Paul Sophus Epstein (Warsaw, then part of Imperial Russia, now Poland, March 20, 1883 – Pasadena, February 8, 1966) was a Russian-American mathematical physicist. He was known for his contributions to the development of quantum mechanics, part of a group that included Lorentz, Einstein, Minkowski, Thomson, Rutherford, Sommerfeld, Röntgen, von Laue, Bohr, de Broglie, Ehrenfest and Schwarzschild.
Paul Epstein's parents, Siegmund Simon Epstein and Sarah Sophia (Lurie) Epstein were of a middle class Jewish family. He said that his mother recognized his potential at the age of four years and predicted that he would be a mathematician. He went to the Hochschule in Minsk, and from 1901-1905 studied mathematics and physics at the Imperial University of Moscow under Pyotr Nikolaevich Lebedev. In 1909 he graduated, and became a Privatdozent at the University of Moscow. In 1910 he went to Munich, Germany, to do research under Arnold Sommerfeld, who was his advisor, and Epstein was granted a Ph.D. on a problem in the theory of diffraction of electromagnetic waves. from the Technische Universität München, in 1914. At the outbreak of World War I he was in Munich, and considered an "enemy alien". Thanks to Sommerfeld's intervention he was allowed to stay in Munich as a private citizen, and could continue with his research. By that time Epstein became interested in the quantum theory of atomic structure. In 1916, he published a seminal paper explaining the Stark effect using the Bohr Sommerfeld ("old") quantum theory. After the war he went to Leiden, to become Hendrik Lorentz' and Paul Ehrenfest's assistant. In 1921 he was recruited by Robert Millikan to come to the California Institute of Technology, where he remained for the rest of his career. In 1922 he published 3 papers on Bohr's quantum mechanics in the Zeitschrift fur Physik and one in the Physical Review. In 1926 he published the paper "The Stark Effect from the Point of View of Schrodinger's Quantum Theory" in the Physical Review, as well as "The New Quantum Theory and the Zeeman Effect" (1926), and "The Magnetic Dipole in Undulatory Mechanics" (1927).