861The Italian mathematician Paolo Ruffini,born in 1765, is responsible forsynthetic division, also known asRuffini’s rule, a technique used for thedivision of polynomials that is coveredin this chapter.Ruffini was not merely a mathematicianbut also held a licence to practisemedicine. During the turbulent years ofthe French Revolution, Ruffini lost hischair of mathematics at the university ofModena by refusing to swear an oath tothe republic. Ruffini seemed unbotheredby this, indeed the fact that he could nolonger teach mathematics meant that hecould devote more time to his patients,who meant a lot to him. It also gave hima chance to do further mathematicalresearch.The project he was working onwas to prove that the quintic equation cannot be solved by radicals. BeforeRuffini, no other mathematician published the fact that it was not possible to solvethe quintic equation by radicals. For example, Lagrange in his paper Reflections on theresolution of algebraic equationssaid that he would return to this question, indicatingthat he still hoped to solve it by radicals. Unfortunately, although his work wascorrect, very few mathematicians appeared to care about this new finding. Hisarticle was never accepted by the mathematical community, and the theorem isnow credited to being solved by Abel.