James Joseph Sylvester—the mathematical genius snubbed by Cambridge

The rule among the dons of Oxford and Cambridge up to the end of the nineteenth century was that you were permitted to take a degree at these  'august' institutions as long as you weren’t a dissenter or a Jew. At around about the same time, when the first colleges for women were established, similar restrictions were applied to women, who were only granted degrees at Oxford in 1920, and shamefully, at Cambridge in 1948. At the latter University, woman  were palmed off with 'certificates' up to that date.

Today, when we are so aware of discrimination against minorities, mathematicians who admire the astonishing achievements of the Jewish-born James Joseph Sylvester (1814- 97) invariably pick up on the fact that despite being ranked second wrangler in the 1837 Cambridge University Tripos, Sylvester, as someone who as a Jew had refused to take the Thirty Nine Articles of the Church of England, was barred from graduating. Nor was he permitted to compete for a fellowship or obtain a Smith’s prize. A year later, and still without a degree,  Sylvester was appointed Professor of Natural Philosophy at the University of London, where he had been a student for a short time from the age of 14.
It was only in 1841, when Trinity College, Dublin awarded him the degrees he needed that Sylvester was officially qualified to teach students.

However, anti-semitism in the academic community continued to dog the man. Although, as a newly qualified graduate, he had been formally appointed to a professorship at the University of Virginia in 1841, WASP feeling among both the local community and the trustees of the institution, allied to disgusting racial slurs heaped on him by the undergraduates he taught, forced Sylvester to resign after just six months. Back in England, he decided to make himself more employable by reading law alongside the lawyer/ mathematician Arthur Cayley, while working as an actuary and a private tutor. In this period he made significant advances in matrix theory while teaching mathematics to, among others, Florence Nightingale. It was only in 1854, when he was appointed professor of mathematics at the Royal Military Academy, Woolwich, that the gifted mathematician was able to teach the subject he loved at University level.

Having been forced to retire from Woolwich at the age of 55 in 1869, Sylvester spent some of his time polishing up his modern and ancient languages ( he was a gifted linguist too) and publishing The Laws of Verse, which attempted to impose mathematical rules on prosody—a precursor, perhaps, of that hated book in The Dead Poet’s Society. In 1877 he left once more for the USA to take up a well paid ($5,000 p.a.) professorship at the newly founded John Hopkins University, which saw him establish the American Journal of Mathematics. His final appointment was in 1883, when he became the Savilian Professor of Geometry at Oxford, though by now his best work as a mathematician had been done. The letter (above) featured in this Jot is a product of this period. Dated 8th July 1889 and written to his niece Beatrice, who had asked him to send her some autographs for her collection, he promises to ask the ‘distinguished men of  Oxford ‘ for their signatures on their return from the holidays. He also vows to send her a letter from the novelist Rhoda Broughton, though in a possibly ironic comment on the  discrimination from which  he himself had suffered for most of his life, he regrets that she cannot "claim to take a place, through the misfortune of her sex, among the 'womini illustri.' "

Perhaps the letter is most interesting on the light it sheds on the role of Sylvester’s brilliant mathematical assistant , James Hammond, with whom he was staying at the time and who, in Sylvester’s judgment

‘is as clever at drawing geometrical figures, and  generally with his fingers, as he is with his brain, which he obligingly puts at my disposition’. 

Sylvester died in harness at his home in Oxford in 1897. Four years later the Royal Society instituted the Sylvester Medal to encourage mathematical research at Oxford.

Sylvester invented a large number of significant mathematical terms, including ‘ graph’ (1878) and ‘discriminant’ (1851). His work, which fills four volumes, is still being discussed and assessed and in 1998 a full length biography appeared from the OUP. [RH]