James Joseph Sylvester

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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,[1] 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.[2] 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.>

On his return to England, he was hired in 1844 by the Equity and Law Life Assurance Society for which he developed successful actuarial models and served as de facto CEO, a position that required a law degree. As a result, he studied for the Bar, meeting a fellow British mathematician studying law, Arthur Cayley, with whom he made significant contributions to invariant theory and also matrix theory during a long collaboration [Parshall]. He did not obtain a position teaching university mathematics until 1855, when he was appointed professor of mathematics at the Royal Military Academy, Woolwich, from which he retired in 1869, because the compulsory retirement age was 55. The Woolwich academy initially refused to pay Sylvester his full pension, and only relented after a prolonged public controversy, during which Sylvester took his case to the letters page of The Times.

One of Sylvester's lifelong passions was for poetry; he read and translated works from the original French, German, Italian, Latin and Greek, and many of his mathematical papers contain illustrative quotes from classical poetry. Following his early retirement, Sylvester (1870) published a book entitled The Laws of Verse in which he attempted to codify a set of laws for prosody in poetry.

In 1872, he finally received his B.A. and M.A. from Cambridge, having been denied the degrees due to his being a Jew.[1]

In 1876[3] Sylvester again crossed the Atlantic Ocean to become the inaugural professor of mathematics at the new Johns Hopkins University in Baltimore, Maryland. His salary was $5,000 (quite generous for the time), which he demanded be paid in gold. After negotiation, agreement was reached on a salary that was not paid in gold.[4] In 1878 he founded the American Journal of Mathematics. The only other mathematical journal in the US at that time was the Analyst, which eventually became the Annals of Mathematics.

In 1883, he returned to England to take up the Savilian Professor of Geometry at Oxford University. He held this chair until his death, although in 1892 the University appointed a deputy professor to the same chair.

Sylvester invented a great number of mathematical terms such as "matrix" (in 1850),[5] "graph" (combinatorics)[6] and "discriminant".[7] He coined the term "totient" for Euler's totient function φ(n).[8] His collected scientific work fills four volumes. In 1880, the Royal Society of London awarded Sylvester the Copley Medal, its highest award for scientific achievement; in 1901, it instituted the Sylvester Medal in his memory, to encourage mathematical research after his death in Oxford. In Discrete geometry he is remembered for Sylvester's Problem and a result on the orchard problem.

Sylvester House, a portion of an undergraduate dormitory at Johns Hopkins University, is named in his honor. Several professorships there are named in his honor also.


See also[edit]


  1. ^ a b "Sylvester, James Joseph (SLVR831JJ)". A Cambridge Alumni Database. University of Cambridge. 
  2. ^ Bell, Eric Temple (1986). Men of Mathematics. Simon Schuster. 
  3. ^ "Preliminary Outline of Instructions for the Session Beginning October 3, 1876". Johns Hopkins University. Official Circulars. No. 5. September 1876. 
  4. ^ Hawkins, Hugh (1960). Pioneer: A History of the Johns Hopkins University, 1874-1889. Ithaca, NY: Cornell University Press. pp. 41–43. 
  5. ^ Matrices and determinants, The MacTutor History of Mathematics archive
  6. ^ See:
  7. ^ J. J. Sylvester (1851) "On a remarkable discovery in the theory of canonical forms and of hyperdeterminants," Philosophical Magazine, 4th series, 2 : 391–410; Sylvester coins the word "discriminant" on page 406.
  8. ^ J. J. Sylvester (1879) "On certain ternary cubic-form equations," American Journal of Mathematics, 2 : 357–393; Sylvester coins the term "totient" on page 361: "(the so-called Φ function of any number I shall here and hereafter designate as its τ function and call its Totient)"
  9. ^ a b Dickson, L. E. (1909). "Review: Sylvester's Mathematical Papers, vols. I & II, ed. by H. F. Baker". Bull. Amer. Math. Soc. 15 (5): 232–239. doi:10.1090/S0002-9904-1909-01746-X. 
  10. ^ Dickson, L. E. (1911). "Review: Sylvester's Mathematical Papers, vol. III, ed. by H. F. Baker". Bull. Amer. Math. Soc. 17 (5): 254–255. doi:10.1090/S0002-9904-1911-02040-7. 


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