Ruffini (Paolo, 1756-1822) was an Italian mathematician, physician and philosopher. Born in Valentano, Italy, and died in Modem. He studied at the University of Modena, obtained a doctor's degree in 1788, and was employed as a professor in the same year. In 1814, he became President of the University of Modena.
Ruffini has made important contributions in mathematics, medicine, philosophy and other fields. In mathematics, it is proved that equations higher than 4 times generally cannot be solved by radical method (1799), which is called Abel Ruffini theorem. This work is of great significance to the generation of permutation group theory and the development of algebra. He introduced the concepts of transitive group and primitive group, and proved that "a group may not have subgroups whose rank is any factor of its rank". The division of polynomials is also studied, and the rule of solving algebraic equations by approximation is obtained. A similar rule was obtained by the British mathematician Homer (W. G.) 15 years later, which is called Ruffini Horner rule. In fact, this law was discovered by Chinese mathematician Qin Jiushao 500 years ago, so it should be called Qin Jiushao Law.
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