Ralph Hartzler 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. Ralph Fox attended Swarthmore College for two years, while studying piano at the Leefson Conservatory of Music in Philadelphia. He earned a master's degree from Johns Hopkins University, and a Ph.D.

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  • Ralph Hartzler 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. Ralph Fox attended Swarthmore College for two years, while studying piano at the Leefson Conservatory of Music in Philadelphia. He earned a master's degree from Johns Hopkins University, and a Ph.D. degree from Princeton University in 1939. His doctoral dissertation, On the Lusternick-Schnirelmann Category, was directed by Solomon Lefschetz. (In later years he disclaimed all knowledge of Lyusternik-Schnirelmann category, and certainly never published on the subject again. ) He directed 21 doctoral dissertations, including those of John Milnor, John Stallings, Francisco González-Acuña, Guillermo Torres-Diaz and Barry Mazur. His mathematical contributions include Fox n-coloring of knots and the free differential calculus. Aside from his strictly mathematical contributions, 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. He popularized the playing of the oriental game of Go at both Princeton and the Institute for Advanced Study.
  • Ralph Hartzler Fox war ein US-amerikanischer Mathematiker, der sich vor allem mit Knotentheorie beschäftigte. Fox besuchte das Swarthmore College, während er am Leefson-Konservatorium in Philadelphia Klavier studierte. Seinen Master-Abschluss in Mathematik machte er an der Johns Hopkins University. 1939 wurde er bei Solomon Lefschetz an der Princeton University promoviert. Danach war er am Institute for Advanced Study, der University of Illinois und der Syracuse University, bevor er 1945 wieder als Professor an der Princeton University war, wo er bis zu seinem Tod blieb. Er war u.a. Gastprofessor in Mexico City, Japan, der Universität Delft und der Universität Stockholm. Fox beschäftigte sich mit niedrigdimensionaler Topologie, speziell Knotentheorie. Sein Lehrbuch (mit seinem Schüler Richard H. Crowell) Introduction to Knot Theory, aus Vorlesungen am Haverford College 1956 entstanden, war lange ein Standardwerk. Er berichtete über die Arbeiten zur Knotentheorie auch auf dem Internationalen Mathematikerkongress 1950 in Cambridge (Massachusetts). Zu seinen Doktoranden zählen Barry Mazur, John Stallings und John Willard Milnor. Fox war aktiver Quäker, war verheiratet und hatte einen Sohn. Er war ein versierter Go-Spieler, der 1963 die USA im ersten internationalen Go-Wettbewerb in Tokio vertrat und den Grad des 4. Dan erreichte.
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  • Ralph Winston Fox
  • the American mathematician
  • the English writer
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  • Ralph Hartzler 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. Ralph Fox attended Swarthmore College for two years, while studying piano at the Leefson Conservatory of Music in Philadelphia. He earned a master's degree from Johns Hopkins University, and a Ph.D.
  • Ralph Hartzler Fox war ein US-amerikanischer Mathematiker, der sich vor allem mit Knotentheorie beschäftigte. Fox besuchte das Swarthmore College, während er am Leefson-Konservatorium in Philadelphia Klavier studierte. Seinen Master-Abschluss in Mathematik machte er an der Johns Hopkins University. 1939 wurde er bei Solomon Lefschetz an der Princeton University promoviert.
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  • Ralph Fox
  • Ralph Fox
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