The decline of Cayley's invariant theory (1863–1895)

Abstract

From the 1860s the German symbolic approach to invariant theory was in ascendancy. This article discusses the of work Arthur Cayley (1821–1895) and his reaction to this new line of enquiry. The symbolic method is outlined and compared with Cayley's viewpoint in which the calculation and exhibition of invariants and covariants were of primary importance. Cayley's Law and Gordan's finiteness theorem, two principal results in the theory, are discussed. Also covered is J. J. Sylvester's Fundamental Postulate, which both reveals the character of the English empirical approach to invariant theory and illustrates its inherent weakness. The article examines the background to Cayley's final three memoirs on quantics, his last work in invariant theory, and it makes use of correspondence with his friend Sylvester.