Education
Conway earned his Bachelor of Science from Loyola University and Doctor of Philosophy from Louisiana State University under the direction of Heron Collins in 1965, with a dissertation on The Strict Topology and Compactness in the Space of Measures.
Career
He is currently a professor emeritus at the George Washington University. His specialty is functional analysis, particularly bounded operators on a Hilbert space. He served on the faculty there from 1965 to 1990, when he became head of the mathematics department at University of Tennessee.
He is the author of a two-volume series on Functions of One Complex Variable (Springer-Verlag), which is a standard graduate text.
He is the father of John Bligh Conway II, who currently teaches history at the Anglo American School of Street St. Petersburg (AASSP), Russia.