Domb possessed both an excellent memory and skill in mathematics. At the age of 17 he won a scholarship to Pembroke College, Cambridge. He graduated with a degree in mathematics in 1941. He then joined the Admiralty Signal Establishment in Portsmouth as one of several young scientists working on developing radar systems during World War II. Until that point, radar operators were only able to determine the distance of an approaching object; Domb's group worked out a method for determining the height of an object as well.