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 medical doctor including scientific work on typhus.