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SYLVESTER, JAMES

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Originally appearing in Volume V26, Page 284 of the 1911 Encyclopedia Britannica.
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SYLVESTER, See also:JAMES See also:JOSEPH (1814–1897), See also:English mathe- m4tician, was See also:born in See also:London on the 3rd of See also:September 1814. He went to school first at See also:Highgate and then at See also:Liverpool, and in 1831 entered St See also:John's See also:College, See also:Cambridge. In his Tripos examination, which through illness he was prevented from taking till 1839, he was placed as second wrangler, but being a See also:Jew and unwilling to sign the See also:Thirty-nine Articles, he could not compete for one of the See also:Smith's prizes and was ineligible for a fellowship, nor could he even take a degree: this last, however, he obtained at Trinity College, See also:Dublin, where religious restrictions were no longer in force. After leaving Cambridge he was appointed to the See also:chair of natural See also:philosophy at University College, London, where his friend A. De See also:Morgan was one of his colleagues, but he resigned in 184o in See also:order to become See also:professor of See also:mathematics in the university of See also:Virginia. There, however, he remained only six months, for certain views on See also:slavery, strongly held and injudiciously expressed, entailed unpleasant consequences, and necessitated his return to See also:England, where he obtained in 1844 the See also:post of See also:actuary to the Legal and Equitable See also:Life Assurance See also:Company. In the course of the ensuing ten years he published a large amount of See also:original See also:work, much of it dealing with the theory of invariants, which marked him as one of the foremost mathematicians of the See also:time. But he failed to obtain either of two posts—the professorships of mathematics at the Royal Military See also:Academy and of See also:geometry in See also:Gresham College—for which he applied in 1854, though he was elected to the former in the following See also:year on the See also:death of his successful competitor. At See also:Woolwich he remained until 187o, and although he was not a See also:great success as an elementary teacher, that See also:period of his life was very See also:rich in mathematical work, which included remarkable advances in the theory of the See also:partition of See also:numbers and further contributions to that of invariants, together with an important See also:research which yielded a See also:proof, hitherto lacking, of See also:Newton's See also:rule for the See also:discovery of imaginary roots for algebraical equations up to and including the fifth degree. In 1874 he produced several papers suggested by A. Peaucellier's discovery of the straight See also:line See also:link See also:motion associated with his name, and he also invented the skew pentagraph. Three years later he was appointed professor of mathematics in the Johns See also:Hopkins University, See also:Baltimore, stipulating for an See also:annual See also:salary of $5000, to be paid in See also:gold.

At Baltimore he gave an enormous impetus to the study of the higher mathematics in See also:

America, and during the time he was there he contributed to the See also:American See also:Journal of Mathematics, of which he was the first editor, no less than thirty papers, some of great length, dealing mainly with See also:modern See also:algebra, the theory of numbers, theory of partitions and universal algebra. In 1883 he was chosen to succeed See also:Henry Smith in the Savilian chair of geometry at See also:Oxford, and there he produced his theory of reciprocants, largely by the aid of his " method of infinitesimal variation." In 1893 loss of See also:health and failing eyesight obliged him to give up the active duties of his chair, and a See also:deputy professor being appointed, he went to live in London, where he died on the 15th of See also:March 1899. Sylvester's work suffered from a certain lack of steadiness and method in his See also:character. For See also:long periods he was mathematically unproductive, but then sudden See also:inspiration would come upon him and his ideas and theories poured forth far more quickly than he could See also:record them. All the same his output of work was as large as it was valuable. The See also:scope of his researches was described by See also:Arthur See also:Cayley, his friend and See also:fellow worker, in the following words: " They relate chiefly to finite See also:analysis, and See also:cover by their subjects a large See also:part of it—algebra, determinants, elimination, the theory of equations, partitions, tactic, the theory of forms, matrices, reciprocants, the Hamiltonian numbers, &c.; See also:analytical and pure geometry occupy a less prominent position; and See also:mechanics, See also:optics and See also:astronomy are not absent." Sylvester was a See also:good linguist, and a diligent composer of See also:verse, both in English and Latin, but the See also:opinion he cherished that his poems were on a level with his mathematical achievements has not met with See also:general See also:acceptance. The first See also:volume of his Collected Mathematical Papers, edited by H. F. See also:Baker, appeared in 1904.

End of Article: SYLVESTER, JAMES

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