In 1799 an Italian built upon the work of Joseph Lagrange and used permutat
In 1799 an Italian built upon the work of Joseph Lagrange and used permutation groups to approach this mathematical result. Despite this one can achieve good numerical results, for instance with Newton-Raphson methods. It shows that an analog of Cardano's formula cannot exist in some cases. In 1824, it was shown that a certain group did not have a composition series with Abelian quotients, and hence was not solvable. The group of interest is called a Galois group. FTP, name this algebraic result proved by Niels Abel which demonstrates the inability to generalize the exact forms of solutions for polynomials above a certain degree.
In 1799 an Italian built upon the work of Joseph Lagrange and used permutation groups to approach this mathematical result.
insolvability of the quintic (accept Abel-Ruffini theorem; also accept clear knowledge equivalents, so long as they refer to 5th degree polynomials)