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The Polish School of Mathematics

was a group of Polish mathematicians who worked in the interwar period in Lwów. The mathematicians often met at the famous Scottish Café 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, set theory and functional analysis.

Notable members of the Lwów school of mathematics includes:

Stefan Banach
Feliks Barański
Władysław Orlicz
Stanisław Saks
Hugo Steinhaus
Stanisław Mazur
Stanisław Ulam
Józef Schreier
Juliusz Schauder
Mark Kac
Antoni Łomnicki
Stefan Kaczmarz
Herman Auerbach
Włodzimierz Stożek
Stanisław Ruziewicz

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.

Notable members of the Warsaw School of Mathematics have includes:

Wacław Sierpiński
Kazimierz Kuratowski
Edward Marczewski
Bronisław Knaster
Zygmunt Janiszewski
Stefan Mazurkiewicz
Stanisław Saks
Karol Borsuk
Roman Sikorski
Nachman Aronszajn
Samuel Eilenberg
Stanisław Leśniewski
Adolf Lindenbaum
Alfred Tarski
Jan Łukasiewicz
Andrzej Mostowski
Helena Rasiowa 
Aleksander Rajchman
Antoni Zygmund
Józef Marcinkiewicz
Otton M. Nikodym
Jerzy Spława-Neyman 

was represented by mathematicians from the Kraków universities—Jagiellonian University, and the AGH University of Science and Technology–active during the interwar period (1918–1939).  Their areas of study were primarily classical analysis, differential equations, and analytic functions.

The Kraków School of Differential Equations was founded by Tadeusz Ważewski, a student of Stanisław Zaremba The Kraków School of Analytic Functions was founded by Franciszek Leja.

Other notable members includes:

Kazimierz Żorawski
Władysław Ślebodziński
Stanisław Gołąb
and Czesław Olech

Antoni Zygmund
Józef Marcinkiewicz

In mathematics, the Marcinkiewicz–Zygmund inequality, named after Józef Marcinkiewicz and Antoni Zygmund, gives relations between moments of a collection of independent random variables.

The Copernicus University in Toruń is often considered to be the successor to the Polish traditions of the Stefan Batory University.


1917 - 1939

Warsaw School of Mathematics

The Mianowski Foundation, while not alone, did as much as possible to support Polish science and mathematics.
With its considerable financial resources (its assets included an oilfield in the Caucauses) it supported doctoral students studying abroad, scholars engaged in significant research, student scholarships, and publications.

It supported a series of books called Poradnik dla Samoukow (Guidebooks for Self-Instruction). These were designed to get around the Russian and German educational restrictions and were written by prominent mathematicians including Janiszewski, Sierpinski, and Zaremba; they covered topics such as series, differential and integral equations, and topology. Another series it supported was Nauka Polska jej Potrzeby Organizacja I Rozwój (Sciences and Letters in Poland, Their Needs, Organization and Progress); the first issue (1917) contained two articles which were to be very important to the establishment of the Polish School of Mathematics.

The first article was by Stanislaw Zaremba, who noted that a number of secondary school teachers had the potential to be future scholars; he urged that a way be found to have them sent abroad for further study. The second article `On the Needs of Mathematics in Poland' by Zygmunt Janiszewski outlined the plan for what was to be the Polish School of Mathematics.

The next year a third article appeared in Nauka Polska; it was written by Stefan Mazurkiewicz.

Nationhood was restored to Poland at the end of World War I, and the University of Warsaw opened in 1918 with Janiszewski, Mazurkiewicz, and Sierpinski as professors of mathematics. The three initiated Janiszewki's proposals with Warsaw serving as the proposed mathematical research center, and with set theory, including related areas such as topology and parts of real analysis, being chosen as the area of concentration.

The mathematicians published in the journal Fundamenta Mathematicae, founded in 1920—one of the world's first specialist pure-mathematics journals. It was in this journal, in 1933, that Alfred Tarski—whose illustrious career would a few years later take him to the University of California, Berkeley—published his celebrated theorem on the undefinability of the notion of truth.

While Fundamenta was conceived as an international journal, the first volume deliberately contained only papers by Polish authors.

1918 - 1939

Kraków School of Mathematics

Development of classical analysis, differential equations, and analytic functions.

1920 - 1941

Lwów School of Mathematics

A second center concentrating on functional analysis was started in Lwow, where Banach and Steinhaus were professors, and the journal Studia Mathematica was founded in 1929, also devoted to functional analysis. The publication of Banach's thesis in Volume 3 of Fundamenta Mathematicae had marked the beginning of functional analysis as a discipline, and much of its development was recorded in Studia Mathematica. While both centers were very strong, cooperation between them was very good and their identities merged into the Polish School of Mathematics.

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

1920 - 1922

Banach Space

is a vector space with a metric that allows the computation of vector length and distance between vectors and is complete in the sense that a Cauchy sequence of vectors always converges to a well defined limit that is within the space.


Polish Notation

was invented in 1924 by Polish logician
Jan Łukasiewicz. It is also known as normal Polish notation (NPN), Łukasiewicz notation, Warsaw notation, Polish prefix notation or simply prefix notation, is a mathematical notation in which operators precede their operands.

1936 - 2020

Polish Spaces

Polish space is a separable completely metrizable topological space; that is, a space homeomorphic to a complete metric space that has a countable dense subset.
Polish spaces were first extensively studied by Polish topologists and logicians—Sierpiński, Kuratowski, Tarski and others
They are mostly studied today because they are the primary setting for descriptive set theory, measure theory, and probability theory.


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