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Prior to moving to Boston University, he was Professor and Chair of Biomathematical Sciences and Professor of Molecular Biology at the Mount Sinai School of Medicine (1987–1989), Director of the United States Department of Energy's Health and Environmental Research Programs (1985–1987), Section Chief at National Institutes of Health (1975–1985), and Theoretical Division Staff Scientist at Los Alamos National Laboratory (1972–1975).
Originally best known for his collaboration with Barry Simon on an extensive series of widely adopted graduate texts, Methods of Modern Mathematical Physics (four volumes) published from 1972 to 1978, Reed has since worked predominantly in applications of analysis to biology.