Profesor Doob is well known for his work in probability theory and potential theory. He was a founding member of the Center for Advanced Study, appointed in 1959.
He was a member of the National Academy of Sciences and the American Academy of Arts and Sciences and a foreign associate of the Académie des Sciences. He is a past president of the Institute of Mathematical Statistics and of the American Mathematical Society. In 1979 he was awarded the National Medal of Science; and in 1981, an honorary doctor of science degree from the University of Illinois.