Building an International Reputation: The Case of J. J. Sylvester (1814–1897)

Abstract

James Joseph Sylvester prolific, gifted, flamboyant, egocentric, cantankerous. At the time of his death in London on 15 March, 1897, Sylvester's reputation internationally as one of the nineteenth century's principal mathematical figures had long been secure. He had worked hard to assure this. Obviously, he had done much seminal work in building the theory of invariants, and this had contributed to his renown. Yet, Sylvester had felt compelled to establish ties directly with mathematicians at home but more importantly abroad in order to make his name known. Was this just a matter of egocentrism, or did other factors contribute to his international focus? What did it take to become an internationally recognized British mathematician in the latter half of the nineteenth century, when first France and then Germany very much set the mathematical standard? Why was this even important? As the centenary of Sylvester's death brings historians and mathematicians together in England to celebrate his life and research, we examine some of the reasons why Sylvester valued the international mathematical arena so highly and how he used it to his advantage during the course of his career. It is well-known that Sylvester, as a Jew, was, like all non-Anglicans, debarred by the Test Acts from taking the Cambridge degree he had earned as Second Wrangler in 1837 and from holding a Cambridge fellowship or professorship. His first position, the professorship of natural philosophy at nonsectarian University College London, was too far from his real interests and expertise to satisfy him, so he gave it up in 1841 after only three years for the uncertain fortunes of a professorship of mathematics in exile far from home (and, he quickly came to think, far from civilization!) at the University of Virginia. He lasted there for four-and-a-half months before resigning over a matter of principle and fleeing northward to New York City and his brother's home. From there, he tried in vain for some eighteen months to secure a new position in the United States at Columbia College, at Harvard with Benjamin Peirce, in the Washington, D.C. area, and even at the University of South Carolina before returning to England to resume what he termed the fruitless and hopeless struggle with an adverce [sic] tide of affairs [39]. By the close of 1844, though, he proudly reported having recovered [his] footing in the world's slippery path [39] thanks to his assumption of the post of actuary and secretary at the Equity and Law Life Assurance Company in London. During the decade from 1845 to 1855, he prepared for and passed the Bar; he met his mathematical alter ego, Arthur Cayley; and he produced his ground-breaking series of papers in what would come to be known as invariant theory. The next fifteen years found him in his first sustained academic post, the professorship of mathematics at the Royal Military Academy in Woolwich, where he taught drudgerous mathematics to mostly uncaring students and fought with the military authorities over teaching loads destined, he was convinced, to bring the extinction of my scientific existence [40]. Sylvester's career trajectory