The family moved to the Kielce province in south-eastern Poland after the German invasion of 1939 but returned to Poznań after the war.

[1] Stanisław completed his high school education in 1949 excelling at math and continued on at Poznań University to study mathematics.

Later in 1952 he continued his studies at University of Wrocław and earned his master's degree in 1954.

Knapowski was appointment an assistant at Adam Mickiewicz University in Poznań under Władysław Orlicz and worked towards his doctorate.

He studied under the direction of Pál Turán starting in Lublin in 1956.

[2] Knapowski began to work in this area and finished his doctorate in 1957 “Zastosowanie metod Turaná w analitycznej teorii liczb” ("Certain applications of Turan's methods in the analytical theory of numbers").

Knapowski spent a year in Cambridge where he worked with Louis J. Mordell and listened to classes by J.W.S.

Knapowski returned to Poznań to finish another thesis to complete a post-doctoral qualification needed to lecture at a German university.

[3] In 1962 the Polish Mathematical Society awarded him their Mazurkiewicz Prize and he moved to Tulane University in New Orleans, United States.

He died in a traffic accident where he lost control of his car while leaving the Miami airport.

[2] Knapowski expanded on the work of others in several fields of number theory, prime number theorem, modular arithmetic and non-Euclidean geometry.

Mathematicians work on primality tests to develop easier ways to find prime numbers when finding them by trial division is not practical.

At the start of the 19th century, Adrien-Marie Legendre and Carl Friedrich Gauss suggested that as

Littlewood proved that there are arbitrarily large values of x for which and that there are also arbitrarily large values of x for which Thus the difference π(x) − Li(x) changes sign infinitely many times.

Stanley Skewes then added an upper bound on the smallest natural number

[6] Knapowski worked in other areas of number theory.

One area was on the distribution of prime numbers in different residue classes modulo

Any other natural number can be mapped into this system by replacing it by its remainder after division by

Knapowski worked to determine the parameters of this modular distribution[8]