The rise of Cayley's invariant theory (1841–1862)

Abstract

In his pioneering papers of 1845 and 1846, Arthur Cayley (1821–1895) introduced several approaches to invariant theory, the most prominent being the method of hyperdeterminant derivation. This article discusses these papers in the light of Cayley's unpublished correspondence with George Boole, who exercised considerable influence on Cayley at this formative stage of invariant theory. In the 1850s Cayley put forward a new synthesis for invariant theory framed in terms of partial differential equations. In this period he published his memoirs on quantics, the first seven of which appeared in quick succession. This article examines the background of these memoirs and makes use of unpublished correspondence with Cayley's lifelong friend, J. J. Sylvester.