Paolo Ruffini


Paolo Ruffini 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 that quintic equations cannot be solved by radicals, 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 and a medical doctor including scientific work on typhus.

Group Theory

In 1799 Ruffini marked a major improvement for group theory, developing Joseph Louis Lagrange's work on permutation theory. Lagrange's work was largely ignored until Ruffini established strong connections between permutations and the solvability of algebraic equations. Ruffini was the first to controversially assert the unsolvability by radicals of algebraic equations higher than quartics. This angered many members of the community such as Gian Francesco Malfatti. Work in this area was later carried on by those such as Abel and Galois who succeeded in such a proof.

Publications