[1] James later adopted the surname Sylvester when his older brother did so upon emigration to the United States.

Although his studies were interrupted for almost two years due to a prolonged illness, he nevertheless ranked second in Cambridge's famous mathematical examination, the tripos, for which he sat in 1837.

However, Sylvester was not issued a degree, because graduates at that time were required to state their acceptance of the Thirty-nine Articles of the Church of England, and he could not do so because he was Jewish.

[4] He left his appointment after only four months after a classroom incident in which a student he had criticized hit him with a bludgeon and he struck back with a sword-cane.

However, he left in November 1843 after being denied appointment as Professor of Mathematics at Columbia College (now University), again for his Judaism, and returned to England.

[2] In 1876[8] Sylvester again crossed the Atlantic Ocean to become the inaugural professor of mathematics at the new Johns Hopkins University in Baltimore, Maryland.

[12] When they did realize her gender, the board tried to revoke the offer, but Sylvester insisted that Ladd should be his student, and so she was.

[12] She held a fellowship at Johns Hopkins University for three years, but the trustees did not allow her name to be printed in circulars with those of other fellows, for fear of setting a precedent.

[14] Sylvester invented a great number of mathematical terms such as "matrix" (in 1850),[15][16] "graph" in the sense of network[17] and "discriminant".

Sylvester House, a portion of an undergraduate dormitory at Johns Hopkins University, is named in his honor.