Born at Cranleigh, Hardy had his mathematical education at Cambridge University and remained there as a fellow of Trinity College until 1919, when he became Savilian Professor of Geometry at Oxford. From 1931 to 1942 he was back in Cambridge as Sadleirian Professor of Pure Mathematics.

His central field of interest was in analysis and such related areas as convergence and number theory. Hardy classes of complex functions are named for him. For 35 years, starting in 1911, Hardy collaborated with J. E. Littlewood and together they wrote nearly a hundred papers. The principal areas they covered were Diophantine approximations, the theory of numbers, inequalities, series and definite integrals, and the Riemann zeta-function.

Although primarily a pure mathematician Hardy made one lasting contribution to applied mathematics; the Hardy–Weinberg law was discovered independently by Hardy and the physician Wilhelm Weinberg in 1908 and proved to be fundamental to the science of population genetics. It gives a mathematical description of the genetic equilibrium in a large random-mating population and explains the surprising fact that, unless there are outside changing forces, the proportion of dominant to recessive genes tends not to vary from generation to generation. The law offered strong confirmation for the Darwinian theory of natural selection.

Hardy was one of the outstanding British mathematicians of his day, an excellent teacher, and one of the first to introduce modern work on the rigorous presentation of analysis into Britain. His Course of Pure Mathematics (1908) was influential on the teaching of mathematics in British universities. One of his achievements was his discovery of the young Indian mathematician Srinivasa Ramanujan. Partly through Hardy's efforts Trinity College made funds available for Ramanujan to go to Cambridge to pursue his mathematical researches under Hardy.

Hardy was a passionate devotee of cricket and an equally passionate enemy of the Christian religion. During World War I he was a staunch supporter of Bertrand Russell when Trinity College set about depriving Russell of his position on account of his pacifist activities. Hardy wrote a lively autobiographical sketch A Mathematician's Apology (1940).