Sylvester, James Joseph

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SYLVESTER, JAMES JOSEPH

(b. London, England, 3 September 1814; d. London, 15 March 1897), mathematics.

For the original article on Sylvester see DSB, vol. 13.

Recent scholarship—as reflected in the accompanying bibliography—has provided deeper insights into the context of James Sylvester’s life and work. In particular, Sylvester’s formative years and the role that his sense of his Jewish identity played in shaping his carreer are much better understood in the early twenty first century, as are his contributions to the emergent acturial profession in Victorian Britain and his efforts both in England and the United States to establish “research mathematician” as a professional category.

Sylvester, as a Jew in Victorian Britain, had to forge for himself a career path to his self-conscious goal of becoming a professional research mathematician; he lived at a time when and in a place where that category did not yet exist. In successfully realizing his goal he gained a reputation primarily as one of the founders of the theory of invariants, an area that developed largely independently in Britain and on the Continent.

Formative Years Sylvester was a second-generation Anglo Jew; his paternal grandparents had emigrated from Germany and had established themselves in Liverpool by the 1770s. When Sylvester’s father, Abraham, married his mother, Miriam Woolf of Portsmouth, in 1790, the extended family had secured itself financially as silversmiths, watchmakers, and naval and privateers’ agents and had achieved prominence both in Liverpool’s Jewish community and among its intelligentsia.

Sometime between 1807 and 1810 Abraham and Miriam moved their family of eight children—four girls and four boys (two other children, one son and one daughter, had died in infancy)—to London; at least two more boys followed, the last of whom was James. In London, Abraham prospered as a merchant in the predominantly Jewish area of Goodman’s Fields. Intent that his son should get a secular as well as a religious education, Abraham sent him to Highgate to England’s first boarding school for Jewish boys, an establishment founded in 1799 for sons of the Anglo-Jewish elite. While there, James’s mathematical talents were recognized, perhaps sparking his move to a school in Islington that offered specialized mathematical tuition and then to nonsectarian London University (later University College London) in its first year of operation in 1828. James enrolled as James Joseph Sylvester, thus following at least three of his older brothers in formally abandoning the Jewish surname Joseph and adopting that of Sylvester. In February 1829, after less than six months under the mathematical tutelage of Augustus De Morgan, Sylvester was withdrawn by his family from the university and sent to live with his elder sisters in Liverpool; his immaturity had apparently resulted in inappropriate behavior. He was next enrolled in Liverpool’s Royal Institution School, a preparatory school geared toward admission to Oxbridge. At this time, however, Oxbridge was effectively closed to Jews: they could not matriculate at Oxford, and although they could matriculate at Cambridge they could not take degrees. Still, moves were afoot nationally in the early 1830s that might have changed this by removing the obstacles that debarred Jews from rights and privileges enjoyed by their Anglican and even dissenting brethren.

Sylvester entered St. John’s College, Cambridge, as a sizar—a scholarship student—in 1831, ranking first freshman prizeman in 1832 but a disappointing fifth a year later in 1833. After returning to Cambridge for the fall of what would have been his third year, a two-year hiatus ensued, ostensibly due to his own ill health but during which the Jewish question was hotly debated by the university; his father died in Liverpool (in 1834), and he published a 132-page Collection of Examples on the Integral Calculus as a study guide principally for the culminating examination, the mathematical tripos. Sylvester returned to St. John’s in January 1836 as a full fee-paying pensioner, thanks most likely to the favorable settlement of his father’s estate, but he was once again in absentia during the Easter term of 1836 owing both to a burst ocular blood vessel and to his mother’s death in Liverpool. He finally sat the tripos in January 1837, placing second in the order of merit, but he was debarred from taking his degree because of his refusal as a Jew to swear the required oath “on the true faith of a Christian.” This refusal, shaped by his Jewish identity, forced him to define for himself the career of a research mathematician.

Career That process began at University College London, where his distinction at Cambridge helped win for him the chair of natural philosophy in 1838. Sylvester spent only three years in this post, struggling with its laboratory side but producing several of his works on applied mathematics (related to the theory of light and to fluid and rigid body motion) as well as on the algebraic theory of elimination (see the original DSB entry). He ultimately escaped the physics professorship in 1841—on the heels of taking a BA and an MA from Trinity College Dublin on the basis of his work at Cambridge—by boldly accepting the chair of mathematics at Thomas Jefferson’s non-sectarian University of Virginia. By March 1842, only four-and-a-half months after his arrival in Charlottesville, however, Sylvester had resigned this position over a matter of principle: he had called for the expulsion of one of his students, while his colleagues would only recommend censure. Jobless, he headed to New York City, where two of his elder brothers brokered lottery tickets. From there he tried to no avail to secure another academic post in the United States. Following a proposal of marriage that failed at least partly on religious grounds, he returned to England on 20 November 1843 to face an uncertain future.

By December 1844 Sylvester had become the actuary at the Equity and Law Life Assurance Society in London, a post he would hold until 1855. In this decade he established himself as both an actuary and a research mathematician. Beginning in 1848 he was instrumental in founding the Institute of Actuaries as a professional society for governing the emergent actuarial profession, while from the early 1850s on he self-consciously worked to establish a reputation at home and abroad based on the wholly new mathematical area of invariant theory, which he, together with Arthur Cayley, was developing (see the original entry). By 1854, however, the pressures of the business world had begun to weigh on him as he tried to sustain his research momentum. A second failed proposal of marriage, this time to Barbara Smith (later Bodichon), and two unsuccessful attempts to reenter academia in 1854 were followed in 1855 by his assumption of the chair of mathematics at the Royal Military Academy, Woolwich.

The Woolwich years, which lasted until his fifty-sixth birthday on 3 September 1870 when then-recent changes in the academy’s regulations required his retirement, witnessed much turmoil in Sylvester’s life. Research successes in partition theory in 1859 and in providing the first proof of Newton’s rule for the isolation of pairs of imaginary roots of polynomial equations in 1864 and 1865 (see the original entry) were overshadowed by research droughts and periods of what he termed in an 1867 letter to Cayley “paralysis of the will” (Parshall, 1998, p. 132). Concurrently, however, his professional stature was cemented and prominently recognized both nationally and internationally. Following six years spent in London unemployed, Sylvester won in 1876 the first professorship of mathematics at the explicitly research-oriented Johns Hopkins University in Baltimore based on the mathematical reputation he had secured.

Sylvester’s second transatlantic move proved an unqualified success. In a seven-and-a-half-year tenure from the fall of 1876 through December 1883 he not only resuscitated his invariant-theoretic research and produced new results in number theory, the theory of partitions, and the theory of algebras (see the original entry) but also established America’s first sustained, research-level journal, the American Journal of Mathematics, and created the country’s first research-level program in mathematics. He idiosyncratically but effectively trained a number of members of America’s first generation of research mathematicians, among them, Fabian Franklin, who helped Sylvester carry out the British invariant-theoretic program by explicitly exhibiting the elements in a minimum generating set of covariants for binary forms of successive degrees from two through ten.

Although Sylvester realized in Baltimore precisely the kind of professional research career he had for so long sought, the pressures of his responsibilities as a researcher, journal editor, and trainer of aspiring researchers ultimately proved too much for a man almost in his seventieth year. On hearing in the winter of 1883 of the death of Henry John Stephen Smith, the Savilian Professor of Geometry at Oxford, Sylvester resolved to apply for that prestigious post and at the same time to test, as he explained in an 1883 letter to Cayley, “an important principle,” namely, Oxford’s commitment actually to opening its faculty to Jews (Parshall, 1998, p. 222). (The passage of the Universities Tests Act of 1871 had finally made it legal for Jews and other dissenters to hold positions at Oxbridge.) Oxford passed Sylvester’s test. In naming him Smith’s successor in December 1883, the university appointed its first Jew to the faculty.

Sylvester hoped to transplant to Oxford the research ethos he had so effectively inspired in Baltimore. As he soon realized, however, Oxford was not ready in the 1880s and 1890s to embrace his professional, research-oriented goals. He did enjoy some success in 1886 in sparking interest in new research on what he called reciprocants, that is, differential invariants, and again in 1888 in founding the Oxford Mathematical Society, but when ill health exacerbated by worsening cataracts finally forced him to relinquish his post in 1894, Oxford was still a tradition-bound, undergraduate institution.

Sylvester died in London on 15 March 1897 trying to push his partition-theoretic techniques through to a proof of the Euler-Goldbach conjecture, namely, every even number can be written as the sum of two primes. His burial in the Jewish cemetery in Ball’s Pond (present-day Islington) was attended by representatives of groups that had played key roles in his life and career: Cambridge and Oxford universities, the London Mathematical Society, the Royal Society, and the Jewish community in Britain. His memory and his achievements as a research mathematician were honored by the latter two in the endowment of the Sylvester Medal of the Royal Society of London, the first of which was awarded in 1901.

SUPPLEMENTARY BIBLIOGRAPHY

WORKS BY SYLVESTER

Collection of Examples on the Integral Calculus, in Which Every

Operation of Each Example Is Completely Effected. Cambridge, U.K.: J. and J.J. Düghton, 1835.

“A Supplement to Newton’s First Section, Containing a Rigid

Demonstration of the Fifth Lemma, and the General Theory of the Equality and Proportion of Linear Magnitudes.” Privately printed, 1836.

The Laws of Verse; or, Principles of Versification Exemplified in

Metrical Translations. London: Longmans, Green, 1870. Sylvester’s only published book on versification. He did have privately printed a number of booklets and pamphlets of varying lengths containing collections of his poetry. For a list of some of those as well as for references to Sylvester’s mathematical works, see the original entry.

OTHER SOURCES

Cantor, Geoffrey. “Creating the Royal Society’s Sylvester Medal.” British Journal for the History of Science 37 (2004): 75–92.

Grattan-Guinness, Ivor. “The Contributions of J. J. Sylvester,

F.R.S., to Mechanics and Mathematical Physics.” Notes and Records of the Royal Society of London55 (2001): 253–265.

Lavrinenko, Tatiana. “Solving an Indeterminate Third Degree

Equation in Rational Numbers: Sylvester and Lucas.” Revue d’Histoire des Mathématiques8 (2002): 67–111.

Parshall, Karen Hunger. “America’s First School of Mathematical

Research: James Joseph Sylvester at the Johns Hopkins University.” Archive for History of Exact Sciences38 (1988): 153–196.

———. “Chemistry through Invariant Theory?: James Joseph Sylvester’s Mathematization of the Atomic Theory.” In Experiencing Nature: Proceedings of a Conference in Honor of Allen G. Debus, edited by Paul Theerman and Karen Hunger Parshall, 81–111, Dordrecht, Netherlands: Kluwer Academic, 1997.

———. James Joseph Sylvester: Life and Work in Letters. Oxford:

Clarendon Press, 1998. A selection of Sylvester’s previously unpublished letters with detailed historical and mathematical commentary.

———. “The Mathematical Legacy of James Joseph Sylvester.”

Nieuw Archief voor Wiskunde 17 (1999): 247–267.

———. James Joseph Sylvester: Jewish Mathematician in a

Victorian World. Baltimore, MD: Johns Hopkins University Press, 2006. The first full-length biography of Sylvester.

Parshall, Karen Hunger, and David E. Rowe. The Emergence of the American Mathematical Research Community, 1876–1900:

J. J. Sylvester, Felix Klein, and E. H. Moore. Providence, RI: American Mathematical Society, and London: London Mathematical Society, 1994.

Parshall, Karen Hunger, and Eugene Seneta. “Building an

International Reputation: The Case of J. J. Sylvester.” American Mathematical Monthly104 (1997): 210–222.

Sabidussi, Gert. “Correspondence between Sylvester, Petersen,

Hilbert, and Klein on Invariants and the Factorisation of Graphs 1889–1891.” Discrete Mathematics100 (1992): 99–155.