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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 ...
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, invariant theory,
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, "Ma ...
, partition theory, and
combinatorics Combinatorics is an area of mathematics primarily concerned with counting, both as a means and an end in obtaining results, and certain properties of finite structures. It is closely related to many other areas of mathematics and has many a ...
. 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''. 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 the ...
.


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 degr ...
. 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 John Hymers (1803–1887) was an English mathematician and cleric, and, together with his brother Robert, founder of Hymers College, Hull. Life Hymers was born 20 July 1803 at Ormesby in Yorkshire; his father was a farmer, and his mother was dau ...
. 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 mat ...
, 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 Brit ...
, 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. 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 ...
) 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 Arthur Cayley (; 16 August 1821 – 26 January 1895) was a prolific British mathematician who worked mostly on algebra. He helped found the modern British school of pure mathematics. As a child, Cayley enjoyed solving complex maths problem ...
, with whom he made significant contributions to invariant theory and also matrix theory 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'' ( ...
''. 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 languages, 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 ...
and Greek, 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 most populous city in the U.S. state of Maryland, fourth most populous city in the Mid-Atlantic, and the 30th most populous city in the United States with a population of 585,708 in 2020. Baltimore wa ...
. 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 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 th ...
''. In 1883, he returned to England to take up the Savilian Professor of Geometry 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 the ...
. 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, London on 15 March 1897. He is buried in Balls Pond Road Cemetery on Kingsbury Road in London.


Legacy

Sylvester invented a great number of mathematical terms such as "
matrix Matrix most commonly refers to: * ''The Matrix'' (franchise), an American media franchise ** '' The Matrix'', a 1999 science-fiction action film ** "The Matrix", a fictional setting, a virtual reality environment, within ''The Matrix'' (franchi ...
" (in 1850), " graph" (in the sense of ''network'') and "
discriminant In mathematics, the discriminant of a polynomial is a quantity that depends on the coefficients and allows deducing some properties of the roots without computing them. More precisely, it is a polynomial function of the coefficients of the orig ...
". He coined the term "totient" for Euler's totient function φ(''n''). In discrete geometry he is remembered for Sylvester's problem and a result on the orchard problem, and in matrix theory he discovered Sylvester's determinant identity, 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, r ...
awarded Sylvester the
Copley Medal The Copley Medal is an award given by the Royal Society, for "outstanding achievements in research in any branch of science". It alternates between the physical sciences or mathematics and the biological sciences. Given every year, the medal is t ...
, 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 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 * Covariance and contravariance of vectors * Evectant * Inclusion–exclusion principle * Invariant of a binary form * 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 The mathematician J. J. Sylvester was known for his ability to coin new names and new notation for mathematical objects, not based on his own name. Nevertheless, many objects and results in mathematics have come to be named after him: *The Sylves ...


References


Sources

*. * * *


External links

* *
Collected papers
nbsp;– 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 page

Selected 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