 50 U.S. state, states, a Washington, D.C., federal district, five ma ...

References

* {{DEFAULTSORT:Lwow School Of Mathematics History of mathematics History of education in Poland History of Lviv Science and technology in Poland Lviv Polytechnic

Members

The end of the school

See also

References