He was born in to a Jewish family in New York City, the oldest child of a Leah (Rosenfeld) and Israel Hauptman. He was married to Edith Citrynell since November 10, 1940, with two daughters, Barbara (1947) and Carol (1950).
He was interested in science and mathematics from an early age which he pursued at Townsend Harris High School, graduated from the City College of New York (1937) and obtained an M.A. degree in mathematics from Columbia University in 1939.
After the war he started a collaboration with Jerome Karle at the Naval Research Laboratory in Washington, D.C. and at the same time enrolled in the Ph.D. program at the University of Maryland, College Park. He received his Ph.D. from the University of Maryland in 1955 in physics, which is part of the University of Maryland College of Computer, Mathematical, and Natural Sciences. This combination of mathematics and physical chemistry expertise enabled them to tackle head-on the phase problem of X-ray crystallography. His work on this problem was criticized because, at the time, the problem was believed unsolvable.
By 1955 he had received his Ph.D. in mathematics, and they had laid the foundations of the direct methods in X-ray crystallography. Their 1953 monograph, "Solution of the Phase Problem I. The Centrosymmetric Crystal", contained the main ideas, the most important of which was the introduction of probabilistic methods through a development of the Sayre equation.
In 1970 he joined the crystallographic group of the
Medical Foundation of Buffalo of which he was Research Director in 1972. During the early years of this period he formulated the neighborhood principle and extension concept. These theories were further developed during the following decades.
In 2003, as an atheist and secular humanist, he was one of 22 Nobel laureates who signed the Humanist Manifesto.