J.J. SYLVESTER

SYLVESTER

James Joseph Sylvester was the most influential mathematician in America in the 19th century. Sylvester was born on September 3, 1814, in London and showed his mathematical genius early. At the age of 14, he studies under De Morgan and won several prizes for his mathematics, and at the age of 25, he was elected a Fellow of the ROYAL SOCIETY.

After receiving B.A. and M.A. degrees from Trinity College in Dublin in 1841, Sylvester began a professional life that would include academics, law and actuarial careers. In 1876, at the age of 62, he was appointed to a prestigious position at the newly founded Johns Hopkins University. During his seven years at Johns Hopkins, Sylvester pursued research in pure mathematics, the first ever done in America, with tremendous vigor and enthusiasm. He also founded the American Journal of Mathematics, the first journal in America devoted to mathematical research. Sylvester returned to England in 1884 to a professorship at Oxford, a position he hold  until his death on March 15, 1897.

Sylvester's major contributions to mathematics were in the theory of equations, matrix theory, determinant theory, and invariant theory (which is founded with Caylay). His writings and lectures- flowery and eloquent, pervaded with poetic flights, emotional expressions, bizarre utterances, and paradoxes-reflected the personality of this sensitive, excitable and enthusiastic man. We quote three of his students. E.W. Davis commented on Sylvester's teaching methods.

Sylvester's methods! He had none. "Three lectures will be delivered on a New Universal Algebra," he would say; then, "The course must be extended to twelve." It did last all the rest of that year. The following year the course was to be Substitutions- Theorie, by Netto. We all got the text. He lectured about three times, following the text closely and stopping sharp at the end of the hour. Then he began to think about matrices again. "I must give one lecture a week on those," he said. He could not confine himself to the hour, nor to Jo one lecture a week. Two weeks were passed, and Netto was forgotten entirely and never mentioned again. Statements like the following were not infrequent in his lectures: 'I haven't proved this, but I am as sure as I can be of anything that it must be so. From this it will follow, etc." At the next lecture it turned out that what he was so sure of was false. Never mind, he kept on forever guessing and trying, and presently a wonderful discovery followed, then an-other and another. Afterward he would go back and work it all over again, and surprise us with all sorts of side lights. He then made another leap in the dark, more treasures were discovered, and so on forever.

Sylvester's enthusiasm for teaching and his influence on his students are captured in the following passage written by Sylvester's first student at Johns Hopkins, G.B.Halsted.

A short, broad man of tremendous vitality.... Sylvester's captions head was ever lost on the highest cloud-lands of pure mathematics. Often in the dead of night he would get his favorite pupil, that he might  communicate the very last product of his creative thought. Everything he saw suggested to him something new in higher algebra. This transmutation of everything into new mathematics was a revelation to those who knew him intimately. They began to do it themselves.

Another characteristic of Sylvester, which is very unusual among mathematicians, was his apparent inability to remember mathematics! W.P. Durfee had the following to say:

Sylvester had one remarkable peculiarity. He seldom remembered theorems, propositions, etc., but had always to deduce them when he wished to use them. In this he was the very antithesis of Caylay, who was thoroughly conversant with everything that had been done in every branch of mathematics.

   I remember once submitting to Sylvester some investigations that I had been engaged on, and he immediately denied my first statement, saying that such a proposition had never been heard of, let alone proved. To his astonishment, I showed him a paper of his own in which he had proved that proposition; in fact, I belive the object of his paper had been the very proof which was so strange to him.