Sylvester, James Joseph

b. , Sept. 3, 1814, London
d. March 15, 1897, London

British mathematician who with Arthur Cayley founded the theory of algebraic invariants, algebraic-equation coefficients that are unaltered when the coordinate axes are translated or rotated.

In 1838 Sylvester became professor of natural philosophy at University College, London. In 1841 he accepted the professorship of mathematics at the University of Virginia, Charlottesville, but resigned after only three months. Four years later he went to London, where he became an actuary for an insurance company, retaining his interest in mathematics only through tutoring. One of the most notable of his private pupils was Florence Nightingale. In 1846 he became a law student at the Inner Temple, and in 1850 he was admitted to the bar. While working as a lawyer Sylvester began an enthusiastic and profitable partnership with Cayley. Together, they created the theory of algebraic forms.

From 1855 to 1870 Sylvester was professor of mathematics at the Royal Military Academy, Woolwich. He went to the United States once again in 1876 to become professor of mathematics at Johns Hopkins University, Baltimore. While there he founded (1878) and became the first editor of the American Journal of Mathematics, introduced graduate work in mathematics into U.S. universities, and greatly stimulated the development of mathematics in that country. In 1883 he returned to England to occupy the chair of Savilian professor of geometry at Oxford University.

Sylvester was primarily an algebraist. He did brilliant work in the theory of numbers, particularly in partitions (the possible ways a number can be expressed as a sum of positive integers) and diophantine analysis (a means for finding whole-number solutions to certain algebraic equations). He worked by inspiration, and frequently it is difficult to detect a proof in what he confidently asserted. All his work is characterized by powerful imagination and inventiveness. Although he published hundreds of papers, his only book on mathematics is Treatise on Elliptic Functions (1876). Sylvester also wrote verse and published Laws of Verse (1870).