The Secret History of Mathematicians

Daniel S. Silver in American Scientist:

Fullimage_200610512181_307Historian George Sarton often said that science advances in darkness, invisible to the majority of people, who are more interested in battles and other noisier activities. In his 1957 book The Study of the History of Mathematics, Sarton went on to say that if the history of science is secret, then the history of mathematics is doubly so, “for the growth of mathematics is unknown not only to the general public, but even to scientific workers.”

Sarton’s words help us understand why few have ever heard of Arthur Cayley (1821-95) or James Joseph Sylvester (1814-97), two of the most profound and prolific mathematicians of the Victorian era. Cayley’s seminal investigations of matrix algebra, which constituted only a tiny portion of his 967 papers, were crucial for the development of linear algebra. The terms matrix, determinant and Jacobian, familiar to most science students, were invented by Sylvester, an enthusiastic poet who called himself the “mathematical Adam.”

It is not clear when Cayley and Sylvester first met, but by 1847 they were corresponding to share thoughts about mathematics.

More here.  [Photo shows Arthur Cayley.]