Herbert Aaron Hauptman was born February 14, 1917 in New York, New York. He attended the City College of New York where he earned a Bachelor of Science. He continued his studies at Columbia University (M.A., 1939) and the University of Maryland (Ph.D. Mathematics, 1955). While enrolled at the University of Maryland, Hauptman began a partnership with Jerome Karle, whose background was in physical chemistry, at the U.S. Naval Research Laboratory. This collaboration led to significant work on the phase problem of x-ray crystallography and influenced Hauptman's dissertation, "An N-Dimensional Euclidean Algorithm." Their work in direct methods of x-ray crystallography ultimately led them to be named co-recipients of the 1985 Nobel Prize in Chemistry. Hauptman is the only mathematician to be awarded the Nobel Prize in Chemistry.

Herbert Hauptman joined the crystallographic group of the Medical Foundation of Buffalo in 1970. He became research director in 1972, and later President, where he continued work on the phase problem. Hauptman's work on direct methods is used to solve complicated molecular structures of crystallized materials and resulted in the development of new and more effective drugs. The Medical Foundation of Buffalo was renamed the Hauptman-Woodward Medical Research Institute in 1994 to honor Hauptman and Helen Woodward-Rivas, a benefactor of the institute.

Hauptman took a position as Research Professor of Biophysical Sciences at the University at Buffalo in 1970. The University and the Hauptman-Woodward Institute reached a significant partnership in 2001 that resulted in the formation of the UB Department of Structural Biology. Hauptman was also a faculty member in the departments of Biophysics and Computer Science.

Herbert Hauptman remained active with research, teaching, speaking, and writing until his death in 2011.