James Joseph Sylvester Biography

James Joseph Sylvester was one of the most colorful mathematicians of the Victorian age. His role in giving an impetus to the American mathematical community in the late 19th century provided a sense of national independence from European scholarship.

Sylvester was born on September 3, 1814 in London, the son of Abraham Joseph. He was the youngest son out of a total of nine children and received his early education at Jewish schools in Highgate and Islington. Sylvester entered St. John's College at Cambridge in 1831. His undergraduate career was interrupted by illness that kept him at home for several years. Finally, in 1837 he took the Tripos (the final mathematical examinations) and placed second. Ordinarily, a student in that situation would have proceeded to take his degree and to compete for the Smith's Prize. Since, however, Sylvester was Jewish, he could not subscribe to the ThirtyNine Articles of the Church of England, a requirement at that time for receiving a degree from Oxford or Cambridge. Sylvester later earned both bachelor and master's degrees from Trinity College in Dublin, which did not have the same requirements. Some 35 years after passing the Tripos, Sylvester received his B.A. from Cambridge when the doctrinal requirements were dropped.

Sylvester began teaching at University College, London, as the colleague of Augustus De Morgan, but did not find the chair of natural philosophy a congenial one. By 1839, he was a Fellow of the Royal Society and two years later made his first venture at transatlantic teaching, accepting a position at the University of Virginia. This proved to be a complete fiasco, as Sylvester encountered intense antiSemitism. In the absence of offers from other American universities, Sylvester returned to England and took a position as actuary and secretary to the Equity and Law Life Assurance Company ("assurance" is the English term for "insurance"). He took private pupils in mathematics as well, the most notable of them being Florence Nightingale. In 1846, three years after returning from the United States, Sylvester entered the Inner Temple, one of the Inns of Court designed to prepare students for the bar. He was called to the bar in 1850, but never made a success at it as did his colleague Arthur Cayley.

Finds a Position in the Educational Establishment

In 1855, Sylvester finally managed to secure a position teaching mathematics in England. He was appointed to the chair of mathematics at the Royal Military Academy at Woolwich. That same year he became the editor of the Quarterly Journal of Pure and Applied Mathematics, which he transformed into one of the leading periodicals about mathematical research in England. He remained its editor until 1877, during which period he also served as president of the London Mathematical Society from 1866 to 1868.

As a mathematician Sylvester occasionally indulged in hasty generalizations, but his imagination at its best could create whole new fields of study. He did not take the trouble to study the contributions of contemporary mathematicians outside his circle, with the result that some of his work amounts to an independent rediscovery. He did a good deal of work in the area of invariant theory, the study of algebraic expressions that remain fixed under various classes of transformations. He certainly introduced an enormous amount of terminologyincluding "discriminant"an activity of which he was especially proud.

In addition to his work on invariant theory, Sylvester deserves much credit for the early study of the subject of partitions. A partition is a way of breaking up a positive whole number as a sum of other positive whole numbers, so that 3 + 3, 2 + 2 + 2, and 5 + 1 are all partitions of the number 6. Counting the number of partitions of various kinds required some inventiveness and Sylvester helped to get the subject welllaunched. The subject of partitions turned out to have a good deal of importance in analysis, although Sylvester did not push this aspect of his studies very far.

Returns to America

Sylvester had resigned from Woolwich in 1870 and was busily engaged in his mathematical work, but he could not resist an invitation from the eminent American physicist Joseph Henry to come to the newlyfounded Johns Hopkins University in Baltimore. Henry assured Sylvester that he would be involved with serious students and have ample opportunities for research. He arrived in Baltimore in 1876 to find his expectations fulfilled. In addition to his work with some of the best students in the country, Sylvester also founded the American Journal of Mathematics. At this point in history there was no serious American publication devoted to mathematics and Sylvester's journal filled the void. In particular, to make certain that it would be taken seriously, he contributed 30 of his own papers to the journal. Despite his successes at Johns Hopkins, Sylvester could not pass up the opportunity to succeed H.J.S. Smith as Savilian Professor of Geometry at Oxford University.

Among the many honors Sylvester had received was the Royal Medal in 1861 and the Copley Medal in 1880, both from the Royal Society, and the De Morgan Medal from the London Mathematical Society in 1887. He was a corresponding member of numerous foreign societies and received four honorary degrees.

Sylvester died on March 15, 1897 and was buried at the Jewish Cemetery at Ball's Pond, London. In 1997, the London Mathematical Society held a memorial service on the centenary of his death. There was also a day's conference devoted during that centenary year to his life and the areas of mathematics to which he contributed. Without question, the mathematical communities on both sides of the Atlantic are beneficiaries of Sylvester's ideas and energy.