[2] Riley earned a bachelor's degree in mathematics from MIT in 1957; shortly thereafter he dropped out of the graduate program and went on to work in industry, eventually moving to Amsterdam in 1966.
[4] For the next two years he occupied a postdoctoral position in Boulder where William Thurston was employed at the time, before moving on to Binghamton University as a professor.
Early on, following work of Ralph Fox, he was interested in morphisms to finite groups.
-representations sending peripheral elements to parabolics led him to discover the hyperbolic structure on the complement of the figure-eight knot and some others.
[7] One notable feature of Riley's work is that it relied much on the assistance of a computer.