Gluckstern received a B.S. in electrical engineering at the City College of New York in 1944. In 1948, he received his Ph.D. in physics at the Massachusetts Institute of Technology.

Prior to being named chancellor in 1975, Gluckstern was the vice chancellor for academic affairs and provost at the University of Massachusetts, Amherst, where he had been a professor since 1964. In his seven-year tenure as chancellor at the University of Maryland, Gluckstern worked to upgrade the academic quality of the campus by raising entrance standards. He also established scholarshiip programs that served as the models elsewhere in the state, including the Banneker minority scholarship. He resigned in 1982 because of a strong desire to return to full-time teaching and research as a physicist.

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