There were two men, companions for many years but, like many companions, of very different character, who stand out with special prominence [in the mid-19th century]. The first of these was James Joseph Sylvester 1. [The second is Arthur Cayley.] Educated at St. John's College, Cambridge, and one of the most gifted members of his class, he was n ot allowed to take a degree because of his Jewish faith, and for the same reason he was barred from a fellowship. For the degree he went to Dublin, but after the abolition of the theological tests in 1872 the University of Cambridge awarded him both the bachelor's and master's degrees. Soon after leaving the university he was appointed (1837) professor of natural philosophy in University College, London, and two years later (1839) was elected a Fellow of the Royal Society. Opportunities for advancement not being promising in England, he accepted an appointment (1841) as a professor of mathematics in the University of Virginia. His election took place on July 3, 1841, and he began his work in the autumn. He made a failure of his teaching, had a seriou s personal encounter with a student who is said to have attacked him, and hurriedly left the university in the following March. The official records of March 22, 1842, contain the following resolution:

Resolved, That the resignation of Mr. Sylvester be accepted, to take effect from and after the 29th day of the present month or at any earlier period that he may elect;--that a copy of this resolution be forthwith communicated to him by the Secretary, and that he be informed that in accepting his resignation the Board has not deemed it necessary to investigate the merits of the matter in difference between himself and the student Ballard, and does not mean to impute to Mr. Sylvester any blame in the ma tter.

Evidently, therefore, the university authorities were convinced that Sylvester's further relations with the faculty were not desirable.

He seems to have returned to London about three years after leaving Virginia. Here he took up actuarial work, became a student in the Inner Temple (1846), and was called to the bar (1850). He became professor of mathematics at the Military Academy in Woolwich in 1855 and remained there until his forced retirement on account of age (1869). In 1877 he was called to Johns Hopkins University and did more than any other man of his time to establish graduate work in mathematics in America. Among his othe r contributions to the advance of the science in this country was his foundling of the American Journal of Mathematics. In 1883 he was elected to succeed H.J.S. Smith in the Savilian professorship at Oxford, but his lectures were not popular and i n 1892 he gave place to a deputy professor and spent his last years in London.

Sylvester was often looked upon as unsystematic, domineering, impractical, conceited, and unhappy, but those who knew him well have testified to his genial nature and his enthusiasm in his work with students. Hi contributions show that he was a genius in mathematical investigation, his chief line of interest being in higher algebra, including the study of invariants.

(Smith, pp. 463-465.)