Steinhaus was born in Jasło in a Jewish family. He gained his PhD from the University of Göttingen, at David Hilbert. From 1920 to 1941 he was professor at the University ofLwów, from 1945 to 1961 at the University of Wrocław, from 1961 to 1952 at the University of Notre Dame in Indiana and in 1966 at the University of Sussex. From 1945 he was a corresponding member of PAU (the Polish Academy of higher education). From 1952 he was a member of the Polish Academy of Sciences and of many international scientific societies and academies.
In 1920 he was one of co-founders of the Lwów school of mathematics. He wrote more than 170 works in the field of mathematical analysis, probability theory and statisticthe. Together with Stefan Banach in 1929 he founded the mathematical journal, Studia Mathematica on.
He described the mathematics once as the "Science of nonexistent things."