Sylvester, James Joseph (1814–1897)

English mathematician who was one of the discoverers of the theory of algebraic invariants. He coined the term ‘matrix’ in 1850 to describe a rectangular array of numbers out of which determinants can be formed.

Sylvester was born in London and studied mainly at Cambridge. He became professor of natural philosophy at University College, London in 1837. In 1841 he went to the USA to become professor at the University of Virginia, but resigned in 1845 and returned to England. For the next ten years he abandoned academic life, although he took in private pupils, including nursing pioneer Florence Nightingale. In 1844 he joined an insurance company, and in 1850 he became a barrister. In 1855 he returned to academic life, becoming professor of mathematics at the Royal Military Academy in Woolwich, London.

In 1877 he again went to the USA, becoming professor at the newly founded Johns Hopkins University in Baltimore. Returning to the UK, he was from 1883 professor at Oxford.

Sylvester laid the foundations, with English mathematician Arthur Cayley (with whom he did not collaborate), of modern invariant algebra. He also wrote on the nature of roots in quintic equations and on the theory of numbers, especially in partitions and Diophantine analysis.