The object of pure physics is the unfolding of the laws of the intelligible world; the object of pure mathematics that of unfolding the laws of human intelligence.

He coined the term "totient" for Euler's totient function φ(n). His father Abraham Joseph was a merchant. James Joseph Sylvester FRS (3 September 1814 – 15 March 1897) was an English mathematician.

At his death he was professor at Oxford. He played a leadership role in American mathematics in the later half of the 19th century as a professor at the Johns Hopkins University and as founder of the American Journal of Mathematics. James Joseph Sylvester FRS (3 September 1814 – 15 March 1897) was an English mathematician.