Warsaw School of Mathematics
The term Warsaw School of Mathematics refers to a group of mathematicians active in logic, set theory, point-set topology, and real functions during the 1920s and 1930s. Their journal, Fundamenta Mathematicae (founded in 1920), was the first specialized mathematical journal in the world.
Members of this school included: Wacław Sierpiński, Kazimierz Kuratowski, Edward Marczewski, Bronisław Knaster, Zygmunt Janiszewski, Stefan Mazurkiewicz, Stanisław Saks, Karol Borsuk, and Roman Sikorski.
Members of the Warsaw topology group who emigrated in the 1930s include Nachman Aronszajn (1907–1980) and Samuel Eilenberg (later
based in New York).
The group of logicians in Warsaw also included Stanisław Leśniewski (1886–1939), Adolf Lindenbaum (1904–1942), and Alfred Tarski (based in Berkeley since 1942). In 1933, Tarski published his celebrated theorem on the undefinability of the notion of truth. Jan Łukasiewicz and Andrzej Mostowski were also members of this group.
Fourier analysis in Warsaw was developed by Aleksander Rajchman and Antoni Zygmund (1900–1992). Zygmund later moved to the University of Vilna (founded in 1578), where he led an analysis group in the 1930s. During the war, he settled in the USA. Other members of this group included Józef Marcinkiewicz, Otton M. Nikodym, and Jerzy Spława-Neyman.
Lvov School of Mathematics
The term Lvov School of Mathematics refers to a group of more than a dozen mathematicians working in functional analysis, real functions, and probability during the 1920s and 1930s. Their journal, Studia Mathematica, was founded in 1929. The Lvov School included Stefan Banach, Juliusz P. Schauder, Stanisław Mazur, Hugo Steinhaus, and Władysław Orlicz.
Other members of the Lvov School included Herman Auerbach, Stefan Kaczmarz, Antoni Łomnicki, Mark Kac, and Stanisław Ulam (both later based in the USA).
Cracow School of Mathematics
The Jagiellonian University in Cracow (Kraków), the ancient capital of Poland, was founded in 1364. Copernicus studied mathematics and astronomy there from 1491 to 1495. In the 20th century, Cracow became a center for classical analysis, differential equations, and analytic functions.
This school included Stanisław Zaremba, Tadeusz Ważewski, Kazimierz Żórawski, Władysław Ślebodziński, and Franciszek Leja.