Abel-Ruffini's theorem

from Wikipedia, the free encyclopedia

The set of Abel-Ruffini stating that a general polynomial equation fifth or higher degree not d by radicals. H. Root expressions , is solvable.


Paolo Ruffini , Teoria generale delle equazioni , 1799

The first proof of this theorem was published by Paolo Ruffini in 1799. However, this evidence was sketchy and largely ignored. A complete proof was provided by Niels Henrik Abel in 1824 .

The Galois theory, developed a little later by Évariste Galois , provides a deeper insight into the problem . Using the more general results of Galois theory, only two points need to be shown to prove Abel-Ruffini's theorem: