Mathematician. Sylvester was born in Liverpool in 1814. Originally admitted at St John's in 1831, he secured second wrangler in the mathematical tripos of 1837. Being a Jew he could not take a degree at Cambridge but he gained a BA in 1841 from Trinity College, Dublin.
In 1837 he was appointed professor of natural philosophy at University College, London and in 1839 he was elected a fellow of the Royal Society. In 1844 he was appointed Professor of Mathematics in the University of Virginia, USA, but he resigned after a few months. A student who had been reading a newspaper in one of Sylvester's lectures insulted him and Sylvester struck him with a sword stick. The student collapsed in shock and Sylvester believed (wrongly) that he had killed him. He fled to New York boarding the first available ship back to England.
He worked as an actuary and lawyer for the next ten years, though still giving mathematical tuition, one of his pupils being Florence Nightingale. Whilst working at Lincoln's Inn in London he also met Arthur Cayley and they became lifelong friends. He also continued his mathematical research, publishing a number of important papers.
In 1855 Sylvester was appointed Professor of Mathematics at the Royal Military Academy, Woolwich and he held the post until he retired in 1870. During this time the Royal Society awarded him the Royal Medal in 1861 and he was president of the London Mathematical Society in 1866.
In 1870 he published his first book and it was on poetry, entitled The Laws of Verse.
In 1877, on the foundation of the Johns Hopkins University at Baltimore, USA, Sylvester was made Professor of Mathematics and held that chair until 1883. During his time in Baltimore he founded the American 'Journal of Mathematics'. He was awarded the Royal Society Copley Medal in 1880. In 1883 he returned to the United Kingdom to take up the post of Savilian Professor of Geometry at Oxford University. He was awarded the De Morgan Medal by the London Mathematical Society in 1887. With his general health failing he was finally relieved of his duties at Oxford in 1894. Sylvester died in 1897.
His mathematical researches covered a wide area but mostly he was interested in pure analysis, in particular with the theories of algebraical form and of numbers, and he is credited with the foundation of invariant algebra.
Letters, notebooks, lecture notes and other miscellaneous paperwork, mainly regarding mathematics.
All material given to the College in c. 1906 by Major P. A. MacMahon, apart from letters from JJS to Arthur Cayley which were presented to the College after the death of Mrs Cayley, through Mr Rouse Ball in 1923.