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 called "Harold" by 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. The apology is often considered one of the layman's best insights into the mind of a working mathematician.
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 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."
After his schooling at
Winchester College, 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 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.
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.
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."[
1]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." â€"
E. C. Titchmarsh (1950)
*
It is not worth an intelligent man's time to be in the majority. By definition, there are already enough people to do that.*
A mathematician, like a painter or a poet, is a maker of patterns. If his patterns are more permanent than theirs, it is because they are made with ideas.*
Hardy notation*
Hardy space*
Pisot-Vijayaraghavan number* Hardy G.H. (1940)
A Mathematician's Apology Cambridge University Press: London. ISBN 0521427061.
* 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*
*
Quotations of G. H. Hardy*Full text of
A Mathematician's Apology, in the
public domain in
Canada, courtesy of the University of Alberta Mathematical Science Society.
*
Hardy's work on Number Theory
