James Joseph Sylvester

James Joseph Sylvester was born on 3 September 1814 into a Jewish family in London. After his early study at boarding schools in Highgate and Islington, he entered the University of London, in its first term in operation in 1828. There, Augustus De Morgan led the mathematics program. After only five months, Sylvester's relatives withdrew him from the institution owing to his apparent immaturity for university life. Sylvester returned to college in 1831, this time at St. John's College, Cambridge. Although he attained the outstanding distinction of Second Wrangler on the Mathematical Tripos in 1837, he was barred from receiving his degree and from competing for a fellowship or a professorship at Cambridge. This resulted from his inability to subscribe to the Thirty-nine Articles of the Church of England, a requirement of all who presented themselves for degrees or for positions at Cambridge. (At Oxford, subscription was required before a student was even allowed to matriculate.) Sylvester did win the professorship of natural philosophy in 1838 at non-sectarian University College London. In 1841, he was awarded an M.A. from Trinity College, Dublin.

Dissatisfied with his teaching duties in the chair of natural philosophy, Sylvester left England for Charlottesville in 1841. In November of that year, he assumed the University's professorship of mathematics, a post left vacant at Charles Bonnycastle's death. Although anti-Semitic articles in Richmond newspapers preceded his arrival, Sylvester was greeted warmly by the University community [2]. His contentment at the university was short-lived, however. Unruly students in his courses and the faculty's unwillingness to exact the punishment demanded by Sylvester for one Mr. Ballard caused his resignation from the University, effective in March 1842. (Sylvester insisted upon expulsion and the faculty would only support a reprimand, given the recent history of student unrest on the Grounds.) "Such were the accidents that accompanied the avoidable loss to the University of Virginia of one of the most extraordinary mathematicians of modern times" [1, 77].

After trying unsuccessfully to secure positions at Columbia, Harvard, and elsewhere in the United States, Sylvester returned to London eventually to became an actuary and secretary at Equity and Law Life Assurance Company for ten years beginning in 1845. During this period, he met Arthur Cayley, who would become a mathematical catalyst and lifelong friend.

By 1850, Sylvester had "exploded onto the mathematical scene, reaching new heights of productivity and creativity" [2, 66]. In 1850 and 1851, drawing from his prior work on determinants and on the theory of forms, he synthesized in a series of twenty papers his ideas and the results of others into what would later be recognized as invariant theory. He spent the rest of his actuarial career further developing this theory with Cayley.

Sylvester returned to academia in 1855, becoming Professor of Mathematics at the Royal Military Academy in Woolwich, England. Although his achievements were highly recognized by the mathematical community during his years at Woolwich, Sylvester did not find his duties at the Academy conducive to his research. "[H]e 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' " [4, 210]. In the late 1860s, the situation had gotten so dire that he wrote to Cayley that "I have done no mathematics--ever intending and ever putting it off. . . . If I thought it would do any good I would ask you to pray for my rescue from this enslaving indolence and paralysis of the will for such it amounts to" [3, 131-132].

After being forced into an early retirement from the Academy in 1870, Sylvester spent six years adrift in London, occupying his time primarily by composing poetry. In 1876, however, his luck changed, and he crossed the Atlantic once more to establish the mathematics program at the newly opened Johns Hopkins University. His professorship there "marked the beginning of a quarter-century-long process of establishing mathematics at the research level in the United States" [4, 218] and reinvigorated his study of invariants. In particular, he crafted America's first true graduate program in mathematics, guided nine students in their doctoral research, and made major advances in invariant theory, combinatorics, and the theory of matrix algebras.

Seven years later, Sylvester traveled back to England to assume the Savilian Chair of Geometry at New College, Oxford, a position which, after the 1871 repeal of the religious restrictions, was finally open to him. He tried to build a school of mathematical research at Oxford like the one he had animated at Hopkins, but his efforts were premature. As he put it in a letter to Hopkins President, Daniel Coit Gilman, in March of 1887: "It seems to me that Mathematical science here is doomed and must eventually fall off like a withered branch from a Tree which derives no nutriment from its roots" [3, 264].

Failing health and eyesight caused Sylvester to step down officially from his chair in 1894. He died in London on 15 March 1897, one of England's nineteenth-century mathematical luminaries.

Selected References

1. Philip Alexander Bruce, History of the University of Virginia, 5 vols. (1920).
2. Lewis S. Feuer, "America's First Jewish Professor: James Joseph Sylvester at the University of Virginia," American Jewish Archives 36 (1984), 151-201.
3. Karen Hunger Parshall, James Joseph Sylvester: Life and Work in Letters, Oxford: Clarendon Press, 1998.
4. Karen Hunger Parshall and David E. Rowe, The Emergence of the American Mathematical Research Community, 1876-1900: J. J. Sylvester, Felix Klein, and E.H. Moore (Providence: American Mathematical Society and London: London Mathematical Society, 1994).