He made fundamental contributions to matrix theory, invariant theory, number theory, partition theory, and combinatorics.
Ia memberikan kontribusi mendasar pada teori matriks, teori invarian, teori bilangan, teori partisi, dan kombinatorika.
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.
Ia memainkan peran kepemimpinan dalam matematika Amerika pada paruh kedua abad ke-19 sebagai profesor di Universitas Johns Hopkins dan sebagai pendiri American Journal of Mathematics.
At his death, he was a professor at Oxford University.
Pada saat kematiannya, ia menjabat sebagai profesor di Universitas Oxford.
James Joseph was born in London on 3 September 1814, the son of Abraham Joseph, a Jewish merchant.
James Joseph lahir di London pada 3 September 1814, putra dari Abraham Joseph, seorang pedagang Yahudi.
At the age of 14, Sylvester was a student of Augustus De Morgan at the University of London (now University College London).
Pada usia 14 tahun, Sylvester menjadi murid Augustus De Morgan di Universitas London (sekarang University College London).
Subsequently, he attended the Liverpool Royal Institution.
Selanjutnya, ia menempuh pendidikan di Liverpool Royal Institution.
Sylvester began his study of mathematics at St John's College, Cambridge in 1831, where his tutor was John Hymers.
Sylvester memulai studi matematikanya di St John's College, Cambridge pada tahun 1831, di bawah bimbingan tutor 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.
Meskipun studinya sempat terhenti selama hampir dua tahun karena penyakit yang berkepanjangan, ia tetap berhasil menempati peringkat kedua dalam ujian matematika terkenal di Cambridge, Tripos, yang ia ikuti pada tahun 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 he could not do so because he was Jewish.
Namun, Sylvester tidak diberikan gelar karena lulusan pada waktu itu diwajibkan untuk menyatakan penerimaan mereka terhadap Tiga Puluh Sembilan Pasal dari Gereja Inggris, dan ia tidak dapat melakukannya karena ia adalah seorang Yahudi.
For the same reason, he was unable to compete for a Fellowship or obtain a Smith's prize.
Karena alasan yang sama, ia tidak dapat bersaing untuk mendapatkan posisi Fellow atau memperoleh Hadiah Smith.
In 1838, Sylvester became professor of natural philosophy at University College London and in 1839 a Fellow of the Royal Society of London.
Pada tahun 1838, Sylvester menjadi profesor filsafat alam di University College London dan pada tahun 1839 menjadi Fellow dari Royal Society of London.
In 1841, he was awarded a BA and an MA by Trinity College Dublin.
Pada tahun 1841, ia dianugerahi gelar BA dan MA oleh 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 first Jewish professor at any American college or university.
Pada tahun yang sama, ia pindah ke Amerika Serikat untuk menjadi profesor matematika di Universitas Virginia, menjadikannya profesor Yahudi pertama di perguruan tinggi atau universitas Amerika mana pun.
He left his appointment after only four months after a classroom incident in which a student he had criticized hit him with a bludgeon and he struck back with a sword-cane.
Ia meninggalkan jabatannya setelah hanya empat bulan menyusul sebuah insiden di kelas di mana seorang mahasiswa yang ia kritik memukulnya dengan tongkat pemukul, dan ia membalasnya dengan tongkat pedang (sword-cane).
The student collapsed in shock and Sylvester believed (wrongly) that he had killed him.
Mahasiswa tersebut pingsan karena terkejut dan Sylvester percaya (secara keliru) bahwa ia telah membunuhnya.
Sylvester resigned when he felt that the university authorities had not sufficiently disciplined the student.
Sylvester mengundurkan diri ketika ia merasa pihak universitas tidak memberikan disiplin yang memadai kepada mahasiswa tersebut.
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.
Ia pindah ke New York City dan menjalin persahabatan dengan matematikawan Harvard Benjamin Peirce (ayah dari Charles Sanders Peirce) dan fisikawan Princeton 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.
Namun, ia pergi pada November 1843 setelah lamarannya sebagai Profesor Matematika di Columbia College (sekarang Universitas Columbia) ditolak, lagi-lagi karena agamanya, dan ia kembali ke Inggris.
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.
Ia tidak mendapatkan posisi mengajar matematika di universitas sampai tahun 1855, ketika ia diangkat sebagai profesor matematika di Akademi Militer Kerajaan, Woolwich.
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.
Akademi Woolwich awalnya menolak untuk membayar pensiun penuh kepada Sylvester, dan baru melunak setelah kontroversi publik yang panjang, di mana Sylvester membawa kasusnya ke kolom surat kabar 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.
Sylvester adalah puisi; ia membaca dan menerjemahkan karya-karya dari bahasa asli Prancis, Jerman, Italia, Latin, dan Yunani.
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.
Setelah pensiun dini, Sylvester menerbitkan sebuah buku berjudul The Laws of Verse di mana ia mencoba mengkodifikasi serangkaian hukum untuk prosodi dalam puisi.
In 1861 Sylvester was elected an honorary member of the Manchester Literary and Philosophical Society and in 1872, he finally received his B.A. and M.A. from Cambridge, having been denied the degrees due to his being a Jew.
Pada tahun 1861, Sylvester terpilih sebagai anggota kehormatan Masyarakat Sastra dan Filosofis Manchester dan pada tahun 1872, ia akhirnya menerima gelar B.A. dan M.A. dari Cambridge, setelah sebelumnya ditolak karena statusnya sebagai seorang Yahudi.
In 1876 Sylvester again crossed the Atlantic Ocean to become the inaugural professor of mathematics at the new Johns Hopkins University in Baltimore, Maryland.
Pada tahun 1876, Sylvester kembali menyeberangi Samudra Atlantik untuk menjadi profesor matematika pertama di Universitas Johns Hopkins yang baru didirikan di Baltimore, Maryland.
His salary was $5,000 (quite generous for the time), which he demanded be paid in gold.
Gajinya adalah $5.000 (sangat besar untuk saat itu), yang ia minta untuk dibayarkan dalam bentuk emas.
After negotiation, agreement was reached on a salary that was not paid in gold.
Setelah negosiasi, kesepakatan tercapai pada gaji yang tidak dibayarkan dalam emas.
In 1877, he was elected as a member to the American Philosophical Society.
Pada tahun 1877, ia terpilih sebagai anggota American Philosophical Society.
In 1878 he founded the American Journal of Mathematics.
Pada tahun 1878, ia mendirikan 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.
Satu-satunya jurnal matematika lain di AS pada waktu itu adalah The Analyst, yang akhirnya menjadi Annals of Mathematics.
Also in 1878, Christine Ladd-Franklin was accepted into Johns Hopkins University with his help.
Juga pada tahun 1878, Christine Ladd-Franklin diterima di Universitas Johns Hopkins dengan bantuannya.
Ladd's application for a fellowship was signed "C. Ladd", and the university offered her the position without realizing she was a woman.
Lamaran Ladd untuk beasiswa ditandatangani dengan nama "C. Ladd", dan pihak universitas menawarkan posisi tersebut tanpa menyadari bahwa ia adalah seorang wanita.
When they did realise her gender, the board tried to revoke the offer, but Sylvester insisted that Ladd should be his student, and so she was.
Ketika mereka menyadari jenis kelaminnya, dewan mencoba membatalkan tawaran tersebut, tetapi Sylvester bersikeras bahwa Ladd harus menjadi muridnya.
In 1883, Sylvester returned to England to take up the position of Savilian Professor of Geometry at Oxford University.
Pada tahun 1883, Sylvester kembali ke Inggris untuk mengambil posisi sebagai Profesor Geometri Savilian di Universitas Oxford.
He was on the governing body of Abingdon School.
Ia juga merupakan anggota badan pengelola Sekolah Abingdon.
Sylvester died at 5 Hertford Street, London on 15 March 1897.
Sylvester meninggal di 5 Hertford Street, London pada 15 Maret 1897.
He is buried in Balls Pond Road Cemetery on Kingsbury Road in London.
Ia dimakamkan di Pemakaman Balls Pond Road di Kingsbury Road, London.
Sylvester invented a great number of mathematical terms such as "matrix" (in 1850), "graph" in the sense of network and "discriminant".
Sylvester menciptakan sejumlah besar istilah matematika seperti "matriks" (pada tahun 1850), "graf" dalam artian jaringan, dan "diskriminan".
His collected scientific work fills four volumes.
Kumpulan karya ilmiahnya mengisi empat jilid.
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.
Pada tahun 1880, Royal Society of London menganugerahi Sylvester Medali Copley, penghargaan tertinggi untuk pencapaian ilmiah; pada tahun 1901, lembaga tersebut mendirikan Medali Sylvester untuk mengenangnya, guna mendorong penelitian matematika setelah kematiannya di Oxford.
Sylvester House, a portion of an undergraduate dormitory at Johns Hopkins University, is named in his honour.
Sylvester House, bagian dari asrama mahasiswa sarjana di Universitas Johns Hopkins, dinamai untuk menghormatinya.
Several professorships there are named in his honour also.
Beberapa jabatan profesor di sana juga dinamai menurut namanya.