Quintic history

His first demonstration was regarded as insufficient, and he published a revised version in 1813 after discussions with several prominent mathematicians.

Unperturbed, Ruffini practiced medicine and continued his mathematical research until the defeat of Napoleon in 1814, when he returned permanently to the University of Modena as rector, in addition to holding professorships in mathematics and medicine.

22, 1765, Valentano, Papal States—died May 9, 1822, Modena, Duchy of Modena), Italian mathematician and physician who made studies of equations that anticipated the algebraic theory of groups.

In 1824 Norwegian mathematician Niels Abel also presented a proof that, in general, quintic equations could not be solved by radicals.

Systems obeying the group laws first appeared in 1770 in Joseph-Louis Lagrange’s studies of permutations of roots of equations; however, the word group was first attached to a system of permutations by Évariste Galois in 1831.

His work on group theory was not widely recognized until it was published in 1846, 14 years after his death.

In 1849 he published a paper in which he proposed the 32 classes of molecular structures found in crystals.

In 1878 Ludwig Kiepert, a German mathematician, wrote an article describing a systematic procedure that could be used to solve quintic equations based upon Galois's group theory and Hermite's use of elliptic functions.

Systems obeying the group laws first appeared in 1770 in Joseph-Louis Lagrange’s studies of permutations of roots of equations; however, the word group was first attached to a system of permutations by Évariste Galois in 1831. It was Heinrich Weber, in 1882, who first gave a purely axiomatic description of a group independently of the nature of its elements.

Klein first described this relationship in 1884.

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