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Probstein was born in New York City. He graduated from Stuyvesant High School and went on to study engineering at New York City’s night school, while at the same time working during the day for the world-renowned mathematician Richard Courant.
In 1952 he received the first Ph.D. from the Princeton University Department of Aeronautical Engineering.
In 1954 he accepted a joint appointment at Brown University in the Division of Applied Mathematics and Division of Engineering and was given tenure two years later.
He accepted a position as a Professor of Mechanical Engineering at MIT in 1962 and remained there becoming Ford Professor of Engineering until his retirement in 1996 when he became Emeritus.