Sylvester, James Joseph, 1814–97, English mathematician. He studied at Cambridge for four years after 1831, but because degrees were limited to members of the Church of England and he was a Jew, he was not granted a degree until 1872. He was professor of mathematics at the Univ. of Virginia (1841) and at the Royal Military Academy, Woolwich, England (1855–70). Returning to the United States in 1876, he became the first professor of mathematics at Johns Hopkins, where in 1878 he founded the American Journal of Mathematics. He was Savilian professor of geometry at Oxford (1883–94). He is known especially for his work on algebraic invariants, matrices, determinants, and the theory of numbers, much of his most important work being done in collaboration with Arthur Cayley.