Traum became the dean of the computer science department at Carnegie Mellon University in Pittsburgh in 1971 and had built the faculty to 50 people from a handful by 1979, when he left for Columbia, where he had been recruited to become the founding dean of the new computer science department. Joseph attended the Bronx High School of Science and earned an undergraduate degree in math and physics from City College of New York. He enrolled at Columbia in 1954, intending to become a theoretical physicist. But a friend urged him to visit a building with a computer on 116th Street, near the Columbia campus, then the home of the IBM Watson Labs. Columbia did have a “committee on applied mathematics,” with faculty members from several departments. The committee allowed Professor Traub to do his Ph.D. thesis on computing calculations in quantum mechanics, which allowed him to run programs for hours on an IBM 650 computer. Professor Traub’s first marriage, to Susanne Traub, ended in divorce. In addition to Pamela McCorduck, he is survived by two daughters from his first marriage, Claudia Renee Traub and Hillary Ann Spector, and four grandchildren.