Arthur Cayley
By the time of Euclid, the Greeks knew how to solve quadratic equations. The general solution of the cubic equation was found by Tartaglia and Cardano in the 16th century, and the general solution of the quartic equation was found by Ferrari shortly thereafter. Attention then turned to the quintic equation, and the attempt to solve it was one of the central themes in the development of algebra over the next three centuries. Finally, in 1824 Abel showed that there is no formula for the solution of the general quintic. Nowadays, this result is best understood in the context of Galois theory. Galois's work was done in 1832 but did not become known until its posthumous publication by Liouville in 1846. The quintic continued to hold great interest for mathematicians, including Cayley and especially Harley, and many of their joint computations were related to it. (In modern language, they investigated the resolvent and discriminant of the general quintic.) This interest for Cayley continued throughout his lifetime. One of his last published papers, in 1894, dealt with the quintic: “On the Sextic Resolvent Equations of Jacobi and Kronecker”. Moreover, he was preparing a paper on the quintic, which was incomplete at his death. The manuscript here consists of several drafts of this paper. In one of these drafts, he refers to his 1894 paper on the Sextic resolvent equations of Jacobi and Kronecker. -Prof. Steven H. Weintraub, Dept. of Mathematics, Lehigh University
This memoir is available on the digital library project I Remain.