Black was born on 14 June 1924 in Uddingston, Lanarkshire, the fourth of five sons of a Baptist family which traced its origins to Balquhidder, Perthshire. His father was a mining engineer. He was brought up in Fife, educated at Beath High School, Cowdenbeath, and, at the age of 15, won a scholarship to the University of St Andrews. His family had been too poor to send him to university and he had been persuaded to sit the St Andrews entrance exam by his maths teacher at Beath.