The Polish Mathematical Society was established in 1919. (...) Stefan Banach, Franciszek Leja, Otto Nikodym, Stanisław Zaremba and Kazimierz Żorawski were among its founder members, and Stanisław Zaremba was elected as the President of the Society. In 1921, the Mathematical Society in Cracow (Towarzystwo Matematyczne w Krakowie) was transformed into a national Polish Mathematical Society (Polskie Towarzystwo Matematyczne; PTM) with its headquarters in Kraków (Cracow).
According to its first statute, the Society’s aim was "a comprehensive cultivation of pure and applied mathematics by means of scientific sessions combined with lectures". The first change to the statute -  still in 1921 - resulted in the following insertion: "publication of a  periodical and maintenance of contacts
with the mathematical scientific movement".
Members not residing in Cracow were admitted to PTM through local sections. Within the period 1921-1939, the following sections existed: one in Lwów (Lvov), since 1921, and three others since 1923 in Warszawa (Warsaw), Poznań and Wilno (Vilnius). Since 1937, mathematicians from Cracow have constituted part of the Cracow section (after the Society’s headquarters had been moved to Warsaw
and its statute changed).