Arthur Cayley, Robert Harley and the quintic equation: newly discovered letters 1859–1863

Abstract

Beginning in the 1840's, Arthur Cayley (1821–1895) led a vast invariant theory programme in algebra. After learning of results of James Cockle (1819–1895) and Robert Harley (1828–1910), he applied the techniques of invariant theory to the calculation of resolvents of quintic equations. Letters recently discovered reveal the priorities of Cayley and Harley with respect to the quintic, an approach which was at variance with that via the theory of groups. As another recently discovered manuscript reveals, Cayley returned to this subject in his final days.