"In Leibnitz's day... equations of the 2d, 3d, and 4th degrees were reduced to pure equations, but the reduction of equations of higher degrees than the 4th remained an unsolved problem, on which mathematicians spent much labor, until Niels Henrik Abel... a Norwegian mathematician of great ability and acuteness, demonstrated (1824) that the quintic equation and a fortiori the general equation of any order higher than five, is incapable of solution by radicals. Cf. Abel, Démonstration de l'impossibilité de la résolution algébrique des équations générates qui passent le quatriéme degré"
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Alfred Gideon Langley, footnote to Gottfried Wilhelm Leibniz, New Essays Concerning Human Understanding (1916) Tr. Alfred Gideon Langley, citing Euvres complétes, ed. by Holmboe, 2 vols. Christiania, 1839 Vol. 1 pp. 5-24 and in Crelle, "Journ. f. Math.," 1826, Vol. 1 pp. 65-84.—TR
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Niels Henrik Abel
Niels Henrik Abel (5 August 1802 – 6 April 1829) was a Norwegian mathematician who made pioneering contributions in a variety of fields. His most famous single result is the first complete proof demonstrating the impossibility of solving the general quintic equation in radicals. This question was one of the outstanding open problems of his day, and had been unresolved for 250 years. He was also an innovator in the field of elliptic functions, discoverer of Abelian functions. Despite his achievem
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