"Having found a method differing from that of Ferrari for reducing the solution of the general biquadratic equation to that of a cubic equation, Euler had the idea that he could reduce the problem of the quintic equation to that of solving a biquadratic, and Lagrange made the same attempt. The failures of such able mathematicians led to the belief that such a reduction might be impossible. The first noteworthy attempt to prove that an equation of the fifth degree could not be solved by algebraic methods is due to Ruffini (1803, 1805), although it had already been considered by Gauss. The modern theory of equations is commonly said to date from Abel and Galois. ...Abel showed that the roots of a general quintic equation cannot be expressed in terms of its coefficients by means of radicals."