Herman Heine Goldstine (September 13, 1913 – June 16, 2004) was a mathematician and computer scientist, who worked as the director of the IAS machine at the Institute for Advanced Study and helped to develop ENIAC, the first of the modern electronic digital computers. He subsequently worked for many years at IBM as an IBM Fellow, the company's most prestigious technical position.

Goldstine was born in Chicago in 1913 to Jewish parents. He attended the University of Chicago, where he joined the Phi Beta Kappa fraternity, and graduated with a degree in Mathematics in 1933, a master's degree in 1934, and a PhD in 1936. For three years he was a research assistant under Gilbert Ames Bliss, an authority on the mathematical theory of external ballistics.

In 1939 Goldstine began a teaching career at the University of Michigan, until the United States' entry into World War II, when he joined the U.S. Army.

As a result of the United States' entering World War II, Goldstine left the University of Michigan where he was a professor in July 1942 to enlist in the Army. He was commissioned a lieutenant and worked as an ordnance mathematician calculating firing tables at the Ballistic Research Laboratory (BRL) at Aberdeen Proving Ground, Maryland. The firing tables were used in battle to find the appropriate elevation and azimuth for aiming artillery, which had a range of several miles.

The firing table calculations were accomplished by about one hundred women operating mechanical calculators. Each combination of gun, round and geographical region required a unique set of firing tables. It took about 750 calculations to compute a single trajectory and each table had about 3,000 trajectories. It took a human computer at least 7 hours to calculate one trajectory. To increase production, BRL enlisted the computing facilities of the Moore School of Electrical Engineering at the University of Pennsylvania and Goldstine was the liaison between BRL and the university.

While making some adjustments to the Moore School's mechanical differential analyzer, engineer Joseph Chapline suggested Goldstine visit John Mauchly, a physics instructor at the Moore School, who had distributed a memorandum proposing that the calculations could be done thousands of times faster with an electronic computer using vacuum tubes. Mauchly wrote a proposal and in June 1943 he and Goldstine secured funding from the Army for the project. The ENIAC was built in 30 months with 200,000 man hours. The ENIAC was huge, occupying a 30- by 60-foot room and weighing 30 tons with 18,000 vacuum tubes. The device could only store 20 numbers and took days to program. It was completed in late 1945 as World War II was coming to an end.

In spite of disappointment that ENIAC had not contributed to the war effort, interest remained strong in the Army to develop an electronic computer. Prior even to the ENIAC's completion, the Army procured a second contract from the Moore School to build a successor machine known as the EDVAC. Goldstine, Mauchly, J. Presper Eckert and Arthur Burks began to study the development of the new machine in the hopes of correcting the deficiencies of the ENIAC.

In the summer of 1944 Goldstine had a chance encounter with the prominent mathematician John von Neumann on a railway platform in Aberdeen, Maryland, and Goldstine described his project at the University of Pennsylvania. Unbeknownst to Goldstine, von Neumann was then working on the Manhattan Project, which was aiming to build the first atomic bomb. The calculations needed for this project were also daunting.