# SYLVESTER, JAMES JOSEPH:

English mathematician and Savilian professor of geometry in the University of Oxford; born in London Sept. 3, 1814; died there March 15, 1897. He was educated at Neumegen's school, at the Royal Institution, Liverpool, and at St. John's College, Cambridge. In 1837 he passed the examination for the mathematical tripos as second wrangler, but was precluded by his Jewish origin from taking his degree and from competing for either of the Smiths' prizes. In 1872, after the passing of the Tests Act, the complete degree of M. A. "propter merita" was conferred upon him. He became professor of mathematics at University College, London (1837); University of Virginia, Charlottesville (1841); Military Academy, Woolwich (1855-70); Johns Hopkins University, Baltimore (1877-83); and at Oxford (1883), where he founded a mathematical society.

Sylvester was the founder and first editor of the "American Journal of Mathematics." He received the Royal Medal of the Royal Society in 1860, the Copley Medal in 1880, and the triennial De Morgan Commemoration Medal from the London Mathematical Society in 1887. He was made an honorary D.C.L. of Oxford and LL.D. of Dublin and Edinburgh; was a member of many scientific societies in Europe and the United States; and in May, 1890, was created an officer of the Legion of Honor by the President of the French Republic.

Sylvester was chiefly known as an algebraist, and as the fellow worker of Professor Cayley in thefoundation of the doctrine of "invariants." His first printed paper was "On Fresnel's Optical Theory of Wave Surfaces" (in "Philosophical Magazine," 1837). He discovered the proof and extension of Newton's theorem on the imaginary roots of equations, this proof, which was published in the Proceedings of the London Mathematical Society, having been a desideratum since the days of Newton. He also contributed a paper on the reversion of series, solving in its complete form a problem which had been but imperfectly solved by Jacobi. His first paper to attract attention abroad was that in which he gave a new form to Sturm's celebrated theorem on equations. His work on canonical forms is described by Cayley as containing crowds of ideas embodied in the new words "cogredient," "contragredient," "concomitant," "covariant," "contravariant," "invariant," etc., most of which have been adopted into mathematical terminology.

In addition to the foregoing, Sylvester published a theory of versification in a volume entitled the "Laws of Verse" (1870), as well as poetical translations from the German and Latin, and various sonnets and other original pieces in verse.

After his death there was established through the Royal Society a triennial prize and medal in Sylvester's honor. His position as leader in pure mathematics in England in the nineteenth century is challenged only by his colaborer Cayley.

**Bibliography:**

- Jew. Chron. June 6, 1890, and March, 1897;
- Dict. National Biography;
- The Times (London), March 16, 1897;
- Nature, March 25, 1897;
- Science (New York), April 11, 1897;
- F. Franklin, Address Commemorative of J. J. Sylvester, Baltimore, 1897.