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 school, Liverpool, where his name is conspicuous in the report of 1830. Thence he proceeded to St. John's College, Cambridge, matriculating on 14 Nov. 1831. He resided till the end of 1833, and then ‘degraded’ for two years, being readmitted in January 1836. He secured the place of second wrangler in the mathematical tripos of 1837. As a Jew he could not take his degree nor compete for the Smith's prize, still less obtain a fellowship. His first ordinary degree he gained at the university of Dublin in 1841. He graduated B.A. at Cambridge (after the passing of the Tests Act) in February 1872. Meanwhile he entered at the Inner Temple, and was called to the bar in 1850.

Sylvester's life was mainly spent in the study and teaching of mathematics. He was appointed professor of natural philosophy at University College, London, on 25 Nov. 1837. In the same year the first of his many mathematical papers was published in the ‘Philosophical Magazine,’ and in 1839 he was elected a fellow of the Royal Society. In 1841 he became professor of mathematics in the university of Virginia, United States of America, but, finding the work uncongenial, returned to England in 1845, and was for ten years connected with a firm of actuaries, during which period he founded the Law Reversionary Interest Society. Meantime he was busy with mathematical research, and in 1853 published a long and important memoir on ‘Syzygetic Relations’ in the ‘Philosophical Transactions’ of the Royal Society. In 1855 he became professor of mathematics at the Royal Military Academy, Woolwich, and held the post till 1870, when he retired.

His fame was steadily growing, and before 1870 he was recognised as one of the foremost mathematicians of his day. He was president of the London Mathematical Society in 1866, receiving the society's De Morgan medal in 1887, and in 1869 he was president of the mathematical and physical section of the British Association at Exeter, where he gave a characteristic address criticising Huxley's description of mathematics as an ‘almost purely deductive science.’ The Royal Society awarded him the royal medal in 1861, and the Copley medal in 1880. In 1877, on the foundation of the Johns Hopkins University at Baltimore, United States of America, he was made professor of mathematics, and held that chair till 1883. While filling it he founded the American ‘Journal of Mathematics.’ He resigned the post in December 1883, when he was appointed to succeed Henry John Stephen Smith [q. v.] as Savilian professor of geometry at Oxford.

In virtue of his new post Sylvester became a fellow of New College. He lived in college as long as he was in Oxford. There he continued his researches, developed his theory of ‘reciprocants’ with the help of J. Hammond, and was instrumental in founding a mathematical society. In 1892 his eyesight and general health began to fail, and he was allowed to appoint a temporary deputy. In 1894 he was permanently relieved of the active duties of his chair and retired to London, where he spent his leisure at the Athenæum Club. After a paralytic stroke on 26 Feb. 1897, he died unmarried on 15 March. On 19 March he was buried in the Jewish cemetery at Ball's Pond, London.

Sylvester received many honours from learned societies at home and abroad. He was granted honorary degrees from Dublin (1865), Edinburgh (1871), Oxford (1880), Cambridge (1890), and was elected honorary fellow of St. John's College, Cambridge, officer of the Legion of Honour, corresponding member of the Institute of France, of the Imperial Academy of Science of St. Petersburg, of the Royal Academy of Science of Berlin, of the Istituto Lombardo of Milan, of the Société Philomathique of Paris, and a foreign associate of the American Academy of Sciences.

In brilliancy of conception, in acuteness of penetration, in fluency and richness of expression, Sylvester has had few equals among mathematicians. But his strength was not accompanied by restfulness or caution. He worked impulsively and unmethodically. As soon as a new idea entered his brain, he at once abandoned himself to it, even if it came upon him while he was lecturing or writing on another theme. Consequences and collateral ideas crowded upon him, and all else was thrust aside. He was wont to write with eager haste in a style as stimulating as it was excited, in flowery language enriched by poetical imagination, and by illustration boldly drawn from themes alien to pure science. In oral exposition he riveted attention. He was great as a maker of mathematicians no less than of mathematics. He imparted ideas and made them fascinating, thus leading others on to employ more prosaic powers in pursuing lines of investigation to which he introduced them. In youth he was one of the foremost in leading the revival of mathematical activity in England. Later in life when in Baltimore, where he founded the ‘American Journal of Mathematics,’ he brought into being a school of mathematicians which has