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, structure, space, models, and change. History On ...

s who worked in the

interwar period In the history of the 20th century, the interwar period lasted from 11 November 1918 to 1 September 1939 (20 years, 9 months, 21 days), the end of the World War I, First World War to the beginning of the World War II, Second World War. The in ...

in Lwów,

Poland Poland, officially the Republic of Poland, is a country in Central Europe. It is divided into 16 administrative provinces called voivodeships, covering an area of . Poland has a population of over 38 million and is the fifth-most populous ...

(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 Ukraine ...

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 inv ...

). The mathematicians often met at the famous

Scottish Café The Scottish Café ( pl, Kawiarnia Szkocka) was a café in Lwów, Poland (now Lviv, Ukraine) where, in the 1930s and 1940s, mathematicians from the Lwów School of Mathematics collaboratively discussed research problems, particularly in functio ...

to discuss mathematical problems, and published in the journal '' Studia Mathematica'', 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 conce ...

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 space#Definition, inner product, Norm (mathematics)#Defini ...

. 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, (t ...

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 original ...

* Feliks Barański *

Władysław Orlicz Władysław Roman Orlicz (May 24, 1903 in Okocim, Austria-Hungary (now Poland) – August 9, 1990 in Poznań, Poland) was a Polish mathematician of Lwów School of Mathematics. His main interests were functional analysis and topology: Orlicz sp ...

* Stanisław Saks *

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 Unive ...

Stanisław Mazur Stanisław Mieczysław Mazur (1 January 1905, Lwów – 5 November 1981, Warsaw) was a Polish mathematician and a member of the Polish Academy of Sciences. Mazur made important contributions to geometrical methods in linear and nonlinear functio ...

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 weapon ...

Józef Schreier Józef Schreier (; 18 February 1909, Drohobycz, Austria-Hungary – April 1943, Drohobycz, Occupied Poland) was a Polish mathematician of Jewish origin, known for his work in functional analysis, group theory and combinatorics. He was a member o ...

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 mathema ...

Mark Kac Mark Kac ( ; Polish: ''Marek Kac''; August 3, 1914 – October 26, 1984) was a Polish American mathematician. His main interest was probability theory. His question, " Can one hear the shape of a drum?" set off research into spectral theory, the ...

Antoni Łomnicki Antoni Marian Łomnicki (17 January 1881 – 4 July 1941) was a Polish mathematician. Antoni Łomnicki was educated at Jan Kazimierz University in Lwów in Poland and the University of Göttingen in Germany. In 1920 he became professor of the L ...

Stefan Kaczmarz Stefan Marian Kaczmarz (March 20, 1895 in Sambor, Galicia, Austria-Hungary – 1939) was a Polish mathematician. His Kaczmarz method provided the basis for many modern imaging technologies, including the CAT scan.. Kaczmarz was a professor of ...

Herman Auerbach Herman Auerbach (October 26, 1901, Tarnopol – August 17, 1942) 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 ...

Włodzimierz Stożek Włodzimierz Stożek (23 July 1883 – 3 or 4 July 1941) was a Polish mathematician of the Lwów School of Mathematics. Head of the Mathematics Faculty on the Lwów University of Technology. He was arrested and murdered together with his two son ...

Stanisław Ruziewicz Stanisław Ruziewicz (29 August 1889 – 12 July 1941) was a Polish mathematician and one of the founders of the Lwów School of Mathematics. He was a former student of Wacław Sierpiński, earning his doctorate in 1913 from the University of Lw ...

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""Th ...

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, is a country in Central Europe. It is the second most populous country in Europe after Russia, and the most populous member state of the European Union. Germany is situated betwe ...

. 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 vast majority of the world's countries—including all of the great powers—forming two opposin ...

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

Wrocław Wrocław (; german: Breslau, or . ; Silesian German: ''Brassel'') is a city in southwestern Poland and the largest city in the historical region of Silesia. It lies on the banks of the River Oder in the Silesian Lowlands of Central Europe, rou ...

, 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 Second Polish Republic, Poland (also known as the expulsions of Poles from the Kresy macroregion), were the forced migrations of Poles toward the end and in the after ...

. 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 states, a federal district, five major unincorporated territorie ...

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