Rudolf Otto Sigismund Lipschitz (14 May 1832 – 7 October 1903) was a German mathematician and professor at the University of Bonn from 1864. Peter Gustav Lejeune Dirichlet was his teacher. He supervised the early work of Felix Klein.

Lipschitz was Jewish. While Lipschitz gave his name to the Lipschitz continuity condition, he worked in a broad range of areas. These included number theory, algebras with involution, mathematical analysis, differential geometry and classical mechanics.

He wrote: Lehrbuch der Analysis (two volumes, Bonn 1877, 1880); Wissenschaft und Staat (Bonn, 1874); Untersuchungen \xfcber die Summen von Quadraten (Bonn, 1886); Bedeutung der theoretischen Mechanik (Berlin, 1876).