J. J. Sylvester

J. J. Sylvester. James Joseph Sylvester was a preeminent English mathematician who made foundational contributions to algebra, number theory, and combinatorics. He played a pivotal role in the development of invariant theory alongside Arthur Cayley and was a key figure in establishing Johns Hopkins University as a leading center for mathematical research in North America. His prolific career, marked by passionate and poetic engagement with his subject, spanned institutions in England and the United States.

Biography

Born in London into a Jewish family, he faced religious barriers at Cambridge University, where he studied at St John's College, Cambridge but could not graduate with a degree until 1871 due to his faith. His early career included work as an actuary at the Equitable Life Assurance Society and a professorship at University College London. After a period at the Royal Military Academy, Woolwich, he moved to the United States in 1876 to become the first professor of mathematics at the new Johns Hopkins University in Baltimore, where he founded the influential American Journal of Mathematics. He later returned to England to become the Savilian Professor of Geometry at the University of Oxford, a position he held until his death.

Mathematical contributions

Sylvester's work was vast and innovative, deeply shaping modern algebra. With Arthur Cayley, he pioneered the theory of algebraic invariants, a central theme in 19th-century mathematics. He coined the term "matrix" in its modern mathematical sense and developed fundamental concepts in linear algebra, including the Sylvester's law of inertia for quadratic forms. In number theory, he investigated the partition of integers and defined the curious Sylvester's sequence. His contributions extended to elimination theory, Diophantine equations, and the theory of canonical forms. He also made significant studies in the theory of equations, including work on Sturm's theorem and the Sylvester matrix for resultants.

Legacy and recognition

Sylvester's legacy is profound, both in the content of his discoveries and his role as an institution-builder. At Johns Hopkins University, he trained a generation of American mathematicians, including William Pitt Durfee and George B. Halsted, elevating the status of pure mathematics in the United States. His energetic and florid style of lecturing and writing left a lasting impression. He received numerous honors, including the Royal Medal from the Royal Society in 1861, the Copley Medal in 1880, and the first De Morgan Medal from the London Mathematical Society in 1887. The Sylvester Medal was later established by the Royal Society in his memory to honor outstanding research in mathematics.

Selected works

* "On the relation between the minor determinants of linearly equivalent quadratic functions" (1851) * "A demonstration of the theorem that every homogeneous quadratic polynomial is reducible by real orthogonal substitutions to the form of a sum of positive and negative squares" (Sylvester's law of inertia, 1852) * "On the partition of numbers" (1857) * "Lectures on the Principles of Universal Algebra" published in the American Journal of Mathematics (1884) * "The Collected Mathematical Papers of James Joseph Sylvester" (4 volumes, published 1904–1912)

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