G. H. Hardy

Godfrey Harold Hardy (7 February 1877 – 1 December 1947) was an English mathematician, known for his achievements in number theory and mathematical analysis. In biology, he is known for the Hardy–Weinberg principle, a basic principle of population genetics.

Hardy is famed for his 1940 essay A Mathematician's Apology, often considered one of the best insights into the mind of a working mathematician written for the layperson. The 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."

thumb|right|Charles F. Wilson, [[Srinivasa Ramanujan (centre), G. H. Hardy (extreme right), and other scientists at Trinity College at the University of Cambridge, ]]

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".

Biography

G. H. Hardy was born on 7 February 1877, in Cranleigh, Surrey, England, into a teaching family. His father was Bursar and Art Master at Cranleigh School; his mother had been a senior mistress at Lincoln Training College for teachers. Both of his parents were mathematically inclined, though neither had a university education. He and his sister Gertrude "Gertie" Emily Hardy (1878–1963) were brought up by their educationally enlightened parents in a typical Victorian nursery attended by a nurse. At an early age, he argued with his nurse about the existence of Santa Claus and the efficacy of prayer. He read aloud to his sister books such as Don Quixote, Gulliver's Travels, and Robinson Crusoe.

After schooling at Cranleigh, Hardy was awarded a scholarship to Winchester College for his mathematical work. In 1896, he entered Trinity College, Cambridge. He was first tutored under Robert Rumsey Webb, but found it unsatisfying, and briefly considered switching to history. He then 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". After only two years of preparation under his coach, Robert Alfred Herman, Hardy was fourth in the Mathematics Tripos examination. 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. While at university, Hardy joined the Cambridge Apostles, an elite, intellectual secret society.

Hardy cited as his most important influence his independent study of Cours d'analyse de l'École polytechnique, through which he became acquainted with the more precise mathematics tradition in continental Europe. In 1900 he passed part II of the Tripos, and in the same year he was elected to a Prize Fellowship at Trinity College. In 1903 he earned his M.A., which was the highest academic degree at English universities at that time. When his Prize Fellowship expired in 1906 he was appointed to the Trinity staff as a lecturer in mathematics, where teaching six hours per week left him time for research. Hardy read the letter in the morning, suspected it was a crank or a prank, but thought it over and realized in the evening that it was likely genuine because "great mathematicians are commoner than thieves or humbugs of such incredible skill". He then invited Ramanujan to Cambridge and began "the one romantic incident in my life".

In the aftermath of the Bertrand Russell affair during World War I, in 1919 he left Cambridge to take the Savilian Chair of Geometry (and thus become a Fellow of New College) at Oxford. Hardy spent the academic year 1928–1929 at Princeton University in an academic exchange with Oswald Veblen, who spent the year at Oxford. Hardy left Oxford and returned to Cambridge in 1931, becoming again a fellow of Trinity College and holding the Sadleirian Professorship until 1942.

In 1939, he suffered a coronary thrombosis, which prevented him from playing tennis, squash, etc. He also lost his creative powers in mathematics. He was constantly bored and distracted himself by writing a privately circulated memoir about the Bertrand Russell affair. In the early summer of 1947, he attempted suicide by barbiturate overdose. After that, he resolved to simply wait for death. He died suddenly one early morning while listening to his sister read out from a book of the history of Cambridge University cricket.

In November 1919, Hardy wrote to Bertrand Russell about his work with 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 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.

Hardy was elected an international honorary member of the American Academy of Arts and Sciences in 1921, an international member of the United States National Academy of Sciences in 1927, and an international member of the American Philosophical Society in 1939.

Hardy's collected papers have been published in seven volumes by Oxford University Press.

Pure mathematics

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:

However, aside from formulating the Hardy–Weinberg principle in population genetics, his famous work on integer partitions with his collaborator 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. Though Hardy wanted his maths to be "pure" and devoid of any application, much of his work has found applications in other branches of science.

Moreover, Hardy deliberately pointed out in his Apology that mathematicians generally do not "glory in the uselessness of their work", but rather – because science can be used for evil ends as well as good – "mathematicians may be justified in rejoicing that there is one science at any rate, and that their own, whose very remoteness from ordinary human activities should keep it gentle and clean." Hardy also rejected as a "delusion" the belief that the difference between pure and applied mathematics had anything to do with their utility. Hardy regards as "pure" the kinds of mathematics that are independent of the physical world, but also considers some "applied" mathematicians, such as the physicists Maxwell and Einstein, to be among the "real" mathematicians, whose work "has permanent aesthetic value" and "is eternal because the best of it may, like the best literature, continue to cause intense emotional satisfaction to thousands of people after thousands of years." Although he admitted that what he called "real" mathematics may someday become useful, he asserted that, at the time in which the Apology was written, only the "dull and elementary parts" of either pure or applied mathematics could "work for good or ill".

Socially, Hardy was associated with the Bloomsbury Group and the Cambridge Apostles; G. E. Moore, Bertrand Russell and J. M. Keynes were friends. Apart from close friendships, he had a few platonic relationships with young men who shared his sensibilities, and often his love of cricket. He liked to speak of the best class of mathematical research as "the Hobbs class", and later, after Bradman appeared as an even greater batsman, "the Bradman class". He admired America and the Soviet Union roughly equally. He found both sides of the Second World War objectionable.</blockquote>

Paul Hoffman writes that "His concerns were wide-ranging, as evidenced by six New Year's resolutions he set in a postcard to a friend: <blockquote> prove the Riemann hypothesis; (2) make 211 not out in the fourth innings of the last Test Match at the Oval; (3) find an argument for the nonexistence of God which shall convince the general public; (4) be the first man at the top of Mount Everest; (5) be proclaimed the first president of the U. S. S. R. of Great Britain and Germany; and (6) murder Mussolini.</blockquote>

Cultural references

Hardy is a key character, played by Jeremy Irons, in the 2015 film The Man Who Knew Infinity, based on the biography of Ramanujan with the same title. Hardy is a major character in David Leavitt's historical fiction novel The Indian Clerk (2007), which depicts his Cambridge years and his relationship with John Edensor Littlewood and Ramanujan. Hardy is a secondary character in Uncle Petros and Goldbach's Conjecture (1992), a mathematics novel by Apostolos Doxiadis. Hardy is also a character in the 2014 Indian film, Ramanujan, played by Kevin McGowan.

Bibliography

Full text The reprinted Mathematician's Apology with an introduction by C.P. Snow was recommended by Marcus du Sautoy in the BBC Radio program A Good Read in 2007.
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Notes

References

External links

Quotations of G. H. Hardy
Hardy's work on Number Theory