In mathematics, the Abel–Ruffini theorem states that there is no solution in radicals to general polynomial equations of degree five or higher with arbitrary coefficients. Here, general means that the coefficients of the equation are viewed and manipulated as indeterminates.
Paolo Ruffini, Teoria generale delle equazioni, 1799
Niels Henrik Abel 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 over 250 years. He was also an innovator in the field of elliptic functions, discoverer of Abelian functions. He made his discoveries while living in poverty and died at the age of 26 from tuberculosis.
Niels Henrik Abel
Postcard of Gjerstad church and rectory in 1890–95. The main building of the rectory was the same as when Abel lived here.
From the notebook of Niels Henrik Abel
Christine Kemp