Paolo Ruffini (September 22, 1765 – May 10, 1822) was an Italian mathematician and philosopher.

By 1788 he had earned university degrees in philosophy, medicine/surgery, and mathematics. Among his work was an incomplete proof (Abel – Ruffini theorem) that quintic (and higher-order) equations cannot be solved by radicals (1799), and Ruffini's rule, which is a quick method for polynomial division. Ruffini also made contributions to group theory in addition to probability and quadrature of the circle.

He practiced as both a professor of mathematics (University of Modena) and a doctor including scientific work on typhus.