# G. H. Hardy

Professor **Godfrey Harold Hardy** FRS (February 7, 1877 – December 1, 1947) was a prominent British mathematician, known for his achievements in number theory and mathematical analysis. He was Harold to a few close friends, and otherwise 'G. H.'.

Non-mathematicians usually know him for *A Mathematician's Apology*, his essay from 1940 on the aesthetics of mathematics (ISBN 0521427061), which is often considered the layman's best insight into the mind of a working mathematician.

His relationship as mentor from 1914 on 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 Erdős, 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."

## Contents

## Life

After his schooling at Winchester, Hardy entered Trinity College, Cambridge in 1896 after standing 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 being a means to an end. While at university, Hardy joined the Cambridge Apostles, an elite, intellectual secret society.

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.

## Work

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 led (along with much else) 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 also. 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 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.

## Attitudes

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.

## See also

*A Course of Pure Mathematics**A Mathematician's Apology*- Hardy space
- Pisot-Vijayaraghavan number
- Hardy notation

## Books

- Hardy G.H. (1940)
*A Mathematician's Apology*Cambridge University Press: London. - Hardy G.H. (1940)
*Ramanujan*Cambridge University Press: London. - Hardy G.H. and E.M. Wright (1938)
*An Introduction to the Theory of Numbers*(current edition ISBN 0198531710) - Hardy G.H. (1908)
*A Course of Pure Mathematics*