James Joseph Sylvester

James Joseph Sylvester was product the theory of matrices through unique partnership with Arthur Cayley. They met in their twenties and were friends, colleagues, and co-authors for the rest of their lives.


Sylvester's mathematical ability had been recognized at an early age. He studied mathematics at the University of London at the age of fourteen, under Augustus De Morgan. He entered Cambridge University at the age of seventeen and won several prizes. However Cambridge would not award him his degrees because he was Jewish. He completed his bachelor's and master's degrees at Trinity College in Dublin. Many years later, Cambridge changed its discriminatory policy and gave Sylvester his degrees.




Sylvester's tough science at University College in London for two years, found that he didn't like teaching science, and quit. He went to the United States, where he got a job teaching mathematics at the University of Virginia. After three months, he quit when the administration refused to discipline a student who had insulted him. After several unsuccessful attempts to obtain a teaching position, he return to England and worked for an insurance firm as an actuary, retaining his interest in mathematics only through tutoring. Florence Nightingale was one of his private pupils. When Sylvester became thoroughly bored with insurance work, he studied for a legal career and met Cayley.


Cayley and Sylvester revived and intensified each other's interest in mathematics and each started to write mathematics again. During his fourteen year spent practicing law, Cayley wrote almost 300 papers. Each frequently expressed gratitude to the other for assistance and inspiration. In one of his paper, Sylvester wrote that "the theorem above enunciated was in part suggested in the course of a Conversation with Mr Cayley (to whom I am indebted for my restoration to the enjoyment of mathematical life)." In another, he said, "Mr Cayley habitually discourse pearls and rubies."

Sylvester was repeatedly honored for his pioneering work in algebra. He left the law but was unable to obtain a professorship in mathematics at a prominent institution until late in his life. At the age of sixty-two, he accepted a position at the newly founded John hopkins University in Baltimore as its first professor of mathematics. While there, he founded the American Journal of Mathematics, introduced graduate work in mathematis into American universities, and generally stimulated the development of mathematics in America. He also arrange for Cayley to spend a semester at Johns Hopkins as guest lecturer. At the age of seventy, Sylvester returned to England to become Savilian Professor of Geometry at Oxford University.

With Cayley, he responsible for the theory of matrices, including the operation of matrices multiplication. Sixty-seven years after the invention of matrix theory, Heisenberg recognized it as the perfect tools for his revolutionary work in quantum mechanics. The work of Cayley and Sylvester in algebra become quite important for modern physics, particulary in the theory of relativity.

-------------------------------------------------------------------------
wiki : http://en.wikipedia.org/wiki/James_Joseph_Sylvester