James Joseph Sylvester: Wikis


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James Joseph Sylvester

James Joseph Sylvester (1814–1897)
Born September 3, 1814(1814-09-03)
London, England
Died March 15, 1897 (aged 82)
Oxford, Oxfordshire, England
Residence  UK
Nationality  UK
Ethnicity English-Jewish
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 George B. Halsted
Washington Irving Stringham
Other notable students Isaac Todhunter
Florence Nightingale
William Roberts McDaniel
Harry Fielding Reid
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
Umbral calculus
Influenced Morgan Crofton
Christine Ladd-Franklin
George Salmon
Notable awards Copley Medal (1880)
De Morgan Medal (1887)

James Joseph Sylvester (September 3, 1814 London – March 15, 1897 Oxford) 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. His father, Abraham Joseph, was a merchant. The Joseph family were Jewish, and James's career suffered for his being Jewish. 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 started attending the University of London, where he was a student of Augustus De Morgan. His family withdrew him from the University after he was accused of threatening a fellow student with a knife. Following this, he attended the Liverpool Royal Institution. Though he excelled academically, Sylvester was tormented by his fellow students on account of his Jewish origins.[citation needed] Because of the abuse he received, he ran away, taking a boat to Dublin. While there, he was recognized on the street by Richard Keatinge who was Judge of the Prerogative Court of Ireland, and whose wife was a cousin of Sylvester; Keatinge arranged for the boy's return to Liverpool.[citation needed]

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, being Jewish refused to do so. 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 UCL. 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 at the University of Virginia for about six months, and returned to England in November 1843.

On his return to England he studied law, alongside fellow British lawyer/mathematician Arthur Cayley, with whom he made significant contributions to matrix theory while working as an actuary. One of his private pupils was Florence Nightingale. 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. In 1870, following his early retirement, Sylvester published a book entitled The Laws of Verse[2] in which he attempted to codify a set of laws for prosody in poetry.

In 1877 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. In 1878 he founded the American Journal of Mathematics. The only other mathematical journal in the U.S. 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 discriminant. He has given a name to Euler's totient function φ(n). 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.

Sylvester House, a portion of an undergraduate dormitory at Johns Hopkins, is named in his honour.

See also


  1. ^ Sylvester, James Joseph in Venn, J. & J. A., Alumni Cantabrigienses, Cambridge University Press, 10 vols, 1922–1958.
  2. ^ James Joseph Sylvester, The Laws of Verse: or Principles of Versification (Longman Greens and Co, London, 1870).



  • 1904–10. Collected Mathematical Papers in 4 vols. Edited by H. F. Baker. New York. (PDF/DjVu copy of volume 1 at Internet Archive; PDF copy of Vols. 2–4 at University of Michigan)
  • 1839. "On rational derivation from equations of coexistence, that is to say, a new and extended theory of elimination, Part I," Philos. Mag. 15: 428–435.
  • 1857. "On the partition of numbers," Quart. J. Math. I: 141–152.
  • 1869. "Presidential address to Section A of the British Association" in Ewald, William B., ed., 1996. From Kant to Hilbert: A Source Book in the Foundations of Mathematics, 2 vols. Oxford Uni. Press: 511–22.
  • 1897. "Outlines of seven lectures on the partition of numbers," Proc. Lond. Math. Soc. 28: 33–96.


  • Franklin, Address Commemorative of Sylvester, (Baltimore, 1896)

External links



Up to date as of January 14, 2010

From Wikiquote

James Joseph Sylvester

James Joseph Sylvester (3 September 181415 March 1897) was an English mathematician, and a leader in American mathematics in the second half of the 19th century.


  • It seems to be expected of every pilgrim up the slopes of the mathematical Parnassus, that he will at some point or other of his journey sit down and invent a definite integral or two towards the increase of the common stock.
    • Sylvester's Mathematical Papers, Volume 2, page 214.
    • Bigeometric Calculus: A System with a Scale-Free Derivative by Michael Grossman, page 31.
  • The object of pure Physic[s] is the unfolding of the laws of the intelligible world; the object of pure Mathematic[s] that of unfolding the laws of human intelligence.
    • Memorabilia Mathematica by Robert Edouard Moritz, quote #129.
  • Number, place, and combination . . . the three intersecting but distinct spheres of thought to which all mathematical ideas admit of being referred.
    • Sylvester's Collected Mathematical Papers, Volume 1, page 91.
  • As the prerogative of Natural Science is to cultivate a taste for observation, so that of Mathematics is, almost from the starting point, to stimulate the faculty of invention.
    • "A plea for the mathematician", Nature, Volume 1, page 261.

Quotes of others about Sylvester

  • To know him was to know one of the historic figures of all time, one of the immortals; and when he was really moved to speak, his eloquence equalled his genius.
    • G. B. Halsted, in F. Cajori's Teaching and History of Mathematics in the United States (Washington, 1890), page 265.
  • Professor Sylvester's first high class at the new university Johns Hopkins consisted of only one student, G. B. Halsted, who had persisted in urging Sylvester to lecture on the modern algebra. The attempt to lecture on this subject led him into new investigations in quantics.
    • Florian Cajori, in Teaching and History of Mathematics in the United States (Washington, 1890), page 264.

External Link

1911 encyclopedia

Up to date as of January 14, 2010

From LoveToKnow 1911

JAMES JOSEPH SYLVESTER (1814-1897), English mathematician, was born in London on the 3rd of September 1814. He went to school first at Highgate and then at Liverpool, and in 1831 entered St John's College, Cambridge. In his Tripos examination, which through illness he was prevented from taking till 1837, he was placed as second wrangler, but being a Jew and unwilling to sign the Thirty-nine Articles, he could not compete for one of the Smith's prizes and was ineligible for a fellowship, nor could he even take a degree: this last, however, he obtained at Trinity College, Dublin, where religious restrictions were no longer in force. After leaving Cambridge he was appointed to the chair of natural philosophy at University College, London, where his friend A. De Morgan was one of his colleagues, but he resigned in 1840 in order to become professor of mathematics in the university of Virginia. There, however, he remained only six months, for certain views on slavery, strongly held and injudiciously expressed, entailed unpleasant consequences, and necessitated his return to England, where he obtained in 1844 the post of actuary to the Legal and Equitable Life Assurance Company. In the course of the ensuing ten years he published a large amount of original work, much of it dealing with the theory of invariants, which marked him as one of the foremost mathematicians of the time. But he failed to obtain either of two posts - the professorships of mathematics at the Royal Military Academy and of geometry in Gresham College - for which he applied in 1854, though he was elected to the former in the following year on the death of his successful competitor. At Woolwich he remained until 1870, and although he was not a great success as an elementary teacher, that period of his life was very rich in mathematical work, which included remarkable advances in the theory of the partition of numbers and further contributions to that of invariants, together with an important research which yielded a proof, hitherto lacking, of Newton's rule for the discovery of imaginary roots for algebraical equations up to and including the fifth degree. In 1874 he produced several papers suggested by A. Peaucellier's discovery of the straight line link motion associated with his name, and he also invented the skew pentagraph. Three years later he was appointed professor of mathematics in the Johns Hopkins University, Baltimore, stipulating for an annual salary of $5000, to be paid in gold. At Baltimore he gave an enormous impetus to the study of the higher mathematics in America, and during the time he was there he contributed to the American Journal of Mathematics, of which he was the first editor, no less than thirty papers, some of great length, dealing mainly with modern algebra, the theory of numbers, theory of partitions and universal algebra. In 1883 he was chosen to succeed Henry Smith in the Savilian chair of geometry at Oxford, and there he produced his theory of reciprocants, largely by the aid of his "method of infinitesimal variation." In 1893 loss of health and failing eyesight obliged him to give up the active duties of his chair, and a deputy professor being appointed, he went to live in London, where he died on the 15th of March 1897. Sylvester's work suffered from a certain lack of steadiness and method in his character. For long periods he was mathematically unproductive, but then sudden inspiration would come upon him and his ideas and theories poured forth far more quickly than he could record them. All the same his output of work was as large as it was valuable. The scope of his researches was described by Arthur Cayley, his friend and fellow worker, in the following words: "They relate chiefly to finite analysis, and cover by their subjects a large part of it - algebra, determinants, elimination, the theory of equations, partitions, tactic, the theory of forms, matrices, reciprocants, the Hamiltonian numbers, &c.; analytical and pure geometry occupy a less prominent position; and mechanics, optics and astronomy are not absent." Sylvester was a good linguist, and a diligent composer of verse, both in English and Latin, but the opinion he cherished that his poems were on a level with his mathematical achievements has not met with general acceptance.

The first volume of his Collected Mathematical Papers, edited by H. F. Baker, appeared in 1904.

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