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J. J. Sylvester

James Joseph Sylvester
James Joseph Sylvester.jpg
Born (1814-09-03)3 September 1814
London, England
Died 15 March 1897(1897-03-15) (aged 82)
London, England
Nationality British
Fields Mathematics
Institutions Johns Hopkins University
University College London
University of Virginia
Royal Military Academy, Woolwich
Alma mater St. John's College, Cambridge
Academic advisors John Hymers
Augustus De Morgan
Doctoral students William Durfee
George B. Halsted
Washington Irving Stringham
Other notable students Isaac Todhunter
William Roberts McDaniel
Harry Fielding Reid
Christine Ladd-Franklin
Known for coining the term 'graph'
Coining the term 'discriminant'
Chebyshev–Sylvester constant
Sylvester's sequence
Sylvester's formula
Sylvester's determinant theorem
Sylvester matrix (resultant matrix)
Sylvester–Gallai theorem
Sylvester's law of inertia
Sylver coinage
Sylvester's criterion
Sylvester domain
Influenced Morgan Crofton
Christine Ladd-Franklin
George Salmon
Notable awards Royal Medal (1861)
Copley Medal (1880)
De Morgan Medal (1887)

James Joseph Sylvester FRS (3 September 1814 – 15 March 1897) was an English mathematician. He made fundamental contributions to matrix theory, invariant theory, number theory, partition theory, and combinatorics. He played a leadership role in American mathematics in the later half of the 19th century as a professor at the Johns Hopkins University and as founder of the American Journal of Mathematics. At his death, he was professor at Oxford.

Sylvester was born James Joseph in London, England. His father, Abraham Joseph, was a merchant. James adopted the surname Sylvester when his older brother did so upon emigration to the United States—a country which at that time required all immigrants to have a given name, a middle name, and a surname. At the age of 14, Sylvester was a student of Augustus De Morgan at the University of London. His family withdrew him from the University after he was accused of stabbing a fellow student with a knife. Subsequently, he attended the Liverpool Royal Institution.

Sylvester began his study of mathematics at St John's College, Cambridge in 1831, where his tutor was John Hymers. Although his studies were interrupted for almost two years due to a prolonged illness, he nevertheless ranked second in Cambridge's famous mathematical examination, the tripos, for which he sat in 1837. However, Sylvester was not issued a degree, because graduates at that time were required to state their acceptance of the Thirty-Nine Articles of the Church of England, and Sylvester could not do so because he was Jewish, the same reason given in 1843 for his being denied appointment as Professor of Mathematics at Columbia College (now University) in New York City . For the same reason, he was unable to compete for a Fellowship or obtain a Smith's prize. In 1838 Sylvester became professor of natural philosophy at University College London and in 1839 a Fellow of the Royal Society of London. In 1841, he was awarded a BA and an MA by Trinity College, Dublin. In the same year he moved to the United States to become a professor of mathematics at the University of Virginia, but left after less than four months following a violent encounter with two students he had disciplined. He moved to New York City and began friendships with the Harvard mathematician Benjamin Peirce (father of Charles Sanders Peirce) and the Princeton physicist Joseph Henry, but in November 1843, after his rejection by Columbia, he returned to England.


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