He was a member of the Rice board of governors from 1972 to 1976 and was recognized as a distinguished alumnus in 1987. Ryan became vice president for external affairs at Rice in August 1990, increasing annual gifts to the university to a three-year average of $32.8 million for the fiscal years 1992–94 from $21.4 million for the fiscal years 1988–90. In 1995, he resigned his post as vice president for external affairs at Rice, owing to differences with President Malcolm Gillis concerning the future course of external affairs. Ryan ended his institutional career as a professor of mathematics, and professor of computational and applied mathematics at Rice.