Non-mathematicians usually know him for A Mathematician's Apology, his essay from 1940 on the aesthetics of mathematics. The apology is often considered one of the layman's best insights into the mind of a working mathematician.
Read Godfrey Hardy's i>A Mathematician's Apology, free from the University of Alberta, Canada.
His relationship as mentor, from 1914 onwards, of the Indian mathematician Srinivasa Ramanujan has become celebrated. Hardy almost immediately recognized Ramanujan's extraordinary albeit untutored brilliance, and Hardy and Ramanujan became close collaborators. In an interview by Paul Erd?s, when Hardy was asked what his greatest contribution to mathematics was, Hardy unhesitatingly replied that it was the discovery of Ramanujan. He called their collaboration "the one romantic incident in my life."
G.H. Hardy was born in 1877 into a teaching family. His father was Bursar and Art Master at a minor private school called Cranleigh; his mother had been a senior mistress at Lincoln Training College for teachers. Both parents were mathematically inclined.
Hardy's own natural affinity for mathematics was perceptible at a young age. When just two years old, he wrote numbers up to millions, and when taken to church he amused himself by factorizing the numbers of the hymns.
After schooling at Cranleigh, Hardy he was awarded a scholarship to Winchester College (based on some mathematical work he had done). He then entered Trinity College, Cambridge. In 1896 he was fourth in the Tripos examination. Years later, Hardy sought to abolish the Tripos system, as he felt that it was becoming more an end in itself than a means to an end. While at university, Hardy joined the Cambridge Apostles, an elite, intellectual secret society.
Hardy was very self-conscious and felt extremely uncomfortable in front of large groups of people. Later in life he was known not to allow his being picture taken.
Hardy was Sadleirian Professor at Cambridge from 1931 to 1942; he had left Cambridge to take the Savilian Chair of Geometry at Oxford in the aftermath of the Bertrand Russell affair during World War I.
Hardy is credited with reforming British mathematics by bringing rigour into it, which was previously a characteristic of French, Swiss and German mathematics. British mathematicians had remained largely in the tradition of applied mathematics, in thrall to the reputation of Isaac Newton (see Cambridge Mathematical Tripos). Hardy was more in tune with the cours d'analyse methods dominant in France, and aggressively promoted his conception of pure mathematics, in particular against the hydrodynamics which was an important part of Cambridge mathematics.
From 1911 he collaborated with J. E. Littlewood, in extensive work in mathematical analysis and analytic number theory. This (along with much else) led to quantitative progress on the Waring problem, as part of the Hardy-Littlewood circle method, as it became known. In prime number theory, they proved results and some notable conditional results. This was a major factor in the development of number theory as a system of conjectures; examples are the first and second Hardy-Littlewood conjectures. 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's joke that "Nowadays, there are only three really great English mathematicians: Hardy, Littlewood and Hardy-Littlewood."
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, and Hardy thus became the somewhat unwitting founder of a branch of applied mathematics.
His collected papers have been published.
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 made several statements similar to that in his Apology:
"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."
However, aside from formulating the Hardy-Weinberg law in population genetics, some of his work in number theory are reported to have found practical application in cryptography.
Socially he was associated with the Bloomsbury group and the Cambridge Apostles; G. E. Moore, Bertrand Russell and J. M. Keynes were friends. He was an avid cricket fan.
He was at times politically involved, if not an activist. He took part in the Union of Democratic Control during World War I, and For Intellectual Liberty in the late 1930s.
He was an atheist, and, according to those who knew him best, a non-practising homosexual (Littlewood's phrase). Hardy never married, and in his final years he was cared for by his sister.
In his obituary, a former student reports: "He was an extremely kind-hearted man, who could not bear any of his pupils to fail in their researches." — E. C. Titchmarsh (1950)