James Joseph Sylvester - the maths genius you could count on

By Patricia Rothman, March 1, 2014
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Those who value the versatility of their computers and tablets, rely on encryption to keep their data confidential,and wonder at the many marvels of the modern world, may thank James Joseph Sylvester, one of the giants of mathematics, whose work made all these advances possible. Later this year we celebrate the 200th anniversary of his birth.

Sylvester’s was a remarkable life lived against the backdrop of the radical social changes of the 19th century. He simply wanted to use his creative mathematical mind, to teach in a stimulating environment and to live as a gentleman. Considering his extraordinary talents, this should have been easy for him to achieve, but he was a Jew who refused to compromise his Judaism.

As a child he attended the first private boarding school for Jewish boys in Highgate where Hebrew and biblical studies were taught together with secular subjects. The schooling was designed to educate the Anglo-Jewish elite so that they could cherish their Jewish identity as well as be able to interact on an equal educational level with their non-Jewish fellows.

Sylvester’s headmaster was so impressed with his mathematical ability, aged 11, that he arranged for the professor of maths at the Royal Military Academy in Woolwich to examine him in algebra and his talent became more generally recognised.

In 1826 University College London was founded as the first English university to be free from religious restrictions. At that time in Cambridge a student had to sign the 39 Articles of Faith before receiving a degree, and in Oxford, a student couldn’t even be admitted to study without signing this document. These restrictions effectively disbarred Jews, Catholics, and non-conformists from a university education.

UCL opened its doors to students in 1828 and 14-year-old Sylvester was able to enrol in the mathematics department. His professor, Augustus de Morgan, wrote that he had “never before or since [seen] mathematical talent so strongly marked in a boy of that age”. However, he was very young and immature and after a dispute with a fellow student and reports of knives being flourished in the refectory, his family took him away.
Later he went to Cambridge and his results would have entitled him to be Second Wrangler had he not been a professing Jew and therefore unable to be awarded a degree.

UCL was the only university in England where he could take up a post so he returned to become professor of natural philosophy. Mathematics would have been his first choice, but that chair was occupied by his youthful professor, Augustus de Morgan.

He then took up a post at the University of Virginia, becoming the first Jewish professor in America. But plagued by violence and antisemitism Sylvester returned to London to become an actuary and a barrister.

He was instrumental in founding the Institute of Actuaries in 1848 and was vice-president for five years. Later, he became professor of maths at the Royal Military Academy in Woolwich; this was a political appointment through the War Office and did not require the taking of an oath.

When Johns Hopkins University in Baltimore was founded, Sylvester was invited to be its first professor of maths. There he founded the prestigious American Journal of Mathematics.
Finally he was appointed the Savillian Professor of Geometry at Oxford when he was 69. Social reform had moved on and this appointment was now open to dissenters.

All this time he was creating beautiful mathematics. He developed the theory of algebraic invariants as well as matrix theory and revolutionised 19th century mathematics.
He had been elected a Fellow of the Royal Society when only 25 years old years old. Following his death, aged 82, successful moves were made by, among others, the JC, to establish the Sylvester Medal for research into pure mathematics, to be awarded and administered under the trusteeship of the Royal Society.

Patricia Rothman is an honorary research fellow in UCL’s Department of Mathematics

Last updated: 8:45am, March 1 2014