Ważewski attended secondary school in Tarnów, today in the south-east of Poland, but at that time part of Austrian controlled Galicia. On graduating from secondary school his intention was to study physics and he entered the Jagiellonian University in Kraków to study that subject. However, he was strongly influenced by Zaremba and changed his course from physics to mathematics.
Under Zaremba, Ważewski became interested in set theory and topology and decided to study in Paris for his doctorate. This was a typical route for Polish mathematicians of this period, forced to study abroad (as Poland was partitioned) many chose the same route as Ważewski studying in Polish universities in Austrian controlled Galicia and completing their education in France.
Ważewski studied in Paris between 1921 and 1923 continuing his interest in topology acquired during his studies at Kraków under Zaremba. His doctoral dissertation, on topological results relating to dendrites, was examined in 1923 by the powerful examining committee consisting of Borel, Denjoy and Montel.
Having secured his doctorate, Ważewski returned to the Jagiellonian University in Kraków where he was he was appointed a docent in 1927. At about this time his interests shifted away from set theory and topology and he became interested in analysis. In 1933 he was appointed extraordinary professor at the Jagiellonian University.
Kraków was taken by the German army at the beginning of World War II. A German governor was installed in Wawel Castle, and executions members of the teaching staff of the Jagiellonian University took place. Some 55,000 Jews from the city were sent to the Auschwitz-Birkenau concentration camp. Ważewski was sent to the Sachsenhausen- Oranienburg concentration camp north-west of Berlin where he survived for two years. Some were not so lucky, for example A Hoborski was a mathematics professor at the Jagiellonian University who died in the Sachsenhausen- Oranienburg concentration camp in February 1940.
Ważewski returned to Kraków and taught in the underground university there despite the severe risk to his life. In 1945 Kraków was liberated in a surprise attack made by Soviet forces. Ważewski was appointed a full professor at the Jagiellonian University and put all his efforts into restoring the educational system which had been destroyed.
Ważewski made important contributions to the theory of ordinary differential equations, partial differential equations, control theory and the theory of analytic spaces. The contribution for which he is most famous was made after his appointment as professor at the Jagiellonian University after the end of World War II. Kuratowski explains in  how his idea:-
... was to bring him fame and lead to the development of a new school of differential equations. ... he succeeded in applying with amazing effect the topological notion of retract (introduced by K Borsuk) to the study of the solutions of differential equations.Ważewski was invited to explain his ideas in a plenary address at the International Congress of Mathematicians in Amsterdam in 1954 and :-
Lefschetz considered his method of retracts one of the most important achievements in the theory of differential equations since the war.We mentioned above that Ważewski worked in control theory. His interest in that topic began around 1960 and he published a series of important papers on the topic through the 1960s. His work on the time optimal control problem, to which he took a topologically oriented approach, is described in . By this time he was heading his own school of mathematics which was highly successful because of the :-
... broad scope of his problems, his skill in putting forward deeply motivated questions and his great teaching talent.Kuratowski also comments in  about Ważewski's personality describing him as:-
... gifted with immense qualities of character: his proverbial modesty, kindness, and the great care he showed his students meant that, besides general respect for an excellent scholar, everybody who had the good fortune to know him was charmed by his extraordinary personality.
Article by: J J O'Connor and E F Robertson