"Other mathematicians confess that they have been unable to understand this proof and some have made the correct observation that Ruffini, perhaps by proving too much, had proved nothing in a satisfactory manner. Monsieur Abel has shown by a more penetrating analysis that there can be no algebraic [radical] roots, but he does not deny the possibility of transcendental roots. We recommend this problem to the attention of mathematicians specializing in this field."
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Augustin-Louis Cauchy, commenting on Abel's Mémoire sur les équations algébriques où on démontre l'impossibilité de la résolution de l'équation générale du cinquième degré (1824) as quoted by Øystein Ore, Niels Henrik Abel: Mathematician Extraordinary (1957)
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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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