As a professor at Princeton University, he taught and advised many of the contributors to the Golden Age of differential topology, and he played an important role in the modernization of knot theory and of bringing it into the mainstream.

Ralph Fox attended Swarthmore College for two years, while studying piano at the Leefson Conservatory of Music in Philadelphia.

He directed 21 doctoral dissertations, including those of John Milnor, John Stallings, Francisco González-Acuña, Guillermo Torres-Diaz and Barry Mazur, and supervised Ken Perko's undergraduate thesis.

He was an Invited Speaker at the International Congress of Mathematicians held in 1950 in Cambridge, Massachusetts.

[2] His mathematical contributions include Fox n-coloring of knots, the Fox–Artin arc, and the free differential calculus.