Paul Sophus Epstein (Russian: Павел Зигмундович Эпштейн, romanized: Pavel Zigmundovich Epshteyn; March 20, 1883 – February 8, 1966) was a Russian-American mathematical physicist.

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.

He worked on were the settling of gases in the atmosphere, the theory of vibrations of shells and plates and the absorption of sound in fogs and suspensions.

Epstein calculated in 1924 the drag on a sphere moving in a gas in the rarefied (i.e., high, or at least not small, Knudsen number) flow regime.

He was very interested in Freudian psychology and was one of the founding members of a Psychoanalytic Study Group (together with Thomas Libbin) that later merged into the Los Angeles Institute for Psychoanalysis.

In the 1930s he published two articles in the monthly literary and scientific magazine Reflex - "The Frontiers of Science" and "Uses and Abuses of Nationalism".