Mazur made important contributions to geometrical methods in linear and nonlinear functional analysis and to the study of Banach algebras.

He was also interested in summability theory, infinite games and computable functions.

[1] Mazur, with Juliusz Schauder, was an Invited Speaker of the ICM in 1936 in Oslo.

On 6 November 1936, he posed the "basis problem" of determining whether every Banach space has a Schauder basis, with Mazur promising a "live goose" as a reward: 37 years later and in a ceremony that was broadcast throughout Poland, Mazur awarded a live goose to Per Enflo for constructing a counter-example.

He also worked at the State Institute of Mathematics, which was incorporated into the Polish Academy of Sciences in 1952.