01/08/2023
James Joseph Sylvester was the most influ -
ential mathematician in America in the 19th
century. Sylvester was born on September 3,
1814, in London and showed his mathemati-
cal genius early. At the age of 14, he studied
under De Morgan and won several prizes for
his mathematics, and at the unusually young
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 was
to include academics, law, and actuarial ca-
reers. In 1876, at the age of 62, he was ap-
pointed to a prestigious position at the newly
founded Johns Hopkins University. During
his seven years at Johns Hopkins, Sylvester
pursued research in pure mathematics
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 professor-
ship at Oxford, a position he held until his
death on March 15, 1897.
Sylvester’s major contributions to math-
ematics were in the theory of equations,
matrix theory, determinant theory, and in-
variant theory (which he founded with
Cayley). 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 lec-
tures 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 con-
fine himself to the hour, nor to the 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 another and another. Afterward he would
go back and work it all over again, and sur-
prise us with all sorts of side lights. He then
made another leap in the dark, more treasures
were discovered, and so on forever.
