Editing G. H. Hardy

{{Short description|British mathematician (1877–1947)}}
{{Use dmy dates|date=November 2020}}
{{Use British English|date=November 2020}}
{{Infobox scientist
| name              = G. H. Hardy
| honorific_suffix  = {{postnominals|country=GBR|FRS|size=100%}}
| image             = Ghhardy@72.jpg
| image width       =
| caption           = Hardy, {{circa|1927}}
| birth_name        = Godfrey Harold Hardy
| birth_date        = {{birth date|df=y|1877|2|7}}
| birth_place       = [[Cranleigh]], Surrey, England
| death_date        = {{death date and age|df=y|1947|12|1|1877|2|7}}
| death_place       = [[Cambridge]], Cambridgeshire, England
| nationality       = [[British People|British]]
| field             = [[Mathematics]]
| work_institutions = [[University of Cambridge]]<br />[[University of Oxford]]
| alma_mater        = [[Winchester College]]<br />[[Trinity College, Cambridge]]
| academic_advisors = [[Augustus Edward Hough Love|A.&nbsp;E.&nbsp;H. Love]]<br />[[E.&nbsp;T. Whittaker]]
| doctoral_students = [[Mary Cartwright]]<br />[[I.&nbsp;J. Good]]<br />[[Edward Linfoot]]<br />[[Cyril Offord]]<br />[[Harry Pitt]]<br />[[Richard Rado]]<br />[[Robert Alexander Rankin|Robert Rankin]]<br />[[Donald C. Spencer|Donald Spencer]]<br />[[Tirukkannapuram Vijayaraghavan]]<br />[[E. M. Wright]]
| notable_students  = [[Sydney Chapman (mathematician)|Sydney Chapman]]<br />[[Edward Charles Titchmarsh|Edward Titchmarsh]]<br />[[Ethel Newbold]]
| known_for         = [[Hardy–Weinberg principle]]<br />[[Partition function (number theory)#Approximation formulas|Hardy–Ramanujan asymptotic formula]]<br /> [[Critical line theorem]]<br /> [[Hardy–Littlewood tauberian theorem]]<br />[[Hardy space]]<br />[[Hardy notation]]<br />[[Hardy–Littlewood inequality]]<br />[[Hardy's inequality]]<br />[[Hardy's theorem]]<br />[[Hardy–Littlewood circle method]]<br />[[Hardy field]]<br />[[Hardy–Littlewood zeta function conjectures]]
| awards            = [[Smith's Prize]] (1901)<br />[[Royal Medal]] (1920)<br />[[De Morgan Medal]] (1929)<br />[[Chauvenet Prize]] (1932)<br />[[Sylvester Medal]] (1940)<br />[[Copley Medal]] (1947) 
}}
'''Godfrey Harold Hardy''' {{post-nominals|country=GBR|FRS}}<ref name="frs"/> (7 February 1877 – 1 December 1947)<ref>GRO Register of Deaths: DEC 1947 4a 204 Cambridge – Godfrey H. Hardy, aged 70</ref> was an English [[mathematician]], known for his achievements in [[number theory]] and [[mathematical analysis]].<ref name="mactutor">{{MacTutor Biography|id=Hardy}}</ref><ref name="mathgene">{{MathGenealogy |id=17806}}</ref> 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.

[[File:RamanujanCambridge.jpg|thumb|right|Charles F. Wilson, [[Srinivasa Ramanujan]] (centre), G. H. Hardy (extreme right), and other scientists at Trinity College at the University of Cambridge, {{Circa|1910s}} ]]

Starting in 1914, Hardy was the mentor of the Indian mathematician [[Srinivasa Ramanujan]], a relationship that has become celebrated.<ref name="cola">[http://robertkanigel.com/_i__b_the_man_who_knew_infinity__b___a_life_of_the_genius_ramanujan__i__58016.htm THE MAN WHO KNEW INFINITY: A Life of the Genius Ramanujan] {{Webarchive|url=https://web.archive.org/web/20171205000101/http://robertkanigel.com/_i__b_the_man_who_knew_infinity__b___a_life_of_the_genius_ramanujan__i__58016.htm |date=5 December 2017 }}. Retrieved 2 December 2010.</ref> Hardy almost immediately recognised Ramanujan's extraordinary albeit untutored brilliance, and Hardy and Ramanujan became close collaborators.<ref>{{Cite book |last1=Littlewood |first1=J.E. |author-link1=John Edensor Littlewood |title=Littlewood's Miscellany |last2=Bollobás |first2=B. |date=1986 |publisher=Cambridge University Press |isbn=978-0-521-33058-9 |edition=Rev. |location=Cambridge [Cambridgeshire]; New York}}</ref> 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.<ref>{{cite journal | title=Ramanujan—An Estimation | journal=[[The Hindu]] | first=Krishnaswami | last=Alladi | date=19 December 1987 | location=Madras, India | issn=0971-751X | mode=cs2}}. Cited in {{cite book | title=The Man Who Loved Only Numbers | url=https://archive.org/details/manwholovedonlyn00hoff_335 | url-access=limited | publisher=Fourth Estate | author-link=Paul Hoffman (science writer) | year=1998 | pages=[https://archive.org/details/manwholovedonlyn00hoff_335/page/n91 82]–83 | isbn=1-85702-829-5 | first=Paul | last=Hoffman | mode=cs2}}</ref> In a lecture on Ramanujan, Hardy said that "my association with him is the one romantic incident in my life".<ref name="hardy-ramanujan">{{cite book |last=Hardy |first=G. H. |title=Ramanujan: Twelve Lectures on Subjects Suggested by his Life and Work |publisher=AMS Chelsea |location=Providence, RI|year=1999 |isbn=978-0-8218-2023-0 | url=https://archive.org/details/in.ernet.dli.2015.212059/}}</ref>{{rp|2}}

==Biography==
G. H. Hardy was born on 7 February 1877, in [[Cranleigh]], Surrey, England, into a teaching family.<ref>GRO Register of Births: MAR 1877 2a 147 Hambledon – Godfrey Harold Hardy</ref> 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]]''.<ref name="frs"/>{{rp|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 [[factorize|factorising]] the numbers of the hymns.<ref>[[Robert Kanigel]], ''[[The Man Who Knew Infinity (book)|The Man Who Knew Infinity]]'', p. 116, Charles Scribner's Sons, New York, 1991. {{isbn|0-684-19259-4}}.</ref>

After schooling at [[Cranleigh School|Cranleigh]], Hardy was awarded a scholarship to [[Winchester College]] for his mathematical work. In 1896, he entered [[Trinity College, Cambridge]].<ref>{{acad|id=HRDY896GH|name=Hardy, Godfrey Harold}}</ref> He was first tutored under [[Robert Rumsey Webb]], but found it unsatisfying, and briefly considered switching to history. He then was tutored by [[Augustus Edward Hough Love|Augustus Love]], who recommended him to 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 [[Cambridge Mathematical Tripos|Mathematics Tripos]] examination.<ref>In the 1898 Tripos competition, [[R. W. H. T. Hudson]] was 1st, [[J. F. Cameron]] was 2nd, and [[James Jeans]] was 3rd. [http://www.clerkmaxwellfoundation.org/WranglersWhatBecame2008_1_24.pdf "What became of the Senior Wranglers?" by D. O. Forfar]</ref> 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.<ref>{{cite journal|last=Grattan-Guinness|first=I.|author-link=Ivor Grattan-Guinness|date=September 2001|doi=10.1098/rsnr.2001.0155|issue=3|journal=Notes and Records of the Royal Society of London|pages=411–424|publisher=The Royal Society|title=The interest of G. H. Hardy, F.R.S., in the philosophy and the history of mathematics|volume=55|s2cid=146374699}}</ref>

Hardy cited as his most important influence his independent study of ''Cours d'analyse de l'École Polytechnique'' by the French mathematician [[Camille Jordan]], 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.<ref name="frs">{{Cite journal | last1=Titchmarsh | first1=E. C. | title=Godfrey Harold Hardy. 1877–1947 | doi=10.1098/rsbm.1949.0007 | journal=Obituary Notices of Fellows of the Royal Society | volume=6 | issue=18 | pages=446–461| year=1949 | s2cid=162237076 | doi-access=free }}</ref>{{rp|448}} 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.<ref name="frs"/>{{rp|448}}

On 16 January 1913, [[Srinivasa Ramanujan|Ramanujan]] wrote to Hardy, who Ramanujan had known from studying ''Orders of Infinity'' (1910).<ref>{{Cite book |last=Hardy |first=G. H. (Godfrey Harold) |url=https://www.gutenberg.org/ebooks/38079 |title=Orders of Infinity: The 'Infinitärcalcül' of Paul Du Bois-Reymond |date=2011-11-21 |language=English}}</ref><ref>{{Cite journal |last1=Berndt |first1=Bruce C. |last2=Rankin |first2=Robert A. |date=August 2000 |title=The Books Studied by Ramanujan in India |url=https://www.tandfonline.com/doi/full/10.1080/00029890.2000.12005244 |journal=The American Mathematical Monthly |language=en |volume=107 |issue=7 |pages=595–601 |doi=10.1080/00029890.2000.12005244 |issn=0002-9890}}</ref> 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".<ref>{{Cite journal |last=Hardy |first=G. H. |date=March 1937 |title=The Indian Mathematician Ramanujan |url=https://www.tandfonline.com/doi/full/10.1080/00029890.1937.11987940 |journal=The American Mathematical Monthly |language=en |volume=44 |issue=3 |pages=137–155 |doi=10.1080/00029890.1937.11987940 |issn=0002-9890}}</ref> He then invited Ramanujan to Cambridge and began "the one romantic incident in my life".<ref name=":1">C. P. Snow, Variety of Men, [[Penguin books]], 1969, pp 25–56.</ref>

In the aftermath of the [[Bertrand Russell#First World War|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, Oxford|New College]]<ref>{{cite web |title=G H Hardy's Oxford Years|url=https://www.maths.ox.ac.uk/system/files/media/Godfrey%20Hardy_0.pdf |archive-url=https://ghostarchive.org/archive/20221009/https://www.maths.ox.ac.uk/system/files/media/Godfrey%20Hardy_0.pdf |archive-date=2022-10-09 |url-status=live |publisher=Oxford University Mathematical Institute |access-date=16 April 2016}}</ref>) at [[Oxford University|Oxford]]. Hardy spent the academic year 1928–1929 at [[Princeton University]] in an academic exchange with [[Oswald Veblen]], who spent the year at Oxford.<ref name="mactutor" /> Hardy gave the [[Josiah Willard Gibbs Lectureship|Josiah Willard Gibbs lecture]] for 1928.<ref>[https://www.ams.org/meetings/lectures/meet-gibbs-lect Josiah Willard Gibbs Lectures]. American Mathematical Society</ref><ref>{{cite journal |author=Hardy, G. H. |title=An introduction to the theory of numbers|journal=[[Bull. Amer. Math. Soc.]] |year=1929 |volume=35 |issue=6 |pages=778–818 |mr=1561815 |doi=10.1090/s0002-9904-1929-04793-1|doi-access=free }}</ref> Hardy left Oxford and returned to Cambridge in 1931, becoming again a fellow of Trinity College and holding the [[Sadleirian Professor of Pure Mathematics|Sadleirian Professorship]] until 1942.<ref name="frs" />{{rp|453}} It is believed that he left Oxford for Cambridge to avoid the compulsory retirement at 65.<ref name=":1" />

He was on the governing body of [[Abingdon School]] from 1922 to 1935.<ref>{{cite web |url=https://www.abingdon.org.uk/uploads/school/files/abingdonian/1924_March_V006_N011.pdf#page=1 |archive-url=https://ghostarchive.org/archive/20221009/https://www.abingdon.org.uk/uploads/school/files/abingdonian/1924_March_V006_N011.pdf#page=1 |archive-date=2022-10-09 |url-status=live|title=School Notes|publisher=The Abingdonian}}</ref>

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.<ref name=":1" />

== Work ==
Hardy is credited with reforming British mathematics by bringing [[Rigour#Mathematical rigour|rigour]] into it, which was previously a characteristic of French, Swiss and German mathematics.<ref name=":0" /> 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]] that was an important part of Cambridge mathematics.{{Citation needed|date=February 2018}}

Hardy preferred to work only 4 hours every day on mathematics, spending the rest of the day talking, playing cricket, and other gentlemanly activities.<ref name=":1" />

From 1911, he collaborated with [[John Edensor Littlewood]], in extensive work in [[mathematical analysis]] and [[analytic number theory]]. This (along with much else) led to quantitative progress on [[Waring's problem]], as part of the [[Hardy–Littlewood circle method]], as it became known. In [[prime number]] theory, they proved results and some notable [[conditional result]]s. This was a major factor in the development of number theory as a system of [[conjecture]]s; examples are the [[first Hardy–Littlewood conjecture|first]] and [[second Hardy–Littlewood conjecture]]s. 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 as saying, "Nowadays, there are only three really great English mathematicians: Hardy, Littlewood, and Hardy–Littlewood."<ref>{{cite book |last=Bohr |first=Harald |author-link=Harald Bohr |title=Collected Mathematical Works |volume=1 |year=1952 |publisher=[[Dansk Matematisk Forening]] |location=Copenhagen |oclc=3172542 |pages=xiii–xxxiv |chapter=Looking Backward |no-pp=true}}</ref>{{Rp|xxvii}}

In November 1919, Hardy wrote to [[Bertrand Russell]] about his work with Littlewood.{{blockquote|"I wish you could find some tactful way of stirring up Littlewood to do a little writing. Heaven knows I am conscious of my huge debt to him ... but in our collaboration he will contribute ideas and ideas only ... all the tedious part has to be done by me [or] it simply won't be done ... I can get absolutely no help from him at all; not even an inquiry as to how I am getting on!" <ref>Unpublished letter in the Bertrand Russell Archives, Box 5.21, William Ready Division of Archives and Research Collections, McMaster University, Hamilton, Ontario, Canada.</ref>}}

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.<ref>{{cite journal |last1=Punnett |first1=R. C. |title=Early Days of Genetics |journal=Heredity |date=1950 |volume=4 |issue=1 |pages=1–10 |doi=10.1038/hdy.1950.1|doi-access=free |bibcode=1950Hered...4....1P }}</ref>{{rp|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.<ref name="hardy-annotated">{{cite book |last=Hardy |first=G. H. |title=An Annotated Mathematician's Apology |year=2019 |url=https://archive.org/details/hardy_annotated/ |contributor-last=Cain |contributor-first=A. J. |contribution=Legacy of the ''Apology''}}</ref>{{rp|117}}

Hardy was elected an international honorary member of the [[American Academy of Arts and Sciences]] in 1921,<ref>{{Cite web |title=Godfrey Harold Hardy |url=https://www.amacad.org/person/godfrey-harold-hardy |access-date=2023-05-08 |website=American Academy of Arts & Sciences |date=9 February 2023 |language=en}}</ref> an international member of the United States [[National Academy of Sciences]] in 1927,<ref>{{Cite web |title=Godfrey Hardy |url=http://www.nasonline.org/member-directory/deceased-members/20001321.html |access-date=2023-05-08 |website=www.nasonline.org}}</ref> and an international member of the [[American Philosophical Society]] in 1939.<ref>{{Cite web |title=APS Member History |url=https://search.amphilsoc.org/memhist/search?creator=Godfrey+H.+Hardy&title=&subject=&subdiv=&mem=&year=&year-max=&dead=&keyword=&smode=advanced |access-date=2023-05-08 |website=search.amphilsoc.org}}</ref>

Hardy's collected papers have been published in seven volumes by [[Oxford University Press]].<ref>{{cite book |last=Hardy |first=Godfrey Harold |date=1979 |title=Collected Papers of G. H. Hardy – Volume 7|url=https://archive.org/details/CollectedPapersOfG.H.Hardy-Volume7 |location=Oxford|publisher=Oxford University Press |isbn=0-19-853347-0}}</ref>

===Pure mathematics===

Hardy preferred his work to be considered ''[[pure mathematics]]'', perhaps because of his [[Pacifism|detestation of war]] and the military uses to which mathematics had been [[applied mathematics|applied]]. He made several statements similar to that in his [[A Mathematician's Apology|''Apology'']]:
{{blockquote|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.<ref>{{cite journal| last=Titchmarsh| first=E.C.|year=1950| title=Godfrey Harold Hardy| url=http://www.numbertheory.org/obituaries/LMS/hardy/page83.html| journal=J. London Math. Soc.| volume=25| issue=2| pages=81–138| doi=10.1112/jlms/s1-25.2.81}}</ref>}}
However, aside from formulating the [[Hardy–Weinberg principle]] in [[population genetics]], his famous work on integer partitions with his collaborator [[Srinivasa Ramanujan|Ramanujan]], known as the [[Partition function (number theory)#Approximation formulas|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 statistics|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.<ref>{{Cite journal |last=Chen |first=John J. |date=2010-08-01 |title=The Hardy-Weinberg principle and its applications in modern population genetics |journal=Frontiers in Biology |language=en |volume=5 |issue=4 |pages=348–353 |doi=10.1007/s11515-010-0580-x |s2cid=28363771 |issn=1674-7992}}</ref>

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."<ref name="Apology">Hardy, G. H.  ''A Mathematician's Apology'', 1992 [1940]</ref>{{rp|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 [[James Clerk Maxwell|Maxwell]] and [[Albert Einstein|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".<ref name="Apology"/>{{rp|39}}

== Personality ==
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.<ref name="snow67">{{cite book |last=Hardy |first=G. H. |title=A Mathematician's Apology |publisher=[[Cambridge University Press]] |year=1967 |contribution=Foreword |contributor-last=Snow |contributor-first=C. P.}}</ref><ref>{{Cite journal |last1=Christenson |first1=H. |last2=Garcia |first2=S. |date=2015 |title=G.H. Hardy: Mathematical Biologist |url=http://scholarship.claremont.edu/jhm/vol5/iss2/8/ |journal=Journal of Humanistic Mathematics |volume=5 |issue=2 |pages=96–102 |doi=10.5642/jhummath.201502.08 |access-date=31 July 2024|doi-access=free }}</ref>

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.<ref name="cricket" /> A mutual interest in cricket led him to befriend the young [[C. P. Snow]].<ref name="snow67" />{{rp|10–12}}<ref name=":1" /> Hardy was a lifelong bachelor and in his final years he was cared for by his sister.

He was an avid cricket fan. Maynard Keynes observed that if Hardy had read the [[stock exchange]] for half an hour every day with as much interest and attention as he did the day's cricket scores, he would have become a rich man.<ref name="cricket">{{cite web | url=http://www.espncricinfo.com/blogs/content/story/781801.html | title=GH Hardy, the mathematician who loved cricket | work=Cricket Blogs | publisher=[[ESPNcricinfo]] | date=18 September 2014 | access-date=19 September 2014 | author=Khan, Haider Riaz}}</ref> He liked to speak of the best class of mathematical research as "the [[Jack Hobbs|Hobbs]] class", and later, after Bradman appeared as an even greater batsman, "the [[Don Bradman|Bradman]] class".<ref name=":1" />

Around the age of 20, he decided that he [[Atheism|did not believe in God]], which proved a minor issue as attending the chapel was compulsory at Cambridge University. He wrote a letter to his parents explaining that, and from then on he refused to go into any college chapel, even for purely ritualistic duties.<ref name=":1" />

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.<ref name=":0">{{Cite web |date=29 March 2022 |title=G.H. Hardy |url=https://famous-mathematicians.com/g-h-hardy/ |access-date=29 March 2022 |website=Famous Mathematicians: Biography and Contributions of Great Mathematicians through History}}</ref> He admired America and the Soviet Union roughly equally. He found both sides of the Second World War objectionable.<ref name=":1" />

[[Paul Hoffman (science writer)|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>{{nobr|(1)}} prove the [[Riemann hypothesis]]; (2) make 211 not out in the fourth innings of the last [[The Oval|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 [[Benito Mussolini|Mussolini]].<ref>{{Cite book |last=Hoffman |first=Paul |title=[[The Man Who Loved Only Numbers]] |year=1998 |page=81}}</ref></blockquote>

==Cultural references==
Hardy is a key character, played by [[Jeremy Irons]], in the 2015 film ''[[The Man Who Knew Infinity (film)|The Man Who Knew Infinity]]'', based on the biography of Ramanujan with the same title.<ref>{{cite web | url=https://www.ams.org/journals/notices/201602/rnoti-p178.pdf |archive-url=https://ghostarchive.org/archive/20221009/https://www.ams.org/journals/notices/201602/rnoti-p178.pdf |archive-date=2022-10-09 |url-status=live | title=Film Review: 'The Man Who Knew Infinity' | date=February 2016 | author=George Andrews | website=Notices of the American Mathematical Society}}</ref> 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.<ref>{{cite news |last1=Taylor |first1=D. J. |title=Adding up to a life. Review of The Indian Clerk by David Leavitt |url=https://www.theguardian.com/books/2008/jan/26/fiction1 |access-date=21 April 2016 |work=[[The Guardian]] |date=26 January 2008}}</ref> Hardy is a secondary character in ''[[Uncle Petros and Goldbach's Conjecture]]'' (1992), a mathematics novel by [[Apostolos Doxiadis]].<ref>{{cite web |last1=Devlin |first1=Keith |title=Review: Uncle Petros and Goldbach's Conjecture by Apostolos Doxiadis |url=https://old.maa.org/press/maa-reviews/uncle-petros-and-goldbachs-conjecture |publisher=Mathematical Association of America |access-date=21 April 2016 |date=1 April 2000}}</ref> Hardy is also a character in the 2014 Indian film, ''[[Ramanujan (film)|Ramanujan]]'', played by Kevin McGowan.

==Bibliography==
* {{cite book |last=Hardy |first=G. H. |title=A Mathematician's Apology |others=With a foreword by [[C. P. Snow]]|publisher=Cambridge University Press |location=Cambridge |year=2012 |orig-date=1st pub. 1940, with foreword 1967 |isbn=978-1-107-29559-9|title-link=A Mathematician's Apology }} [https://archive.org/details/hardy_annotated 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.<ref>{{Cite web|url=https://www.bbc.co.uk/sounds/play/b008dqy5|title=A Good Read - Marcus du Sautoy and David Dabydeen - BBC Sounds|website=www.bbc.co.uk}}</ref>
* {{cite book |last=Hardy |first=G. H. |title=Ramanujan: Twelve Lectures on Subjects Suggested by his Life and Work |orig-date=1st pub. Cambridge University Press: 1940 |publisher=AMS Chelsea |location=Providence, RI|year=1999 |isbn=978-0-8218-2023-0| url=https://archive.org/details/in.ernet.dli.2015.212059/}}
* {{cite book |last1=Hardy |first1=G. H. |last2=Wright |first2=E. M. |author-link2=E. M. Wright |others=Revised by [[Roger Heath-Brown|D. R. Heath-Brown]] and [[Joseph H. Silverman|J. H. Silverman]], with a foreword by [[Andrew Wiles]]|title=[[An Introduction to the Theory of Numbers]] |edition=6th |publisher=Oxford University Press |location=Oxford |year=2008 |orig-date=1st ed. 1938 |isbn=978-0-19-921985-8}}
* {{cite book |last=Hardy |first=G. H. |year=2008 |orig-date=1st ed. 1908 |title=A Course of Pure Mathematics |others=With a foreword by [[Thomas William Körner|T. W. Körner]] |edition=10th | publisher=Cambridge University Press |isbn=978-0-521-72055-7 |title-link=A Course of Pure Mathematics }}
* {{cite book |last=Hardy |first=G. H. |title=Divergent Series |orig-date=1st ed. [[Clarendon Press]]: 1949 |edition=2nd |publisher=American Mathematical Society |location=Providence, RI |year=2013 |lccn=49005496 |oclc=808787 |mr=0030620 |isbn=978-0-8218-2649-2}} [https://archive.org/details/DivergentSeries/ Full text]
* {{cite book |last1=Hardy | first1=G. H. |title=Collected papers of G. H. Hardy; including joint papers with J. E. Littlewood and others |url=https://archive.org/details/collectedpaperso0000hard |url-access=registration |editor=[[London Mathematical Society]] committee |publisher=Clarendon Press |year=1966–1979 |location=Oxford |oclc=823424 |isbn=0-19-853340-3}} 
* {{cite book | last1=Hardy |first1=G. H. |last2=Littlewood |first2=J. E. |author-link2=John Edensor Littlewood |last3=Pólya |first3=G. |author-link3=George Pólya |title=Inequalities | url=https://mathematicalolympiads.files.wordpress.com/2012/08/inequalities-hardy-littlewood-polya.pdf |edition=1st |publisher=Cambridge University Press |location=Cambridge |year=1934 }}
* {{cite book |last=Hardy |first=G. H. |title=Bertrand Russell and Trinity |others= With a foreword by [[C. D. Broad]] |publisher=Cambridge University Press |year=1970 |orig-date=1st pub. 1942|isbn=978-0-521-11392-2}}

==See also==
{{div col|colwidth=30em}}
* [[Critical line theorem]]
* [[Campbell's theorem (probability)|Campbell–Hardy theorem]]
* [[Hardy hierarchy]]
* [[Hardy notation]]
* [[Hardy space]]
* [[Laguerre polynomials#Hardy–Hille formula|Hardy–Hille formula]]
* [[Big O notation#The Hardy–Littlewood definition|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]]
* [[Z function|Hardy Z function]]
* [[Pisot–Vijayaraghavan number]]
* [[Ulam spiral]]

{{div col end}}

==Notes==
{{notelist}}

==References==
{{reflist|26em}}

==Further reading==
*{{Cite book |first=Robert |last=Kanigel |title=The Man Who Knew Infinity: A Life of the Genius Ramanujan |publisher=Washington Square Press |location=New York |year=1991 |isbn=0-671-75061-5 |url-access=registration |url=https://archive.org/details/manwhoknewinfini00kani_1 }}
*{{Cite book |author-link=C. P. Snow |first=C. P. |last=Snow |title=Variety of Men |chapter=G. H. Hardy |pages=15–46 |publisher=Macmillan |location=London |year=1967 |chapter-url-access=registration |chapter-url=https://archive.org/details/varietyofmen0000snow }} Reprinted as {{cite book |contributor-last=Snow |contributor-first=C.P |contributor-link=C. P. Snow |contribution=Foreword |last=Hardy |first=G. H. |title=A Mathematician's Apology |url=https://archive.org/details/mathematiciansap0000hard_u4z4 |url-access=registration |publisher=Cambridge University Press |orig-date=1st pub. 1967 |year=2012 |isbn=978-1-107-29559-9 }}
*{{Cite book|title=The G.H. Hardy Reader|publisher=Cambridge University Press|year=2015|isbn=978-1-10713-555-0|editor-last=Albers|editor-first=D.J.|location=Cambridge|editor-last2=Alexanderson|editor-first2=G.L.|editor-last3=Dunham|editor-first3=W.}}

==External links==
{{Commons category|G. H. Hardy}}
{{wikiquote}}
* {{Gutenberg author | id=39236}}
* {{Internet Archive author |sname=Godfrey Harold Hardy}}
* {{Librivox author |id=9750}}
* {{MacTutor Biography|id=Hardy}}
*[https://web.archive.org/web/20120716185939/http://www-gap.dcs.st-and.ac.uk/~history/Quotations/Hardy.html Quotations of G. H. Hardy]
*[http://www.numbertheory.org/obituaries/LMS/hardy/ Hardy's work on Number Theory]
*{{ScienceWorldBiography | urlname=Hardy | title=Hardy, Godfrey Harold (1877–1947)}}

{{Copley Medallists 1901–1950}}
{{De Morgan Medallists}}
{{Savilian Professors of Geometry}}
{{Chauvenet Prize recipients}}

{{Authority control}}

{{DEFAULTSORT:Hardy, G. H.}}
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