Paolo Ruffini made significant contributions in the areas of medicine and philosophy, as well as mathematics, where he developed the theory that a quintic equation cannot be solved by radicals. This theory later came to be known as the Abel-Ruffini theorem, named after Ruffini and the Norwegian mathematician Niels Abel, who published the first accepted version of this theorem. Ruffini also played a crucial role in the development of group theory.

Ruffini was born September 22, 1765, in Valentano, Papal States (also known as Valentano, Viterbo and now part of Italy), to Basilio Ruffini, a physician, and his wife, Maria Francesca Ippoliti. He moved with his parents to Modena, Duchy of Modena (now also part of Italy) when he was a teenager and attended the University of Modena, where he studied medicine, philosophy, literature, and mathematics. He practiced mathematics with many well-known instructors and mathematicians, including Luigi Fantini, who taught...