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Sylvester, James Joseph

london university theory life

1814–97) British mathematician: with Cayley founded the theory of invariants.

Sylvester was born into a Jewish family of nine children and in 1828 went to the new University of London, founded for Dissenters. Vociferous and hot-headed, Sylvester fought back against the strong anti-Semitism which he encountered and was sent down for threatening a fellow student with a table-knife. He was admitted to St John’s College, Cambridge (1831) and became Second Wrangler; however, as someone unable to accept the 39 articles of the Church of England he could not obtain a degree and only received his Cambridge MA in 1871, when this restriction was lifted. He moved to Trinity College, Dublin and gained his BA in 1841.

After a short period teaching science in London (1837), he decided he preferred mathematics and started in 1841 a disastrous few months as professor at the University of Virginia. He resigned because of the authority’s failure to discipline a student who insulted him. For some years he abandoned university life and worked in London as an actuary and then as a barrister, qualifying in 1850. He also took private pupils; one of the best was Florence Nightingale. Fortunately, in 1850 he met , who rekindled his interest in mathematics, and the two became life-long close friends. He became professor of mathematics at the Royal Military Academy at Woolwich (1855–70) and at the newly founded Johns Hopkins University at Baltimore (1877–83), producing a flood of new ideas in mathematical research and teaching. When he was over 70, he became Savilian Professor at Oxford (1883–94); failure of his eyesight forced his retirement to London.

He was enthusiastic and inventive to the end of his life; at 82 he worked out the theory of compound partitions. Sylvester’s mathematical style was brilliant but not methodical, and his creativity was unfettered by rigour. With Cayley, he inspired many of the basic ideas of algebraic invariance. He also published on the roots of quintic equations and on number theory. In 1850 he coined the term matrix for an array of numbers from which determinants can be obtained. Invariance assumed great importance after his lifetime, as much use was made of it in quantum mechanics and relativity theory.

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