The young Arthur Cayley

Abstract

Arthur Cayley, F.R.S. (1821–1895) is widely regarded as Britain's leading pure mathematician of the 19th century. From his start as a Cambridge prodigy, he built up a formidable record of publication, from incidental notes to extensive memoirs, on a wide range of mathematics. His emergence as a mathematician, before he became the sober–minded eminence of the 1860s and 1870s, is largely unknown. The primary guide to his whole life remains, more than a century later, the obituary written by his student and successor at Cambridge, A.R. Forsyth. The folklore surrounding Cayley's life is dominated by his collaboration with James Joseph Sylvester, F.R.S. (1814–1897). This partnership, tempered by Sylvester's obsession with the apportionment of credit, began in earnest in the 1850s. In this paper, I attempt to signpost Cayley's formative years, when he was at the beginning of his long mathematical journey, the period which ends on 3 June 1852, the date of his election to the Royal Society, when he formally came of age as a Victorian man of science.