James Joseph Sylvester (3 September 1814 – 15 March 1897) was an
English
English usually refers to:
* English language
* English people
English may also refer to:
Peoples, culture, and language
* ''English'', an adjective for something of, from, or related to England
** English national ide ...
mathematician
A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems.
Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change.
History
On ...
. He made fundamental contributions to
matrix theory
In mathematics, a matrix (plural matrices) is a rectangular array or table of numbers, symbols, or expressions, arranged in rows and columns, which is used to represent a mathematical object or a property of such an object.
For example,
\begi ...
,
invariant theory
Invariant theory is a branch of abstract algebra dealing with actions of groups on algebraic varieties, such as vector spaces, from the point of view of their effect on functions. Classically, the theory dealt with the question of explicit descri ...
,
number theory
Number theory (or arithmetic or higher arithmetic in older usage) is a branch of pure mathematics devoted primarily to the study of the integers and integer-valued functions. German mathematician Carl Friedrich Gauss (1777–1855) said, "Mat ...
,
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
Johns Hopkins University (Johns Hopkins, Hopkins, or JHU) is a private research university in Baltimore, Maryland. Founded in 1876, Johns Hopkins is the oldest research university in the United States and in the western hemisphere. It consi ...
and as founder of the ''
American Journal of Mathematics
The ''American Journal of Mathematics'' is a bimonthly mathematics journal published by the Johns Hopkins University Press.
History
The ''American Journal of Mathematics'' is the oldest continuously published mathematical journal in the United S ...
''. At his death, he was a professor at
Oxford University
Oxford () is a city in England. It is the county town and only city of Oxfordshire. In 2020, its population was estimated at 151,584. It is north-west of London, south-east of Birmingham and north-east of Bristol. The city is home to th ...
.
Biography
James Joseph was born in
London
London is the capital and List of urban areas in the United Kingdom, largest city of England and the United Kingdom, with a population of just under 9 million. It stands on the River Thames in south-east England at the head of a estuary dow ...
on 3 September 1814, the son of Abraham Joseph, a
Jewish
Jews ( he, יְהוּדִים, , ) or Jewish people are an ethnoreligious group and nation originating from the Israelites Israelite origins and kingdom: "The first act in the long drama of Jewish history is the age of the Israelites""The ...
merchant. James later 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
The University of London (UoL; abbreviated as Lond or more rarely Londin in post-nominals) is a federal public research university located in London, England, United Kingdom. The university was established by royal charter in 1836 as a degree ...
. 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
At the University of Cambridge, a Tripos (, plural 'Triposes') is any of the examinations that qualify an undergraduate for a bachelor's degree or the courses taken by a student to prepare for these. For example, an undergraduate studying mathe ...
, 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
The Thirty-nine Articles of Religion (commonly abbreviated as the Thirty-nine Articles or the XXXIX Articles) are the historically defining statements of doctrines and practices of the Church of England with respect to the controversies of the ...
of the
Church of England
The Church of England (C of E) is the established Christian church in England and the mother church of the international Anglican Communion. It traces its history to the Christian church recorded as existing in the Roman province of Britai ...
, and Sylvester could not do so because he was Jewish. 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
, mottoeng = Let all come who by merit deserve the most reward
, established =
, type = Public research university
, endowment = £143 million (2020)
, budget = ...
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
, name_Latin = Collegium Sanctae et Individuae Trinitatis Reginae Elizabethae juxta Dublin
, motto = ''Perpetuis futuris temporibus duraturam'' (Latin)
, motto_lang = la
, motto_English = It will last i ...
. In the same year he moved to the United States to become a professor of mathematics at the
University of Virginia
The University of Virginia (UVA) is a public research university in Charlottesville, Virginia. Founded in 1819 by Thomas Jefferson, the university is ranked among the top academic institutions in the United States, with highly selective ad ...
, but left after less than four months. A student who had been reading a newspaper in one of Sylvester's lectures insulted him and Sylvester struck him with a sword stick. The student collapsed in shock and Sylvester believed (wrongly) that he had killed him. Sylvester resigned when he felt that the university authorities had not sufficiently disciplined the student. He moved to New York City and began friendships with the Harvard mathematician Benjamin Peirce (father of
Charles Sanders Peirce
Charles Sanders Peirce ( ; September 10, 1839 – April 19, 1914) was an American philosopher, logician, mathematician and scientist who is sometimes known as "the father of pragmatism".
Educated as a chemist and employed as a scientist for t ...
) and the Princeton physicist Joseph Henry. However, he left in November 1843 after being denied appointment as Professor of Mathematics at Columbia College (now University), again for his Judaism, and 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
In mathematics, a matrix (plural matrices) is a rectangular array or table of numbers, symbols, or expressions, arranged in rows and columns, which is used to represent a mathematical object or a property of such an object.
For example,
\begi ...
during a long collaboration. 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
''The Times'' is a British daily national newspaper based in London. It began in 1785 under the title ''The Daily Universal Register'', adopting its current name on 1 January 1788. ''The Times'' and its sister paper '' The Sunday Times'' (f ...
''.
One of Sylvester's lifelong passions was for poetry; he read and translated works from the original French, German, Italian,
Latin
Latin (, or , ) is a classical language belonging to the Italic branch of the Indo-European languages. Latin was originally a dialect spoken in the lower Tiber area (then known as Latium) around present-day Rome, but through the power of the ...
and
Greek
Greek may refer to:
Greece
Anything of, from, or related to Greece, a country in Southern Europe:
*Greeks, an ethnic group.
*Greek language, a branch of the Indo-European language family.
**Proto-Greek language, the assumed last common ancestor ...
, and many of his mathematical papers contain illustrative quotes from classical poetry. Following his early retirement, Sylvester 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.
In 1876 Sylvester again crossed the Atlantic Ocean to become the inaugural professor of mathematics at the new
Johns Hopkins University
Johns Hopkins University (Johns Hopkins, Hopkins, or JHU) is a private research university in Baltimore, Maryland. Founded in 1876, Johns Hopkins is the oldest research university in the United States and in the western hemisphere. It consi ...
in
Baltimore, Maryland
Baltimore ( , locally: or ) is the List of municipalities in Maryland, most populous city in the U.S. state of Maryland, fourth most populous city in the Mid-Atlantic (United States), Mid-Atlantic, and List of United States cities by popula ...
. 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.
In 1877, he was elected as a member to the
American Philosophical Society
The American Philosophical Society (APS), founded in 1743 in Philadelphia, is a scholarly organization that promotes knowledge in the sciences and humanities through research, professional meetings, publications, library resources, and communit ...
.
In 1878 he founded the ''
American Journal of Mathematics
The ''American Journal of Mathematics'' is a bimonthly mathematics journal published by the Johns Hopkins University Press.
History
The ''American Journal of Mathematics'' is the oldest continuously published mathematical journal in the United S ...
''. The only other mathematical journal in the US at that time was the ''Analyst'', which eventually became the ''
Annals of Mathematics
The ''Annals of Mathematics'' is a mathematical journal published every two months by Princeton University and the Institute for Advanced Study.
History
The journal was established as ''The Analyst'' in 1874 and with Joel E. Hendricks as the ...
''.
In 1883, he returned to England to take up the
Savilian Professor of Geometry
The position of Savilian Professor of Geometry was established at the University of Oxford in 1619. It was founded (at the same time as the Savilian Professorship of Astronomy) by Sir Henry Savile, a mathematician and classical scholar who was ...
at
Oxford University
Oxford () is a city in England. It is the county town and only city of Oxfordshire. In 2020, its population was estimated at 151,584. It is north-west of London, south-east of Birmingham and north-east of Bristol. The city is home to th ...
. He held this chair until his death, although in 1892 the University appointed a deputy professor to the same chair. He was on the governing body of
Abingdon School.
Sylvester died at 5
Hertford Street
Hertford Street is a street in central London's Mayfair district.
It runs between a junction with Park Lane and Old Park Lane at its western end, to Curzon Street at its north-east end.
In 1771, Anne, Duchess of Cumberland and Strathearn marrie ...
, London on 15 March 1897. He is buried in
Balls Pond Road Cemetery
Balls Pond Road Cemetery, also known as Jewish (West London Reform) Cemetery, Kingsbury Road Cemetery, Balls Pond Burial Ground and The Jewish Burial Ground, is a Jewish cemetery on Kingsbury Road, Dalston, London N1. It was founded in 1843 an ...
on Kingsbury Road in London.
Legacy
Sylvester invented a great number of mathematical terms such as "
matrix" (in 1850), "
graph
Graph may refer to:
Mathematics
*Graph (discrete mathematics), a structure made of vertices and edges
**Graph theory, the study of such graphs and their properties
*Graph (topology), a topological space resembling a graph in the sense of discre ...
" (in the sense of ''network'') and "
discriminant". He coined the term "totient" for
Euler's totient function φ(''n''). In
discrete geometry
Discrete geometry and combinatorial geometry are branches of geometry that study combinatorial properties and constructive methods of discrete geometric objects. Most questions in discrete geometry involve finite or discrete sets of basic ge ...
he is remembered for
Sylvester's problem and a result on the
orchard problem, and in matrix theory he discovered
Sylvester's determinant identity
In matrix theory, Sylvester's determinant identity is an identity useful for evaluating certain types of determinants. It is named after James Joseph Sylvester, who stated this identity without proof in 1851. Cited in
Given an ''n''-by-''n'' ma ...
, which generalizes the ''Desnanot–Jacobi identity''. His collected scientific work fills four volumes. In 1880, the
Royal Society of London
The Royal Society, formally The Royal Society of London for Improving Natural Knowledge, is a learned society and the United Kingdom's national academy of sciences. The society fulfils a number of roles: promoting science and its benefits, re ...
awarded Sylvester the
Copley Medal, its highest award for scientific achievement; in 1901, it instituted the
Sylvester Medal
The Sylvester Medal is a bronze medal awarded by the Royal Society (London) for the encouragement of mathematical research, and accompanied by a £1,000 prize. It was named in honour of James Joseph Sylvester, the Savilian Professor of Geometry a ...
in his memory, to encourage mathematical research after his death in
Oxford
Oxford () is a city in England. It is the county town and only city of Oxfordshire. In 2020, its population was estimated at 151,584. It is north-west of London, south-east of Birmingham and north-east of Bristol. The city is home to the ...
.
Sylvester House, a portion of an undergraduate dormitory at
Johns Hopkins University
Johns Hopkins University (Johns Hopkins, Hopkins, or JHU) is a private research university in Baltimore, Maryland. Founded in 1876, Johns Hopkins is the oldest research university in the United States and in the western hemisphere. It consi ...
, is named in his honor. Several professorships there are named in his honor also.
Publications
*
*
*
*
*
See also
*
Catalecticant
In mathematical invariant theory, the catalecticant of a form of even degree is a polynomial in its coefficients that vanishes when the form is a sum of an unusually small number of powers of linear forms. It was introduced by ; see . The word c ...
*
Covariance and contravariance of vectors
*
Evectant
*
Inclusion–exclusion principle
In combinatorics, a branch of mathematics, the inclusion–exclusion principle is a counting technique which generalizes the familiar method of obtaining the number of elements in the union of two finite sets; symbolically expressed as
: , A \cu ...
*
Invariant of a binary form In mathematical invariant theory, an invariant of a binary form is a polynomial in the coefficients of a binary form in two variables ''x'' and ''y'' that remains invariant under the special linear group acting on the variables ''x'' and ''y''.
T ...
*
Sylvester's construction
*
Sylvester pentahedron
*
Sylvester's problem
*
Clock and shift matrices
*
Umbral calculus
In mathematics before the 1970s, the term umbral calculus referred to the surprising similarity between seemingly unrelated polynomial equations and certain "shadowy" techniques used to "prove" them. These techniques were introduced by John Blis ...
*
List of things named after James Joseph Sylvester
References
Sources
*.
*
*
*
External links
*
*
Collected papersnbsp;– from the
University of Michigan
, mottoeng = "Arts, Knowledge, Truth"
, former_names = Catholepistemiad, or University of Michigania (1817–1821)
, budget = $10.3 billion (2021)
, endowment = $17 billion (2021)As o ...
Historical Math Collection
J. J. Sylvester home pageSelected Poetry of James Joseph Sylvester*
{{DEFAULTSORT:Sylvester, James Joseph
1814 births
1897 deaths
19th-century American mathematicians
19th-century English mathematicians
Academics of University College London
Linear algebraists
Alumni of St John's College, Cambridge
British actuaries
Burials at Balls Pond Road Cemetery
English Jews
Combinatorialists
Fellows of the Royal Society
Foreign associates of the National Academy of Sciences
Jewish American scientists
Johns Hopkins University faculty
Number theorists
Alumni of Trinity College Dublin
Recipients of the Copley Medal
Royal Medal winners
Savilian Professors of Geometry
Second Wranglers
De Morgan Medallists
Governors of Abingdon School
Fellows of the Royal Society of Edinburgh
Johns Hopkins University
19th-century British businesspeople