Hall was born in Hampstead, London, England, in 1904 and received the major portion of his education at King's College in Cambridge. In 1932 Hall achieved his greatest recognition for an extraordinary paper he published on the theory of groups of prime power order. It has withstood the test of time and is still one of the basic sources of modern group theory. Hall was honored several times in his native country—election to the Royal Society in 1942, then earning its Sylvester Medal in 1961. Also, because of his innovative work and researches in algebra, he was elected President of the London Mathematical Society for two years and was honored by receiving its De Morgan Medal in 1965.