James Joseph Sylvester

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Born: 3 Sept 1814 in London, England
Died: 15 March 1897 in London, England

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James Joseph Sylvester attended two primary schools in London, then his secondary schooling was at the Royal Institution in Liverpool.

In 1833 he became a student at St John's College, Cambridge. Two other famous mathematicians took the tripos examination in the same year as Sylvester, namely Duncan Gregory and George Green. Sylvester came second, Green who was 20 years older than the other two came fourth with Duncan Gregory fifth. (The mathematician who came first did little work of importance after graduating: this was not at uncommon in the 'speed test' which the tripos was at that time.)

At this time it was necessary for a student to sign a religious oath to the Church of England before graduating and Sylvester, being Jewish, refused to take the oath necessary so could not graduate. For the same reason he was not eligible for a Smith's prize nor for a Fellowship.

From 1838 Sylvester taught physics for three years at the University of London, one of the few places which did not bar him because of his religion. His former teacher De Morgan was one of his colleagues.

At the age of 27 he was appointed to a chair in the University of Virginia 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.

On his return Sylvester worked as an actuary and lawyer but gave mathematics tuition. His pupils included Florence Nightingale. By good fortune Cayley was also a lawyer and both worked at the courts of Lincoln's Inn in London. Cayley and Sylvester discussed mathematics as they walked around the courts and, although very different in temperament, they became life long friends.

Sylvester tried hard to return to being a professional mathematician and he applied for a lectureship in geometry at Gresham College, London in 1854 but he was not appointed. Another failed application was for the chair in mathematics at the Royal Military Academy at Woolwich, but, after the successful applicant died within a few months of being appointed, Sylvester became professor of mathematics at Woolwich.

Sylvester did important work on matrix theory, a topic in which he became interested during walks with Cayley while they were at the courts of Lincoln's Inn. In 1851 he discovered the discriminant of a cubic equation and first used the name 'discriminant' for such expressions of quadratic equations and those of higher order.

In particular he used matrix theory to study higher dimensional geometry. He also contributed to the creation of the theory of elementary divisors of lambda matrices.

De Morgan was the first president of the London Mathematical Society. Sylvester became the second president of that society. He was the first recipient of the gold medal which the Society awarded to honour De Morgan.

Being at a military academy Sylvester had to retire at age 55. At first it looked as though he might give up mathematics since he published his only book at this time and it was on poetry. Clearly Sylvester was proud of this work, entitled The Laws of Verse, since after this he sometimes signed himself "J. J. Sylvester, author of The Laws of Verse".

For three years Sylvester appears to have done no mathematical research but then Chebyshev visited London and the two discussed mechanical linkages which can be used to draw straight lines. After working on this topic Sylvester lectured on it at an evening lecture at the Royal Institution entitled On recent discoveries in mechanical conversion of motion.

One mathematician in the audience at this lecture was Kempe and he became absorbed by this topic. Kempe and Sylvester worked jointly on linkages and made important discoveries.

In 1877 Sylvester accepted a chair at Johns Hopkins University and founded in 1878 the American Journal of Mathematics, the first mathematical journal in the USA.

When Smith died in 1883 Sylvester, although 68 years old at this time, was appointed to the Savilian chair of Geometry at Oxford. However Sylvester only liked to lecture on his own research and this was not well liked at Oxford where students wanted only to do well in examinations. In 1892, at the age of 78, Oxford appointed a deputy professor in his place and Sylvester, by this time partially blind and suffering from loss of memory, returned to London where he spent his last years at the Athenaeum Club.

Macfarlane [14] describes Sylvester in the following way:

Sylvester was fiery and passionate ... Sylvester never wrote a paper without foot-notes, appendices, supplements, and the alterations and corrections in his proofs were such that the printers found their task well-nigh impossible. ... Sylvester satisfied the popular idea of a mathematician as one lost in reflection, and high above mundane affairs. ... Sylvester was an orator, and if not a poet, he at least prided himself on his poetry.

One of Sylvester's students at Johns Hopkins University describes his teaching there

...the substance of his lectures had to consist largely of his own work, and, as a rule, of work hot from the forge. The consequence was that a continuous and systematic presentation of any extensive body of doctrine already completed was not to be expected from him. Any unsolved difficulty, any suggested extension, such would have been passed by with a mention by other lecturers, became inevitably with him the occasion of a digression which was sure to consume many weeks, if indeed it did not take him away from the original object permanently. Nearly all of the important memoirs which he published, while in Baltimore, arose in this way. We who attended his lectures may be said to have seen these memoirs in the making.

The following quote, from Thomas Hirst, tells us something about Sylvester's personality:

On Monday having received a letter from Sylvester I went to see him at the Athenaeum Club. ... He was, moreover, excessively friendly, wished we lived together, asked me to go live with him at Woolwich and so forth. In short he was eccentrically affectionate.

Sylvester sent the following puzzle to the Educational Times. It tells us of one of his hobbies as well as his interest in puzzles:

I have a large number of stamps to the value of 5 pence and 17 pence only. What is the largest denomination which I cannot make up with a combination of these two different values.

[The answer is 63 pence. Can you prove this!]

Texto original por: J J O'Connor and E F Robertson

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JOC/EFR February 1997	School of Mathematics and Statistics University of St Andrews, Scotland
The URL of this page is: http://www-history.mcs.st-andrews.ac.uk/history/Mathematicians/Sylvester.htm