- G. H. Hardy
Infobox Scientist

name = G.H. Hardy

image width = 230px

caption = G.H. Hardy

birth_date = birth date|1877|02|07

birth_place =Cranleigh ,Surrey ,England

death_date = death date and age|1947|12|01|1877|02|07

death_place =Cambridge ,Cambridgeshire ,England

residence =

citizenship = British

nationality = British

ethnicity =

field =

work_institutions =Trinity College, Cambridge

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religion =Atheist

footnotes =**Godfrey Harold Hardy**FRS (February 7 ,1877 Cranleigh ,Surrey ,England [*GRO Register of Births: MAR 1877 2a 147 HAMBLEDON - Godfrey Harold Hardy*] –December 1 ,1947 Cambridge ,Cambridgeshire , England [*GRO Register of Deaths: DEC 1947 4a 204 CAMBRIDGE - Godfrey H. Hardy, aged 70*] ) was a prominent English mathematician, known for his achievements innumber theory andmathematical analysis .Non-mathematicians usually know him for "

A Mathematician's Apology ", hisessay from 1940 on theaesthetics of mathematics. The apology is often considered one of the best insights into the mind of a working mathematician written for thelayman .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 byPaul 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."**Life**G.H. Hardy was born 7 February 1877, in

Cranleigh ,Surrey ,England , into a teaching family. His father wasBursar and Art Master atCranleigh School ; his mother had been a senior mistress atLincoln Training College for teachers. Both parents were mathematically inclined.Hardy's own natural affinity for mathematics was perceptible at a young age. When just two years old, he wrote numbers up to millions, and when taken to church he amused himself by factorizing the numbers of the hymns. [

*Robert Kanigel, "The Man Who Knew Infinity", p. 116, Charles Scribner's Sons, New York, 1991. ISBN 0-684-19259-4.*]After schooling at Cranleigh, Hardy was awarded a scholarship to

Winchester College for his mathematical work. In 1896 he entered Trinity College, Cambridge. After only two years of preparation he was fourth in the Mathematics 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 theCambridge Apostles , an elite, intellectual secret society.As the most important influence Hardy cites the self-study of "Cours d'analyse de l'Ecole Polytechnique" by the French mathematician

Camille Jordan , through which he became acquainted with the more precise mathematics tradition in continentalEurope . In 1900 he passed part II of the tripos and was awarded a fellowship. In 1903 he earned his M.A., which was the highest academic degree at English universities at that time. From 1906 onward he held the position of a lecturer, who had to teach six hours per week leaving him plenty of time for research. In 1919 he left Cambridge to take theSavilian Chair of Geometry at Oxford in the aftermath of the Bertrand Russell affair duringWorld War I . He returned to Cambridge in 1931, where he was Sadleirian Professor until 1942."The Indian Clerk" (2007) is a novel by

David Leavitt based on Hardy's life atCambridge , including his discovery of and relationship withSrinivasa Ramanujan .**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 ofIsaac Newton (see Cambridge Mathematical Tripos). Hardy was more in tune with the "cours d'analyse" methods dominant in France, and aggressively promoted his conception ofpure mathematics , in particular against thehydrodynamics which was an important part of Cambridge mathematics.From 1911 he collaborated with

J. E. Littlewood , in extensive work inmathematical analysis andanalytic number theory . This (along with much else) led to quantitative progress on theWaring problem , as part of theHardy-Littlewood circle method , as it became known. Inprime number theory, they proved results and some notableconditional result s. This was a major factor in the development of number theory as a system ofconjecture s; examples are the first andsecond 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 mathematicianHarald Bohr said, "To illustrate to what extent Hardy and Littlewood in the course of the years came to be considered as the leaders of recent English mathematical research, I may report what an excellent colleague once jokingly said: 'Nowadays, there are only three really great English mathematicians: Hardy, Littlewood, and Hardy-Littlewood.'" [*cite book*] Rp|xxvii

last=Bohr

first=Harald

authorlink=Harald Bohr

title=Collected Mathematical Works

volume=1

year=1952

publisher=Dansk Matematisk Forening

location=Copenhagen

oclc=3172542

pages=xiii-xxxiv

chapter=Looking BackwardHardy is also known for formulating the

Hardy-Weinberg principle , a basic principle ofpopulation genetics , independently fromWilhelm Weinberg in 1908. He playedcricket with the geneticistReginald 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 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"::"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." [*http://www.numbertheory.org/obituaries/LMS/hardy/page83.html*] However, aside from formulating the Hardy-Weinberg principle inpopulation 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-interactingBose-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.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 as well as good ends – "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."

**Attitudes and personality**Socially he was associated with the

Bloomsbury group and theCambridge Apostles ;G. E. Moore ,Bertrand Russell andJ. M. Keynes were friends. He was an avid cricket fan and befriended the youngC. P. Snow who was one also.He was at times politically involved, if not an activist. He took part in the

Union of Democratic Control during World War I, andFor Intellectual Liberty in the late 1930s.Hardy was an atheist. He never married, 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.

In his [

*http://www.numbertheory.org/obituaries/LMS/hardy/page86.html 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." —E. C. Titchmarsh (1950)**Hardy’s aphorisms*** "It is never worth a first class man's time to express a majority opinion. By definition, there are plenty of others 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.

**ee also***

Hardy notation

*Hardy space

*Pisot-Vijayaraghavan number

*Hardy's inequality **Books*** Hardy G. H. (1940) "

A Mathematician's Apology ", Cambridge University Press; Reprint edition (January 31, 1992). ISBN 0-521-42706-1.

* Hardy G. H. (1940) "Ramanujan ", Cambridge University Press: London (1940). Ams Chelsea Pub. (November 25, 1999) ISBN 0-8218-2023-0.

* Hardy G. H. andE. M. Wright (1938) "An Introduction to the Theory of Numbers", Oxford University Press, USA; 5 edition (April 17, 1980). ISBN 0-19-853171-0.

* Hardy G. H. (1908) "A Course of Pure Mathematics ", Cambridge University Press; 10th edition (June 25, 1993). ISBN 0-521-09227-2. Available [*http://www.archive.org/details/coursepuremath00hardrich online*] atarchive.org .

*citation|id=MR|0030620|last= Hardy|first= G. H.|title= Divergent Series|publisher= Oxford, at the Clarendon Press|year= 1949|pages=xvi+396|isbn= 978-0821826492

*cite book | last = Hardy | first = G. H. | coauthors = London Mathematical Society | title = Collected papers of G.H. Hardy; including joint papers with J.E. Littlewood and others | publisher = Clarendon Press | date = 1966 | location = Oxford | oclc = 823424

*cite book

last = Hardy

first = G. H.

coauthors = Littlewood, J.E.; Pólya, G.

title = Inequalities, 2nd ed

publisher = Cambridge University Press

date = 1952

pages =

isbn = 0521358809**Bibliography***Robert Kanigel, "The Man Who Knew Infinity: A Life of the Genius Ramanujan" (Washington Square Press, 1991) ISBN 0-671-75061-5

*C. P. Snow , "Variety of Men" (Macmillan, 1967)**References****External links***MacTutor Biography|id=Hardy

*MathGenealogy |id=17806

* [*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)

*I. Grattan-Guinness, " [*http://mubs.mdx.ac.uk/Research/Discussion_Papers/Mathematics_and_Statistics/maths_dpaper_no_4.pdf The interest of G.H. Hardy, F.R.S. in the philosophy and the history of mathematics*] "

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