G. H. Hardy
G. H. Hardy | |
---|---|
Awards | Fellow of the Royal Society[1] Smith's Prize (1901) Royal Medal (1920) De Morgan Medal (1929) Chauvenet Prize (1932) Sylvester Medal (1940) Copley Medal (1947) |
Scientific career | |
Fields | Mathematics |
Institutions | University of Cambridge University of Oxford |
Academic advisors | A. E. H. Love E. T. Whittaker |
Doctoral students | Mary Cartwright I. J. Good Edward Linfoot Cyril Offord Harry Pitt Richard Rado Robert Rankin Donald Spencer Tirukkannapuram Vijayaraghavan E. M. Wright |
Other notable students | Sydney Chapman Edward Titchmarsh Ethel Newbold |
Godfrey Harold Hardy FRS[1] (7 February 1877 – 1 December 1947)[2] was an English mathematician, known for his achievements in number theory and mathematical analysis.[3][4] In biology, he is known for the Hardy–Weinberg principle, a basic principle of population genetics.
G. H. Hardy is usually known by those outside the field of mathematics 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.
Starting in 1914, Hardy was the mentor of the Indian mathematician Srinivasa Ramanujan, a relationship that has become celebrated.[5] Hardy almost immediately recognised 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.[6] In a lecture on Ramanujan, Hardy said that "my association with him is the one romantic incident in my life".[7]: 2
Early life and career
G. H. Hardy was born on 7 February 1877, in Cranleigh, Surrey, England, into a teaching family.[8] 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.[1]: 447
Hardy's own natural affinity for mathematics was perceptible at an early age. When just two years old, he wrote numbers up to millions, and when taken to church he amused himself by
After schooling at
Hardy cited as his most important influence his independent study of
He was on the governing body of Abingdon School from 1922 to 1935.[16]
Work
Hardy is credited with reforming British mathematics by bringing
From 1911, he collaborated with
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.[19]: 9 Hardy, who had no interest in genetics and described the mathematical argument as "very simple", may never have realised how important the result became.[20]: 117
Hardy was elected an international honorary member of the American Academy of Arts and Sciences in 1921,[21] an international member of the United States National Academy of Sciences in 1927,[22] and an international member of the American Philosophical Society in 1939.[23]
Hardy's collected papers have been published in seven volumes by Oxford University Press.[24]
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:
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.[25]
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. 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.[26]
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."[27]: 33 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."[27]: 39
Personality
Socially, Hardy was associated with the
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.[17]
Apart from close friendships, he had a few platonic relationships with young men who shared his sensibilities, and often his love of cricket.[28] A mutual interest in cricket led him to befriend the young C. P. Snow.[29]: 10–12 [30] Hardy was a lifelong bachelor and in his final years he was cared for by his sister.
Hardy was extremely shy as a child, and was socially awkward, cold and eccentric throughout his life. During his school years he was top of his class in most subjects, and won many prizes and awards but hated having to receive them in front of the entire school. He was uncomfortable being introduced to new people, and could not bear to look at his own reflection in a mirror. It is said that, when staying in hotels, he would cover all the mirrors with towels.[29]
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:
(1) 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.[31]
Cultural references
Hardy is a key character, played by
Bibliography
- Hardy, G. H. (2012) [1st pub. 1940, with foreword 1967]. ISBN 9781107295599. 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.[35]
- Hardy, G. H. (1999) [1st pub. Cambridge University Press: 1940]. Ramanujan: Twelve Lectures on Subjects Suggested by his Life and Work. Providence, RI: AMS Chelsea. ISBN 978-0-8218-2023-0.
- Hardy, G. H.; ISBN 978-0-19-921985-8.
- Hardy, G. H. (2008) [1st ed. 1908]. ISBN 978-0-521-72055-7.
- Hardy, G. H. (2013) [1st ed.
- Hardy, G. H. (1966–1979). Collected papers of G. H. Hardy; including joint papers with J. E. Littlewood and others. Edited by a committee appointed by the OCLC 823424.
- Hardy, G. H.; ISBN 978-0-521-35880-4.
- Hardy, G. H. (1970) [1st pub. 1942]. Bertrand Russell and Trinity. With a foreword by ISBN 978-0-521-11392-2.
See also
- Critical line theorem
- Campbell–Hardy theorem
- Hardy hierarchy
- Hardy notation
- Hardy space
- Hardy–Hille formula
- Hardy–Littlewood definition
- Hardy–Littlewood inequality
- Hardy–Littlewood maximal function
- Hardy–Littlewood tauberian theorem
- Hardy–Littlewood zeta-function conjectures
- Hardy–Ramanujan Journal
- Hardy–Ramanujan number
- Hardy–Ramanujan theorem
- Hardy's inequality
- Hardy's theorem
- Hardy field
- Hardy Z function
- Pisot–Vijayaraghavan number
- Ulam spiral
Notes
References
- ^ S2CID 162237076.
- ^ GRO Register of Deaths: DEC 1947 4a 204 Cambridge – Godfrey H. Hardy, aged 70
- ^ a b O'Connor, John J.; Robertson, Edmund F., "G. H. Hardy", MacTutor History of Mathematics Archive, University of St Andrews
- ^ G. H. Hardy at the Mathematics Genealogy Project
- ^ THE MAN WHO KNEW INFINITY: A Life of the Genius Ramanujan Archived 5 December 2017 at the Wayback Machine. Retrieved 2 December 2010.
- ISBN 1-85702-829-5
- ISBN 978-0-8218-2023-0.
- ^ GRO Register of Births: MAR 1877 2a 147 Hambledon – Godfrey Harold Hardy
- ISBN 0-684-19259-4.
- ^ "Hardy, Godfrey Harold (HRDY896GH)". A Cambridge Alumni Database. University of Cambridge.
- ^ In the 1898 Tripos competition, R. W. H. T. Hudson was 1st, J. F. Cameron was 2nd, and James Jeans was 3rd. "What became of the Senior Wranglers?" by D. O. Forfar
- S2CID 146374699.
- ^ "G H Hardy's Oxford Years" (PDF). Oxford University Mathematical Institute. Archived (PDF) from the original on 9 October 2022. Retrieved 16 April 2016.
- ^ Josiah Willard Gibbs Lectures. American Mathematical Society
- MR 1561815.
- ^ "School Notes" (PDF). The Abingdonian. Archived (PDF) from the original on 9 October 2022.
- ^ a b "G.H. Hardy". Famous Mathematicians: Biography and Contributions of Great Mathematicians through History. 29 March 2022. Retrieved 29 March 2022.
- OCLC 3172542.
- .
- ^ Cain, A. J. (2019). "Legacy of the Apology". An Annotated Mathematician's Apology. By Hardy, G. H.
- ^ "Godfrey Harold Hardy". American Academy of Arts & Sciences. 9 February 2023. Retrieved 8 May 2023.
- ^ "Godfrey Hardy". www.nasonline.org. Retrieved 8 May 2023.
- ^ "APS Member History". search.amphilsoc.org. Retrieved 8 May 2023.
- ISBN 0-19-853347-0.
- .
- S2CID 28363771.
- ^ a b Hardy, G. H. A Mathematician's Apology, 1992 [1940]
- ^ a b Khan, Haider Riaz (18 September 2014). "GH Hardy, the mathematician who loved cricket". Cricket Blogs. ESPNcricinfo. Retrieved 19 September 2014.
- ^ a b Snow, C. P. (1967). Foreword. A Mathematician's Apology. By Hardy, G. H. Cambridge University Press.
- Penguin books, 1969, pp 25–56.
- ^ Hoffman, Paul (1998). The Man Who Loved Only Numbers. p. 81.
- ^ George Andrews (February 2016). "Film Review: 'The Man Who Knew Infinity'" (PDF). Notices of the American Mathematical Society. Archived (PDF) from the original on 9 October 2022.
- ^ Taylor, D. J. (26 January 2008). "Adding up to a life. Review of The Indian Clerk by David Leavitt". The Guardian. Retrieved 21 April 2016.
- ^ Devlin, Keith (1 April 2000). "Review: Uncle Petros and Goldbach's Conjecture by Apostolos Doxiadis". Mathematical Association of America. Retrieved 21 April 2016.
- ^ "A Good Read - Marcus du Sautoy and David Dabydeen - BBC Sounds". www.bbc.co.uk.
Further reading
- Kanigel, Robert (1991). The Man Who Knew Infinity: A Life of the Genius Ramanujan. New York: Washington Square Press. ISBN 0-671-75061-5.
- ISBN 978-1-107-29559-9.
- Albers, D.J.; Alexanderson, G.L.; Dunham, W., eds. (2015). The G.H. Hardy Reader. Cambridge: Cambridge University Press. ISBN 978-1-10713-555-0.
External links
- Works by G. H. Hardy at Project Gutenberg
- Works by or about G. H. Hardy at Internet Archive
- Works by G. H. Hardy at LibriVox (public domain audiobooks)
- O'Connor, John J.; Robertson, Edmund F., "G. H. Hardy", MacTutor History of Mathematics Archive, University of St Andrews
- Quotations of G. H. Hardy
- Hardy's work on Number Theory
- ScienceWorld.