James Joseph Sylvester
|Born||3 September 1814|
|Died||15 March 1897 82) (aged|
|Alma mater||St. John's College, Cambridge|
|Known for||coining the term 'graph' |
Coining the term 'discriminant'
Sylvester's determinant theorem
Sylvester matrix (resultant matrix)
Sylvester's law of inertia
|Awards|| Royal Medal (1861)|
Copley Medal (1880)
De Morgan Medal (1887)
|Institutions|| Johns Hopkins University |
University College London
University of Virginia
Royal Military Academy, Woolwich
University of Oxford
|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
|Influenced|| Morgan Crofton |
James Joseph Sylvester FRS HFRSE LLD (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.
Fellowship of the Royal Society is an award granted to individuals that the Royal Society of London judges to have made a 'substantial contribution to the improvement of natural knowledge, including mathematics, engineering science and medical science'.
The United Kingdom, officially the United Kingdom of Great Britain and Northern Ireland but more commonly known as the UK or Britain, is a sovereign country lying off the north-western coast of the European mainland. The United Kingdom includes the island of Great Britain, the north-eastern part of the island of Ireland and many smaller islands. Northern Ireland is the only part of the United Kingdom that shares a land border with another sovereign state—the Republic of Ireland. Apart from this land border, the United Kingdom is surrounded by the Atlantic Ocean, with the North Sea to the east, the English Channel to the south and the Celtic Sea to the south-west, giving it the 12th-longest coastline in the world. The Irish Sea lies between Great Britain and Ireland. With an area of 242,500 square kilometres (93,600 sq mi), the United Kingdom is the 78th-largest sovereign state in the world. It is also the 22nd-most populous country, with an estimated 66.0 million inhabitants in 2017.
A mathematician is someone who uses an extensive knowledge of mathematics in his or her work, typically to solve mathematical problems.
James Joseph was born in London on 3 September 1814, the son of Abraham Joseph, a 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.
London is the capital and largest city of both England and the United Kingdom. Standing on the River Thames in the south-east of England, at the head of its 50-mile (80 km) estuary leading to the North Sea, London has been a major settlement for two millennia. Londinium was founded by the Romans. The City of London, London's ancient core − an area of just 1.12 square miles (2.9 km2) and colloquially known as the Square Mile − retains boundaries that follow closely its medieval limits. The City of Westminster is also an Inner London borough holding city status. Greater London is governed by the Mayor of London and the London Assembly.
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.
Augustus De Morgan was a British mathematician and logician. He formulated De Morgan's laws and introduced the term mathematical induction, making its idea rigorous.
The University of London is a collegiate federal research university located in London, England. As of October 2018, the university contains 18 member institutions, central academic bodies and research institutes. The university has over 52,000 distance learning external students and 161,270 campus-based internal students, making it the largest university by number of students in the United Kingdom.
The Liverpool Royal Institution was a learned society set up in 1814 for "the Promotion of Literature, Science and the Arts". William Corrie, William Rathbone IV, Thomas Stewart Traill and William Roscoe were among the founders. It was sometimes called the Royal Society of Liverpool.
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. 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. 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.
St John's College is a constituent college of the University of Cambridge. The college was founded by Lady Margaret Beaufort. In constitutional terms, the college is a charitable corporation established by a charter dated 9 April 1511. The aims of the college, as specified by its statutes, are the promotion of education, religion, learning and research.
John Hymers (1803–1887) was an English mathematician and cleric, and, together with his brother Robert, founder of Hymers College, Hull.
At the University of Cambridge, a Tripos is any of the undergraduate examinations that qualify an undergraduate for a bachelor's degree or the courses taken by an undergraduate to prepare. For example, an undergraduate studying mathematics is said to be reading for the Mathematical Tripos, whilst a student of English literature is reading for the English Tripos.
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. [ incomplete short citation ] 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 .
Arthur Cayley F.R.S. was a British mathematician. He helped found the modern British school of pure mathematics.
In mathematics, a matrix is a rectangular array of numbers, symbols, or expressions, arranged in rows and columns. For example, the dimensions of the matrix below are 2 × 3, because there are two rows and three columns:
The Royal Military Academy (RMA) at Woolwich, in south-east London, was a British Army military academy for the training of commissioned officers of the Royal Artillery and Royal Engineers. It later also trained officers of the Royal Corps of Signals and other technical corps. RMA Woolwich was commonly known as "The Shop" because its first building was a converted workshop of the Woolwich Arsenal.
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.
Latin is a classical language belonging to the Italic branch of the Indo-European languages. The Latin alphabet is derived from the Etruscan and Greek alphabets, and ultimately from the Phoenician alphabet.
Greek is an independent branch of the Indo-European family of languages, native to Greece, Cyprus and other parts of the Eastern Mediterranean and the Black Sea. It has the longest documented history of any living Indo-European language, spanning more than 3000 years of written records. Its writing system has been the Greek alphabet for the major part of its history; other systems, such as Linear B and the Cypriot syllabary, were used previously. The alphabet arose from the Phoenician script and was in turn the basis of the Latin, Cyrillic, Armenian, Coptic, Gothic, and many other writing systems.
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 1876Sylvester 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. 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. He was on the governing body of Abingdon School.
Sylvester died in London on 15 March 1897. He is buried in Balls Pond Road Jewish Cemetery on Kingsbury Road in London.
Sylvester invented a great number of mathematical terms such as "matrix" (in 1850),"graph" (combinatorics) and "discriminant". He coined the term "totient" for 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 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.
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