Sylvester was an early pionerr in matrix algebra. Ineligible, because Jewish, for university employment elsewhere in Britain, the he was professor of Natural Philosophy at UCL from 1838 until 1840. He returned after a time in the US and and practised law, then later took up a chair in mathematics.
Sylvester was born in London and attended University College School. He also held appointments in the US and later in Oxford. He returned to London in 1892 and lived at 5 Hartford Street, Mayfair. He is buried in the Jewish cemetery at Kingsbury Road, Dalston.