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Encyclopedia > G. H. Hardy
G. H. Hardy
Born February 7, 1877(1877-02-07)
Cranleigh, Surrey, England
Died December 1, 1947 (aged 70)
Cambridge, Cambridgeshire, England
Religious stance Atheist

Godfrey Harold Hardy FRS (February 7, 1877 Cranleigh, Surrey, England [1]December 1, 1947 Cambridge, Cambridgeshire, England [2]) was a prominent English mathematician, known for his achievements in number theory and mathematical analysis. is the 38th day of the year in the Gregorian calendar. ... 1877 (MDCCCLXXVII) was a common year starting on Monday (see link for calendar). ... Cranleigh has long been associated with the unprovable title of Englands largest village: this settlement is part of the Waverley district of Surrey, and was until the mid 1860s Cranley. The Post Office insisted on changing the spelling to avoid confusion with nearby Crawley in West Sussex. ... This article is about the English county. ... For other uses, see England (disambiguation). ... is the 335th day of the year (336th in leap years) in the Gregorian calendar. ... Year 1947 (MCMXLVII) was a common year starting on Wednesday (link will display full 1947 calendar) of the Gregorian calendar. ... This article is about the city in England. ... Cambridgeshire (abbreviated Cambs) is a county in England, bordering Lincolnshire to the north, Norfolk to the northeast, Suffolk to the east, Essex and Hertfordshire to the south, and Bedfordshire and Northamptonshire to the west. ... For other uses, see England (disambiguation). ... The Fellowship of the Royal Society was founded in 1660. ... is the 38th day of the year in the Gregorian calendar. ... 1877 (MDCCCLXXVII) was a common year starting on Monday (see link for calendar). ... Cranleigh has long been associated with the unprovable title of Englands largest village: this settlement is part of the Waverley district of Surrey, and was until the mid 1860s Cranley. The Post Office insisted on changing the spelling to avoid confusion with nearby Crawley in West Sussex. ... This article is about the English county. ... For other uses, see England (disambiguation). ... is the 335th day of the year (336th in leap years) in the Gregorian calendar. ... Year 1947 (MCMXLVII) was a common year starting on Wednesday (link will display full 1947 calendar) of the Gregorian calendar. ... This article is about the city in England. ... Cambridgeshire (abbreviated Cambs) is a county in England, bordering Lincolnshire to the north, Norfolk to the northeast, Suffolk to the east, Essex and Hertfordshire to the south, and Bedfordshire and Northamptonshire to the west. ... For other uses, see England (disambiguation). ... For other meanings of mathematics or uses of math and maths, see Mathematics (disambiguation) and Math (disambiguation). ... Number theory is the branch of pure mathematics concerned with the properties of numbers in general, and integers in particular, as well as the wider classes of problems that arise from their study. ... Analysis has its beginnings in the rigorous formulation of calculus. ...


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 best insights into the mind of a working mathematician written for the layman. A Mathematicians Apology is a 1940 essay by British mathematician G. H. Hardy. ... For other uses, see Essay (disambiguation). ... Aesthetics is commonly perceived as the study of sensory or sensori-emotional values, sometimes called judgments of sentiment and taste. ... Look up Layman in Wiktionary, the free dictionary. ...


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." Ramanujan redirects here. ... Paul ErdÅ‘s (Hungarian: ErdÅ‘s Pál, in English occasionally Paul Erdos or Paul Erdös, March 26, 1913 – September 20, 1996), was an immensely prolific (and famously eccentric) Hungarian-born mathematician. ...

Contents

Life

G.H. Hardy was born 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 parents were mathematically inclined. Cranleigh has long been associated with the unprovable title of Englands largest village: this settlement is part of the Waverley district of Surrey, and was until the mid 1860s Cranley. The Post Office insisted on changing the spelling to avoid confusion with nearby Crawley in West Sussex. ... This article is about the English county. ... For other uses, see England (disambiguation). ... A Bursar is a senior professional financial administrator in a school or university. ... It has been suggested that Old Cranleighans be merged into this article or section. ...


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.[3]


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 the Cambridge Apostles, an elite, intellectual secret society. It has been suggested that Old Cranleighans be merged into this article or section. ... For the university in Winchester of a similar name, see University of Winchester. ... Full name The College of the Holy and Undivided Trinity Motto Virtus vera nobilitas Virtue is true Nobility Named after The Holy Trinity Previous names King’s Hall and Michaelhouse (until merged in 1546) Established 1546 Sister College(s) Christ Church Master The Lord Rees of Ludlow Location Trinity Street... The University of Cambridge (often Cambridge University), located in Cambridge, England, is the second-oldest university in the English-speaking world and has a reputation as one of the worlds most prestigious universities. ... Results for parts II and III of the Mathematical Tripos are read out inside Senate House, University of Cambridge and then tossed from the balcony. ... Trinity College Great Court. ...


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 continental Europe. 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 the Savilian Chair of Geometry at Oxford in the aftermath of the Bertrand Russell affair during World War I. He returned to Cambridge in 1931, where he was Sadleirian Professor until 1942. Marie Ennemond Camille Jordan (January 5, 1838 – January 22, 1922) was a French mathematician, known both for his foundational work in group theory and for his influential Cours danalyse. ... For other uses, see Europe (disambiguation). ... The Savilian Chair of Geometry is the position of professor of mathematics at the University of Oxford in England. ... The University of Oxford, located in the city of Oxford in England, is the oldest university in the English-speaking world. ... Bertrand Arthur William Russell, 3rd Earl Russell, OM, FRS, (18 May 1872 – 2 February 1970), was a British philosopher, logician, mathematician, advocate for social reform, and pacifist. ... “The Great War ” redirects here. ... The Sadleirian Chair is a Professorship in pure mathematics at Cambridge University. ...


The Indian Clerk (2007) is a novel by David Leavitt based on Hardy's life at Cambridge, including his discovery of and relationship with Srinivasa Ramanujan. David Leavitt (born June 23, 1961) is an American novelist. ... This article is about the city in England. ... Ramanujan redirects here. ...


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 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. Look up Rigour in Wiktionary, the free dictionary. ... Applied mathematics is a branch of mathematics that concerns itself with the mathematical techniques typically used in the application of mathematical knowledge to other domains. ... Sir Isaac Newton FRS (4 January 1643 – 31 March 1727) [ OS: 25 December 1642 – 20 March 1727][1] was an English physicist, mathematician, astronomer, natural philosopher, and alchemist. ... Broadly speaking, pure mathematics is mathematics motivated entirely for reasons other than application. ... Hydrodynamics is fluid dynamics applied to liquids, such as water, alcohol, oil, and blood. ...


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. In a 1947 lecture, the Danish mathematician Harald Bohr reported a colleague's joke that, "Nowadays, there are only three really great English mathematicians: Hardy, Littlewood and Hardy-Littlewood." John Edensor Littlewood (June 9, 1885 - September 6, 1977) was a British mathematician. ... Analysis has its beginnings in the rigorous formulation of calculus. ... Analytic number theory is the branch of number theory that uses methods from mathematical analysis. ... In number theory, Warings Problem, proposed in 1770 by Edward Waring, asks whether for every natural number k there exists an associated positive integer s such that every natural number is the sum of at most s kth powers of natural numbers. ... In mathematics, the Hardy-Littlewood circle method is one of the most frequently used techniques of analytic number theory. ... In mathematics, a prime number (or a prime) is a natural number which has exactly two distinct natural number divisors: 1 and itself. ... Conditional proof is a proof that takes the form of asserting a conditional, and proving that the premise or antecedent of the conditional necessarily leads to the conclusion. ... In mathematics, a conjecture is a mathematical statement which appears likely to be true, but has not been formally proven to be true under the rules of mathematical logic. ... The twin prime conjecture is a famous problem in number theory that involves prime numbers. ... In number theory, the second Hardy-Littlewood conjecture concerns the number of primes in intervals. ... Harald Bohr (22 April 1887 – 22 January 1951) was a Danish mathematician, and younger brother of the physicist Niels Bohr. ...


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. Hardy–Weinberg principle for two alleles: the horizontal axis shows the two allele frequencies p and q, the vertical axis shows the genotype frequencies and the three possible genotypes are represented by the different glyphs In population genetics, the Hardy–Weinberg principle is a relationship between the frequencies of alleles... Population genetics is the study of the distribution of and change in allele frequencies under the influence of the four evolutionary forces: natural selection, genetic drift, mutation, and migration. ... Wilhelm Weinberg Dr Wilhelm Weinberg (1862 — 1937) was a German physician who in 1908 independently of the British mathematician G.H. Hardy, formulated the Hardy-Weinberg principle. ... This article is about the sport. ... Image:Reg Punnet. ...


His collected papers have been published.[citation needed]


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: Broadly speaking, pure mathematics is mathematics motivated entirely for reasons other than application. ... Applied mathematics is a branch of mathematics that concerns itself with the mathematical techniques typically used in the application of mathematical knowledge to other domains. ... A Mathematicians Apology is a 1940 essay by British mathematician G. H. Hardy. ...

"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 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. Population genetics is the study of the distribution of and change in allele frequencies under the influence of the four evolutionary forces: natural selection, genetic drift, mutation, and migration. ... For other topics related to Einstein see Einstein (disambig) In statistical mechanics, Bose-Einstein statistics determines the statistical distribution of identical indistinguishable bosons over the energy states in thermal equilibrium. ...


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." James Clerk Maxwell (13 June 1831 – 5 November 1879) was a Scottish mathematician and theoretical physicist. ... “Einstein” redirects here. ...


Attitudes and Personality

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 and befriended the young C. P. Snow who was one also. The Bloomsbury Group or Bloomsbury Set or just Bloomsbury, as its adherents would generally refer to it, was an English group of artists and scholars that existed from around 1905 until around World War II. // History The group began as an informal socialwe have been great to society assembly of... Trinity College Great Court. ... George Edward Moore George Edward Moore, also known as G.E. Moore, (November 4, 1873 - October 24, 1958) was a distinguished and hugely influential English philosopher who was educated and taught at the University of Cambridge. ... Bertrand Arthur William Russell, 3rd Earl Russell, OM, FRS, (18 May 1872 – 2 February 1970), was a British philosopher, logician, mathematician, advocate for social reform, and pacifist. ... John Maynard Keynes John Maynard Keynes [ˈkeɪns], 1st Baron Keynes of Tilton (June 5, 1883 - April 21, 1946) was an English economist, whose radical ideas had a major impact on modern economic and political thought. ... Charles Percy Snow, Baron Snow, CBE (15 October 1905–1 July 1980) was a scientist and novelist. ...


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. The Union of Democratic Control was a British pressure group formed in 1914 to press for a more responsive foreign policy. ...


He was an atheist, and, according to those who knew him best, a "non-practising homosexual".[4] Hardy never married, and in his final years he was cared for by his sister. For information about the band, see Atheist (band). ... Since its coinage, the word homosexuality has acquired multiple meanings. ...


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 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) Edward Charles (Ted) Titchmarsh (born 1 June 1899 in Newbury died 18 January 1963 at Oxford) was a leading British mathematician. ...


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.

See also

In complexity theory and mathematics, the Hardy notation, introduced by G. H. Hardy, is used for asymptotic comparison of functions, equivalently to Landau notation (also known as Big O notation). It is defined in terms of Landau notation by   and   (Similar symbols are used, like resp. ... In complex analysis, the Hardy spaces are analogues of the Lp spaces of functional analysis. ... In mathematics, a Pisot-Vijayaraghavan number is an algebraic integer α which is real and exceeds 1, but such that its conjugate elements are all less than 1 in absolute value. ... Hardys inequality is an inequality in mathematics, named after G. H. Hardy. ...

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. and E. 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 online at archive.org.
  • Hardy, G. H. (1949), Divergent Series, Oxford, at the Clarendon Press, pp. xvi+396, MR0030620, ISBN 978-0821826492

A Mathematicians Apology is a 1940 essay by British mathematician G. H. Hardy. ... Ramanujan Srinivasa Aiyangar Ramanujan (Tamil: ஸ்ரீனிவாஸ ஐயங்கார் ராமானுஜன்) (December 22, 1887 – April 26, 1920) was a groundbreaking Indian mathematician. ... Sir Edward Maitland Wright (February 13, 1906 - February 2, 2005) was an English mathematician, and collaborator with G.H. Hardy. ... A Course of Pure Mathematics is a classic textbook in introductory mathematical analysis, written by G. H. Hardy. ... Internet Archive, San Francisco The Internet Archive (archive. ... Mathematical Reviews is a scientific journal edited by the American Mathematical Society offering reviews of recent mathematical papers. ...

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)

Charles Percy Snow, Baron Snow, CBE (15 October 1905–1 July 1980) was a scientist and novelist. ...

References

  1. ^ GRO Register of Births: MAR 1877 2a 147 HAMBLEDON - Godfrey Harold Hardy
  2. ^ GRO Register of Deaths: DEC 1947 4a 204 CAMBRIDGE - Godfrey H. Hardy, aged 70
  3. ^ Robert Kanigel, The Man Who Knew Infinity, p. 116, Charles Scribner's Sons, New York, 1991. ISBN 0-684-19259-4.
  4. ^ Miller, Arthur I. (2005), Empire Of The Stars, Houghton Mifflin Books, p. 37, ISBN 061834151X

External links

Wikiquote has a collection of quotations related to:
G. H. Hardy

Image File history File links This is a lossless scalable vector image. ... Wikiquote is one of a family of wiki-based projects run by the Wikimedia Foundation, running on MediaWiki software. ... The MacTutor history of mathematics archive is a website hosted by University of St Andrews in Scotland. ... The Mathematics Genealogy Project is a web-based database that gives an academic genealogy based on dissertation supervision relations. ... ScienceWorld, also known as Eric Weissteins World of Science, is a web site that opened to the general public in January 2002. ... The Savilian Chair of Geometry is the position of professor of mathematics at the University of Oxford in England. ... Henry Briggs (February 1556 - January 26, 1630) was an English mathematician notable for changing Napiers logarithms into common/Briggesian logarithms He was born at Warley Wood, near Halifax, in Yorkshire Enland. ... Peter Turner was an English mathematician: He held the Savilian Chair of Geometry at the University of Oxford from 1631 to 1649. ... John Wallis John Wallis (November 22, 1616 - October 28, 1703) was an English mathematician who is given partial credit for the development of modern calculus. ... // Portrait of Edmond Halley painted around 1687 by Thomas Murray (Royal Society, London) Portrait of Edmond Halley Bust of Edmond Halley in the Museum of the Royal Greenwich Observatory Edmond Halley FRS (sometimes Edmund; IPA: ) (November 8, 1656 – January 14, 1742) was an English astronomer, geophysicist, mathematician, meteorologist, and physicist. ... The Reverend Nathaniel Bliss (28 November 1700-2 September 1764) was a noted English astronomer of the 18th century, serving as Astronomer Royal between 1762 and 1764. ... Joseph Betts was an English mathematician: He held the Savilian Chair of Geometry at the University of Oxford in 1765. ... John Smith was an English mathematician: He held the Savilian Chair of Geometry at the University of Oxford from 1766 to 1797. ... Abraham Robertson was an English mathematician: He held the Savilian Chair of Geometry at the University of Oxford from 1797 to 1809. ... Stephen Peter Rigaud (1774 - 1839), was an English mathematical historian and astronomer: He was a Fellow of Exeter College from 1794 to 1810, held the Savilian Chair of Geometry at the University of Oxford from 1810 to 1827, the Savilian Professor of Astronomy from 1827 to 1839. ... The Reverend Professor Baden Powell, MA, FRS, FRGS (1796-08-22 – 1860-06-11) was an English mathematician: He held the Savilian Chair of Geometry at the University of Oxford from 1827 to 1860. ... Henry John Stephen Smith (November 2, 1826 - February 9, 1883) was an Irish mathematician, remembered for his work in number theory (elementary divisors, quadratic forms) and matrices. ... James Joseph Sylvester James Joseph Sylvester (September 3, 1814 London - March 15, 1897 Oxford) was an English mathematician. ... Edward Charles (Ted) Titchmarsh (born 1 June 1899 in Newbury died 18 January 1963 at Oxford) was a leading British mathematician. ... Sir Michael Francis Atiyah, OM, FRS (b. ... Ioan Mackenzie James (born May 23, 1928) is a British mathematician working in the field of topology particularly in homotopy theory. ... Richard Taylor (born 19 May 1962) is a British mathematician working in the field of number theory. ... Nigel Hitchin (b. ...


 
 

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