# James Joseph Sylvester

**James Joseph Sylvester** (September 3, 1814 - March 15, 1897), born **James Joseph**, was an English mathematician and lawyer.

Sylvester was born in London, and adopted the surname "Sylvester" as his older brother, when emigrating to the United States, was required to adopt a third name. He studied at St John's College, Cambridge from 1831 (although his studies were interrupted for almost two years due to a lengthy illness), but because he was Jewish he did not graduate, as during this period, it was required for potential graduates to accept the Thirty-Nine Articles of the Church of England,and he refused. However, he took Cambridge's famous mathematical tripos examination in 1837 and was ranked second. In 1841, he was awarded a BA and an MA by Trinity College, Dublin. In the same year he moved to the United States for a short period to become a professor at the University of Virginia but he soon returned to England.

On his return to England he studied law (alongside Arthur Cayley, with whom he made significant contributions to matrix theory) while working as an actuary, but his goal was to find work as a professional mathematician. He did not find a post until 1855, when he was appointed professor of mathematics at the Royal Military Academy at Woolwich. However, as this was a military academy, he was forced to retire at age 55.

In 1877 Sylvester again crossed the Atlantic Ocean for a new job at Johns Hopkins University. In 1878 he founded the *American Journal of Mathematics*, the first mathematical journal in the United States.

He finally returned to England in 1883 to take up the position of Savilian Professor of Geometry at Oxford University. He held this chair until his death on March 15, 1897, though in 1892 the University appointed a deputy professor in his place.

It is said that Sylvester invented one of the highest numbers of mathematical terms such as the totient function φ(*n*). His scientific work is collected in a four volume book.

In 1880 the Royal Society of London awarded Sylvester the Copley Medal, their highest award for scientific achievement; in 1901 it instituted the Sylvester Medal in his memory for the encouragement of mathematical research.

Sylvester House, an undergraduate dormitory at Johns Hopkins, is named in his honor.

## Selected works

- James Joseph Sylvester,
*On rational derivation from equations of coexistence, that is to say, a new and extended theory of elimination, Part I,*Philos. Mag.**15**(1839), 428-435. - James Joseph Sylvester,
*On the partition of numbers*, Quart. J. Math.,**I**(1857), 141-152. - James Joseph Sylvester,
*Outlines of seven lectures on the partition of numbers*, Proc. Lond. Math. Soc.**28**(1897), 33-96.

## References

- Sylvester's
*Collected Mathematical Papers*, edited by H. F. Baker (three volumes, New York, 1904-10) - Franklin,
*Address Commemorative of Sylvester*, (Baltimore, 1897)

## See also

- Chebyshev–Sylvester constant
- Coin problem
- Sylvester's identity
- Sylvester's sequence
- Sylvester's theorem
- Sylvester–Gallai theorem

## External links

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