Ralph H. Fox was an American mathematician. 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 and main-streaming of knot theory.
His doctoral dissertation, On the Lusternick-Schnirelmann Category (1939), was directed by Solomon Lefschetz at Princeton University. (In later years he disclaimed all knowledge of Lusternick-Schnirelmann category, and certainly never published on the subject again.) He directed 21 doctoral dissertations, including those of John Milnor, John Stallings , and Barry Mazur.
Aside from his strictly mathematical contributions (including the free differential calculus ), he was responsible for introducing several basic bits of terminology to knot theory: the phrases slice knot , ribbon knot , and Seifert circle all appear in print for the first time under his name, and he also popularized (if he did not introduce) the phrase Seifert surface.