G. H. Hardy

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Lore & Background

Hardy was born on 7 February 1877 in Cranleigh, Surrey, England, into a teaching family. At age two, he wrote numbers up to millions, and when taken to church he amused himself by factorising the numbers of the hymns. After schooling at Cranleigh, he was awarded a scholarship to Winchester College for his mathematical work. In 1896, he entered Trinity College, Cambridge. He was tutored by Augustus Love, who recommended that he read Camille Jordan's Cours d'analyse, which taught him for the first time "what mathematics really meant." While at university, Hardy joined the Cambridge Apostles, an elite, intellectual secret society. Years later, he sought to abolish the Tripos system, as he felt that it was becoming more an end in itself than a means to an end. Starting in 1914, Hardy was the mentor of the Indian mathematician Srinivasa Ramanujan, a relationship that has become celebrated. Hardy almost immediately recognised Ramanujan's extraordinary albeit untutored brilliance, and Hardy and Ramanujan became close collaborators. When asked by a young Paul Erdős what his greatest contribution to mathematics was, Hardy unhesitatingly replied that it was the discovery of Ramanujan. He remarked that on a scale of mathematical ability, his ability would be 25, Littlewood would be 30, Hilbert would be 80, and Ramanujan would be 100. In a lecture on Ramanujan, Hardy said that "my association with him is the one romantic incident in my life."

From 1911, he collaborated with John Edensor Littlewood in extensive work in mathematical analysis and analytic number theory, leading to the Hardy–Littlewood circle method and quantitative progress on Waring's problem. Hardy is also known for formulating the Hardy–Weinberg principle, a basic principle of population genetics, independently from Wilhelm Weinberg in 1908. He played cricket with the geneticist Reginald Punnett, who introduced the problem to him in purely mathematical terms. Hardy, who had no interest in genetics and described the mathematical argument as "very simple," may never have realised how important the result became.

Reader's Guide

Hardy is credited with reforming British mathematics by bringing rigour into it, which was previously a characteristic of French, Swiss and German mathematics. He aggressively promoted his conception of pure mathematics, in particular against the hydrodynamics that was an important part of Cambridge mathematics. Hardy's collaboration with Littlewood is among the most successful and famous collaborations in mathematical history. In a 1947 lecture, the Danish mathematician Harald Bohr reported a colleague as saying, "Nowadays, there are only three really great English mathematicians: Hardy, Littlewood, and Hardy–Littlewood." Hardy's famous work on integer partitions with Ramanujan, known as the Hardy–Ramanujan asymptotic formula, has been widely applied in physics to find quantum partition functions of atomic nuclei (first used by Niels Bohr) and to derive thermodynamic functions of non-interacting Bose–Einstein systems. His work in number theory is also important in cryptography. Hardy's 1940 essay A Mathematician's Apology is often considered one of the best insights into the mind of a working mathematician written for the layperson; novelist Graham Greene ranked it with the notebooks of Henry James as "the best account of what it was like to be a creative artist." Hardy preferred his work to be considered pure mathematics, perhaps because of his detestation of war and the military uses to which mathematics had been applied. He stated, "I have never done anything 'useful'. No discovery of mine has made, or is likely to make, directly or indirectly, for good or ill, the least difference to the amenity of the world." Despite this, much of his work has found applications in other branches of science.

Did You Know?

• At age two, Hardy wrote numbers up to millions and amused himself in church by factorising hymn numbers.
• Hardy remarked that on a scale of mathematical ability, his own ability would be 25, Littlewood 30, Hilbert 80, and Ramanujan 100.
• Hardy formulated the Hardy–Weinberg principle in 1908 after the geneticist Reginald Punnett introduced the problem to him during a game of cricket.
• In 1939, Hardy suffered a coronary thrombosis that prevented him from playing tennis and squash, and he lost his creative powers in mathematics.
• Hardy attempted suicide by barbiturate overdose in the early summer of 1947, and died suddenly while listening to his sister read from a book on the history of Cambridge University cricket.

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