John Charles Burkill, born on 1 February 1900, was the only child of Hugh Roberson Burkill (1867–1951) and Bertha (née Bourne, 1866–1937). His father came from a family which had farmed in Lincolnshire for generations, whereas his mother came from a background of prosperous farming and building. On neither side was there a strong academic tradition, but Charles was soon to show evidence of intellectual distinction by winning a scholarship to St Paul's school at the age of 14. There he profited fully from the excellent teaching that the school offered and which was reflected not only by his mathematical prowess, which led to a scholarship to Trinity College, Cambridge, in 1918, but also in his ability in classical studies in which he maintained a lifelong interest. He was also a formidable chess player, and had a mischievous sense of humour which he retained, albeit in a more restrained mode, in later life. A striking example of his grasp of the essence of a practical joke is recorded in the story of how, as a boy on a visit to a house-proud aunt, he saw the comic potential of a trail of corn from the chicken run through the front door and upstairs to the bedrooms.