James Joseph Sylvester

James Joseph Sylvester
Public domain · source
Name	James Joseph Sylvester
Caption	James Joseph Sylvester, circa 1880
Birth date	3 September 1814
Birth place	London, England
Death date	15 March 1897
Death place	London, England
Fields	Mathematics
Workplaces	University College London, University of Virginia, Royal Military Academy, Woolwich, Johns Hopkins University, University of Oxford
Alma mater	St John's College, Cambridge
Doctoral advisor	None
Doctoral students	William Pitt Durfee, George Bruce Halsted
Known for	Matrix theory, Invariant theory, Number theory, Combinatorics
Prizes	Royal Medal (1861), Copley Medal (1880), De Morgan Medal (1887)

James Joseph Sylvester. A foundational figure in Victorian era mathematics, his prolific career spanned algebra, number theory, and combinatorics. He co-founded the field of invariant theory with Arthur Cayley and made seminal contributions to matrix theory, including coining the term "matrix" itself. His energetic personality and profound insights left an indelible mark on American mathematics during his tenure at Johns Hopkins University and later at University of Oxford.

Early life and education

Born into a Jewish family in London, he faced significant religious barriers to academic advancement in early 19th-century England. He studied at University College London and later entered St John's College, Cambridge, where he excelled in the Mathematical Tripos but, as a Jew, could not graduate with a degree or hold a fellowship until after the Test Acts were reformed. This discrimination led him to study law at the Inner Temple and he was called to the bar, practicing for a time while continuing his mathematical research. His early work attracted the attention of prominent scientists like John Herschel and he was elected a Fellow of the Royal Society in 1839.

Mathematical work

Sylvester's mathematical output was vast and creative, characterized by a distinctive poetic flair in his nomenclature. With Arthur Cayley, he developed the theory of algebraic invariants, a cornerstone of 19th-century algebra. He invented many fundamental concepts in matrix theory, including the discriminant and the theory of elementary divisors. In number theory, he investigated partitions and the sieve problem. His work in combinatorics included studies on graph theory, and he posed the famous Sylvester's problem in projective geometry. He also made contributions to the theory of canonical forms and elimination theory.

Academic career and honors

His academic journey was peripatetic, marked by both brilliance and friction with administrators. He held the chair of natural philosophy at University College London and later a professorship at the University of Virginia, which he left abruptly. After a long period at the Royal Military Academy, Woolwich, he was forced to retire at age 55. In 1876, he was recruited to become the first professor of mathematics at the new Johns Hopkins University in Baltimore, where he founded the American Journal of Mathematics. He returned to England in 1883 to become the Savilian Professor of Geometry at University of Oxford. His honors included the Royal Medal of the Royal Society, the Copley Medal, and the first De Morgan Medal from the London Mathematical Society, of which he was a founding member and president.

Legacy and influence

Sylvester's legacy is profound in both theory and institution-building. He essentially planted the seed for modern American mathematics through his research school at Johns Hopkins University, mentoring students like William Pitt Durfee. The Sylvester Medal of the Royal Society was established in his memory. His coining of terms like "matrix," "discriminant," and "graph" remains standard in mathematical lexicon. His work directly influenced later giants such as David Hilbert, whose basis theorem resolved central questions in invariant theory. The London Mathematical Society continues to honor his memory through lectures and awards.

Personal life and character

Known for his fiery, enthusiastic, and sometimes combative personality, Sylvester was a charismatic and inspiring teacher. He was deeply passionate about poetry, classical literature, and music, often drawing analogies between these arts and mathematics. He never married and had a complex relationship with his colleague Arthur Cayley, combining intense collaboration with periods of rivalry. His later years at Oxford were somewhat isolated, but he remained active in research until his death in London. He is buried in the Jewish cemetery at Balls Pond Road in London.

Category:English mathematicians Category:1814 births Category:1897 deaths