James Joseph Sylvester (1814–1897) was an English mathematician with a gift for inventing words almost as strong as his gift for algebra. We owe him the very terms matrix, discriminant, and a small dictionary of other maths vocabulary. He also wrote poetry, loved music, and once took singing lessons from a young French composer named Charles Gounod.
Sylvester, working closely with his friend Arthur Cayley, helped build the theory of
matrices and their invariants. His law of inertia tells you that no matter how
you rewrite a symmetric matrix, the count of its positive and negative signs never
changes — the beating heart of when a matrix is a
His name is also on Sylvester's sequence, the Sylvester–Gallai theorem in geometry, and a whole zoo of results across algebra and combinatorics.
Because he was Jewish, Sylvester was barred from taking his Cambridge degree for decades and shut out of jobs that lesser mathematicians walked into. He bounced between England and America, once quitting a Virginia post after a dispute with a student, and worked for years as a lawyer and an actuary to pay the bills — it was there he met Cayley, a fellow lawyer-mathematician. Finally, at 62, he founded the mathematics department at Johns Hopkins and started America's first serious research journal in the subject. Late bloomer, unstoppable spirit.