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G. H. Hardy
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
Citizenship British
Nationality British
Institutions Trinity College, Cambridge
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. Events 457 - Leo I becomes emperor of the Byzantine Empire. 1074 - Battle of Montesarchio in which the Prince Year 1877 ( MDCCCLXXVII) was a Common year starting on Monday (link will display the full calendar of the Gregorian calendar (or a Common Cranleigh is a large village proclaimed the largest in England, and is situated 8 miles south east of Godalming in Surrey. Surrey is a county in the South East of England and is one of the Home Counties. England is a Country which is part of the United Kingdom. Its inhabitants account for more than 83% of the total UK population whilst its mainland Events 800 - Charlemagne judges the accusations against Pope Leo III in the Vatican Year 1947 ( MCMXLVII) was a Common year starting on Wednesday (link will display full 1947 calendar of the Gregorian calendar. The city of Cambridge (ˈkeɪmbrɪdʒ is a university town and the administrative centre of the county of Cambridgeshire, England History Cambridgeshire is noted as the site of some of the earliest known Neolithic permanent settlement in the United Kingdom, along with sites at Fengate England is a Country which is part of the United Kingdom. Its inhabitants account for more than 83% of the total UK population whilst its mainland The United Kingdom of Great Britain and Northern Ireland, commonly known as the United Kingdom, the UK or Britain,is a Sovereign state located Trinity College is a constituent college of the University of Cambridge in Cambridge, England. Atheism The Royal Society of London for the Improvement of Natural Knowledge, known simply as The Royal Society, is a Learned society for science that was founded in 1660 Events 457 - Leo I becomes emperor of the Byzantine Empire. 1074 - Battle of Montesarchio in which the Prince Year 1877 ( MDCCCLXXVII) was a Common year starting on Monday (link will display the full calendar of the Gregorian calendar (or a Common Cranleigh is a large village proclaimed the largest in England, and is situated 8 miles south east of Godalming in Surrey. Surrey is a county in the South East of England and is one of the Home Counties. England is a Country which is part of the United Kingdom. Its inhabitants account for more than 83% of the total UK population whilst its mainland Events 800 - Charlemagne judges the accusations against Pope Leo III in the Vatican Year 1947 ( MCMXLVII) was a Common year starting on Wednesday (link will display full 1947 calendar of the Gregorian calendar. The city of Cambridge (ˈkeɪmbrɪdʒ is a university town and the administrative centre of the county of Cambridgeshire, England History Cambridgeshire is noted as the site of some of the earliest known Neolithic permanent settlement in the United Kingdom, along with sites at Fengate England is a Country which is part of the United Kingdom. Its inhabitants account for more than 83% of the total UK population whilst its mainland Mathematics is the body of Knowledge and Academic discipline that studies such concepts as Quantity, Structure, Space and 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 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. A Mathematician's Apology is a 1940 essay by British mathematician G An essay is usually a short piece of writing It is often written from an author's personal point of view. Aesthetics or esthetics ( also spelled æsthetics) is commonly known as the study of sensory or sensori-emotional values sometimes called The apology is often considered one of the best insights into the mind of a working mathematician written for the layman. The term " layman " originated from the use of the term Laity, but over the centuries changed definition to mean a person who is a non-expert in a given field of

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. Paul Erdős ( Hungarian: Erdős Pál, in English occasionally Paul Erdos or Paul Erdös, March 26, 1913 &ndash He called their collaboration "the one romantic incident in my life. "

Contents

Life

G. H. Hardy was born 7 February 1877, in Cranleigh, Surrey, England, into a teaching family. Cranleigh is a large village proclaimed the largest in England, and is situated 8 miles south east of Godalming in Surrey. Surrey is a county in the South East of England and is one of the Home Counties. England is a Country which is part of the United Kingdom. Its inhabitants account for more than 83% of the total UK population whilst its mainland His father was Bursar and Art Master at Cranleigh School; his mother had been a senior mistress at Lincoln Training College for teachers. A Bursar is a senior professional financial administrator in a School or University. Cranleigh School is an independent English Boarding school in the village of Cranleigh, Surrey. 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. [3]

After schooling at Cranleigh, Hardy was awarded a scholarship to Winchester College for his mathematical work. Cranleigh School is an independent English Boarding school in the village of Cranleigh, Surrey. Winchester College is a well-known boys' Independent school, and an example of an English Public school, in the city of Winchester in Hampshire In 1896 he entered Trinity College, Cambridge. Trinity College is a constituent college of the University of Cambridge in Cambridge, England. The University of Cambridge (often Cambridge University) located in Cambridge, England, is the second-oldest university in the After only two years of preparation he was fourth in the Mathematics Tripos examination. The Mathematical Tripos is the taught mathematics course at the University of Cambridge. 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. The Cambridge Apostles, also known as the Cambridge Conversazione Society, is an elite intellectual Secret society at the University of Cambridge founded

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. Marie Ennemond Camille Jordan ( January 5 1838 &ndash January 22 1922) was a French Mathematician, known both for his foundational 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. The Savilian Chair of Geometry is the position of Professor of Mathematics at the University of Oxford in England. The University of Oxford (informally "Oxford University" or simply "Oxford" located in the city of Oxford, Oxfordshire, England is the Bertrand Arthur William Russell 3rd Earl Russell, OM, FRS (18 May 1872 – 2 February 1970 was a British Philosopher, Historian World War I (abbreviated WWI; also known as the First World War, the Great War, and the War to End All He returned to Cambridge in 1931, where he was Sadleirian Professor until 1942. The Sadleirian Chair is a Professorship in Pure mathematics at the University of Cambridge.

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 Biography Born in Pittsburgh Pennsylvania, Leavitt is a graduate The city of Cambridge (ˈkeɪmbrɪdʒ is a university town and the administrative centre of the county of Cambridgeshire, England

Work

Hardy is credited with reforming British mathematics by bringing rigour into it, which was previously a characteristic of French, Swiss and German mathematics. Rigour or rigor (see spelling differences) has a number of meanings in relation to intellectual life and discourse This article is about the country For a topic outline on this subject see List of basic France topics. Switzerland (English pronunciation; Schweiz Swiss German: Schwyz or Schwiiz Suisse Svizzera Svizra officially the Swiss Confederation Germany, officially the Federal Republic of Germany ( ˈbʊndəsʁepuˌbliːk ˈdɔʏtʃlant is a Country in Central Europe. British mathematicians had remained largely in the tradition of applied mathematics, in thrall to the reputation of Isaac Newton (see Cambridge Mathematical Tripos). 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 (ˈnjuːtən 4 January 1643 31 March 1727) Biography Early years See also Isaac Newton's early life and achievements 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. Broadly speaking pure mathematics is Mathematics motivated entirely for reasons other than application Fluid dynamics is the sub-discipline of Fluid mechanics dealing with fluid flow: Fluids ( Liquids and Gases in motion

From 1911 he collaborated with J. E. Littlewood, in extensive work in mathematical analysis and analytic number theory. John Edensor Littlewood ( 9 June 1885 &ndash 6 September 1977) was a British Mathematician, best known for his long collaboration Analysis has its beginnings in the rigorous formulation of Calculus. In Mathematics, analytic number theory is a branch of Number theory that uses methods from Mathematical analysis to solve number-theoretical problems 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 Number theory, Waring's problem, proposed in 1770 by Edward Waring, asks whether for every Natural number k there exists an associated positive In Mathematics, the Hardy–Littlewood circle method is one of the most frequently used techniques of Analytic number theory. In prime number theory, they proved results and some notable conditional results. In Mathematics, a prime number (or a prime) is a Natural number which has exactly two distinct natural number Divisors 1 A conditional proof is a proof that takes the form of asserting a conditional, and proving that the antecedent of the conditional necessarily leads to 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. In Mathematics, a conjecture is a Mathematical statement which appears resourceful but has not been formally proven to be true under the rules of The twin prime conjecture is a famous unsolved problem in Number theory that involves Prime numbers It states There are infinitely many primes In Number theory, the second Hardy-Littlewood conjecture concerns the number of primes in Intervals If &pi( x) is the number of primes up to and 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. Harald August Bohr ( 22 April 1887 &ndash 22 January 1951) was a Danish Mathematician and football player "

Hardy is also known for formulating the Hardy-Weinberg principle, a basic principle of population genetics, independently from Wilhelm Weinberg in 1908. Population genetics is the study of the Allele frequency distribution and change under the influence of the four evolutionary forces Natural selection, Genetic Dr Wilhelm Weinberg (1862 &mdash 1937 was a German Physician who in 1908 independently of the British mathematician G 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. Cricket is a bat-and-ball team Sport that originated in England and is now played in more than 100 countries Professor Reginald Crundall Punnett FRS ( June 20 1875 &ndash January 3 1967) was a British geneticist who

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. 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 He made several statements similar to that in his Apology:

"I have never done anything 'useful'. A Mathematician's Apology is a 1940 essay by British mathematician G 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. Population genetics is the study of the Allele frequency distribution and change under the influence of the four evolutionary forces Natural selection, Genetic 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. James Clerk Maxwell (13 June 1831 &ndash 5 November 1879 was a Scottish mathematician and theoretical physicist. Albert Einstein ( German: ˈalbɐt ˈaɪ̯nʃtaɪ̯n; English: ˈælbɝt ˈaɪnstaɪn (14 March 1879 – 18 April 1955 was a German -born theoretical " 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 the Cambridge Apostles; G. E. Moore, Bertrand Russell and J. M. Keynes were friends. The Bloomsbury Group was an English collectivity of loving friends and relatives who lived in or near London during the first half of the twentieth century The Cambridge Apostles, also known as the Cambridge Conversazione Society, is an elite intellectual Secret society at the University of Cambridge founded "GE Moore" redirects here For the cofounder of Intel see Gordon Moore. Bertrand Arthur William Russell 3rd Earl Russell, OM, FRS (18 May 1872 – 2 February 1970 was a British Philosopher, Historian John Maynard Keynes 1st Baron Keynes CB (ˈkeɪnz "cains" (5 June 1883 &ndash 21 April 1946 was a British Economist whose ideas He was an avid cricket fan and befriended the young C. P. Snow who was one also. Charles Percy Snow Baron Snow CBE ( 15 October 1905 &ndash 1 July 1980) was an English Physicist 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.

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 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

See also

Books

Bibliography

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. Charles Percy Snow Baron Snow CBE ( 15 October 1905 &ndash 1 July 1980) was an English Physicist and Novelist 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.

External links

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