This indicates the geographical distribution and mutual influence of the leading Polish mathematicians, as well as the areas in which they were active. The latter are divided into logic, set theory, topology, functional analysis, classical analysis, differential equations, differential geometry, and applied mathematics.
The term Warsaw School of Mathematics is used to describe a group of mathematicians working in logic, set theory, point-set topology and real functions in the 1920's and 1930's. Their journal was Fundamenta Mathematicae (founded in 1920), the first specialized mathematical journal in the world.
Members of this school were: Wacław Sierpinski, Kazimierz Kuratowski, Edward Marczewski, Bronisław Knaster, Zygmunt Janiszewski, Stefan Mazurkiewicz, Stanisław Saks, Karol Borsuk, Roman Sikorski
Members of the Warsaw topology group who emigrated in the 1930's: Nachman Aronszajn (1907-1980) and Samuel Eilenberg (now in New York).
The group of logicians in Warsaw also included Stanislaw Lesniewski (1886-1939), Adolf Lindenbaum (1904-1942), and Alfred Tarski (since 1942 in Berkeley). Here in 1933 Tarski published his celebrated theorem on the undefinability of the notion of truth. Jan Łukasiewicz and Andrzej Mostowski belonged also to this group.
Fourier analysis was developed in Warsaw by Aleksander Rajchman and Antoni Zygmund (1900-1992). The latter moved to the Uniwesity of Vilna (founded 1578) where he led an analysis group in the 1930's. During the war he settled in the USA. Józef Marcinkiewicz, Otton M. Nikodym and Jerzy Spława-Neyman were other members of this group.
The Lvov School also included Herman Auerbach, Stefan Kaczmarz, Antoni Łomnicki, Mark Kac and Stanisław Ulam (both now in USA).
The Jagiellonian Uniwesity in Cracow (Kraków), the ancient capital of Poland, was founded in 1364. Copernicus studied mathematics and astronomy here from 1491 to 1495. In the 20th century, Cracow became a center of classical analysis, differential equations and analytic functions.This school included Stanisław Zaremba, Tadeusz Ważewski, Kazimierz Żórawski, Władyslaw Ślebodziński and Franciszek Leja.