Epstein was born and brought up in Frankfurt, where his father was a professor.
From 1895 to 1918 he was a Privatdozent at the University in Strasbourg, which at that time was part of the German Empire.
At the end of World War I the city of Strasbourg reverted to France, and Epstein, being German, had to return to Frankfurt.
Epstein was appointed to a non-tenured post at the university and he lectured in Frankfurt from 1919.
Because of his age (68) he was unable to find a new position abroad, and finally committed suicide by barbital overdose at Dornbusch, fearing Gestapo torture because he was a Jew.