"Abel criticised the use of infinite series, and discovered the well-known theorem which furnishes a test for the validity of the result obtained by multiplying one infinite series by another. He also proved the binomial theorem for the expansion of (1 + x)^n when x and n are complex. As illustrating his fertility of ideas... notice his celebrated demonstration that it is impossible to express a root of the general quintic equation in terms of its coefficients by means of a finite number of radicals and rational functions; this theorem was the more important since it definitely limited a field of mathematics which had previously attracted numerous writers. ...this theorem had been enunciated as early as 1798 by Paolo Ruffini... but I believe that the proof he gave was lacking in generality."
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W. W. Rouse Ball, A Short Account of the History of Mathematics (1912)
https://en.wikiquote.org/wiki/Niels_Henrik_Abel
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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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