James Joseph was born in London on 3 September 1814, the son of Abraham Joseph, a Jewish merchant.[1] James later adopted the surname Sylvester when his older brother did so upon emigration to the United States.
At the age of 14, Sylvester was a student of Augustus De Morgan at the University of London (now University College London). His family withdrew him from the university after he was accused of stabbing a fellow student with a knife. Subsequently, he attended the Liverpool Royal Institution.
Sylvester began his study of mathematics at St John's College, Cambridge in 1831,[2] where his tutor was John Hymers. Although his studies were interrupted for almost two years due to a prolonged illness, he nevertheless ranked second in Cambridge's famous mathematical examination, the tripos, for which he sat in 1837. However, Sylvester was not issued a degree, because graduates at that time were required to state their acceptance of the Thirty-nine Articles of the Church of England, and Sylvester could not do so because he was Jewish. For the same reason, he was unable to compete for a Fellowship or obtain a Smith's prize.[3] In 1838, Sylvester became professor of natural philosophy at University College London and in 1839 a Fellow of the Royal Society of London. In 1841, he was awarded a BA and an MAbyTrinity College Dublin. In the same year he moved to the United States to become a professor of mathematics at the University of Virginia, but left after less than four months. A student who had been reading a newspaper in one of Sylvester's lectures insulted him and Sylvester struck him with a sword stick. The student collapsed in shock and Sylvester believed (wrongly) that he had killed him. Sylvester resigned when he felt that the university authorities had not sufficiently disciplined the student.[4] He moved to New York City and began friendships with the Harvard mathematician Benjamin Peirce (father of Charles Sanders Peirce) and the Princeton physicist Joseph Henry. However, he left in November 1843 after being denied appointment as Professor of Mathematics at Columbia College (now University), again for his Judaism, and returned to England.
On his return to England, he was hired in 1844 by the Equity and Law Life Assurance Society for which he developed successful actuarial models and served as de facto CEO, a position that required a law degree. As a result, he studied for the Bar, meeting a fellow British mathematician studying law, Arthur Cayley, with whom he made significant contributions to invariant theory and also matrix theory during a long collaboration.[5] He did not obtain a position teaching university mathematics until 1855, when he was appointed professor of mathematics at the Royal Military Academy, Woolwich, from which he retired in 1869, because the compulsory retirement age was 55. The Woolwich academy initially refused to pay Sylvester his full pension, and only relented after a prolonged public controversy, during which Sylvester took his case to the letters page of The Times.
One of Sylvester's lifelong passions was for poetry; he read and translated works from the original French, German, Italian, Latin and Greek, and many of his mathematical papers contain illustrative quotes from classical poetry. Following his early retirement, Sylvester published a book entitled The Laws of Verse in which he attempted to codify a set of laws for prosody in poetry.[6]
In 1872, he finally received his B.A. and M.A. from Cambridge, having been denied the degrees due to his being a Jew.[2]
In 1876[7] Sylvester again crossed the Atlantic Ocean to become the inaugural professor of mathematics at the new Johns Hopkins UniversityinBaltimore, Maryland. His salary was $5,000 (quite generous for the time), which he demanded be paid in gold. After negotiation, agreement was reached on a salary that was not paid in gold.[8]
In 1883, he returned to England to take up the Savilian Professor of GeometryatOxford University. He held this chair until his death, although in 1892 the university appointed a deputy professor to the same chair. He was on the governing body of Abingdon School.[10]
Sylvester House, a portion of an undergraduate dormitory at Johns Hopkins University, is named in his honor. Several professorships there are named in his honor also.
J. J. Sylvester (7 February 1878) "Chemistry and algebra,"Nature, 17 : 284. From page 284: "Every invariant and covariant thus becomes expressible by a graph precisely identical with a Kekuléan diagram or chemicograph."
^J. J. Sylvester (1851) "On a remarkable discovery in the theory of canonical forms and of hyperdeterminants," Philosophical Magazine, 4th series, 2 : 391–410; Sylvester coined the term "discriminant" on page 406.
^J. J. Sylvester (1879) "On certain ternary cubic-form equations," American Journal of Mathematics, 2 : 357–393; Sylvester coins the term "totient" on page 361: "(the so-called Φ function of any number I shall here and hereafter designate as its τ function and call its Totient)"
^Sylvester, James Joseph (1851). "On the relation between the minor determinants of linearly equivalent quadratic functions". Philosophical Magazine. 1: 295–305.
^C.G.J. Jacobi, "De Formatione et Proprietatibus Determinantium", Journal für die reine und angewandte Mathematik, 22, 285-318 (1841)
Grattan-Guinness, I. (2001), "The contributions of J. J. Sylvester, F.R.S., to mechanics and mathematical physics", Notes and Records of the Royal Society of London, 55 (2): 253–265, doi:10.1098/rsnr.2001.0142, MR1840760, S2CID122748202.