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John Edensor Littlewood

John Edensor Littlewood
Born (1885-06-09)9 June 1885
Rochester, Kent, England
Died 6 September 1977(1977-09-06) (aged 92)
Cambridge, England
Residence United Kingdom
Nationality British
Fields Mathematician
Institutions University of Cambridge
Alma mater University of Cambridge
Doctoral advisor Ernest William Barnes
Doctoral students A. O. L. Atkin
Sarvadaman Chowla
Harold Davenport
Srinivasa Ramanujan
Stanley Skewes
Donald C. Spencer
Albert Ingham
Known for Mathematical analysis
Notable awards Smith's Prize (1908)
Royal Medal (1929)
(1960) Senior Berwick Prize
(1958) Copley Medal
(1943) Sylvester Medal

John Edensor Littlewood (9 June 1885 – 6 September 1977)[1] was a British mathematician, best known for his achievements in analysis, number theory, and differential equations.


  • Life 1
  • Work 2
    • With Hardy 2.1
  • See also 3
  • Notes 4
  • Further reading 5
  • External links 6


Littlewood was born in 1885 in Senior Berwick Prize in 1960.


Most of Littlewood's work was in the field of mathematical analysis. He began research under the supervision of Ernest William Barnes, who suggested that he attempt to prove the Riemann hypothesis: Littlewood showed that if the Riemann hypothesis is true then the Prime Number Theorem follows and obtained the error term. This work won him his Trinity fellowship. However, the link between the Riemann hypothesis and the Prime Number Theorem had been known before in Continental Europe, and Littlewood wrote later in his book, A Mathematician's Miscellany that his rediscovery of the result did not shed a positive light on the isolated nature of British mathematics at the time.

He coined Littlewood's law, which states that individuals can expect "miracles" to happen to them, at the rate of about one per month.

He continued to write papers into his eighties, particularly in analytical areas of what would become the theory of dynamical systems.

Littlewood is also remembered for his book of reminiscences, A Mathematician's Miscellany (new edition published in 1986).

Among his own PhD students were Sarvadaman Chowla, Harold Davenport , Donald C. Spencer and Srinivasa Ramanujan. Spencer reported that in 1941 when he (Spencer) was about to get on the boat that would take him home to the United States, Littlewood reminded him: "n, n alpha, n beta!" (referring to Littlewood's conjecture).

Littlewood's collaborative work, carried out by correspondence, covered fields in Diophantine approximation and Waring's problem, in particular. In his other work, he collaborated with Raymond Paley on Littlewood–Paley theory in Fourier theory, and with Cyril Offord in combinatorial work on random sums, in developments that opened up fields that are still intensively studied.

He worked with Mary Cartwright on problems in differential equations arising out of early research on radar: their work foreshadowed the modern theory of dynamical systems. Littlewood's inequality on bilinear forms was a forerunner of the later Grothendieck tensor norm theory.

With Hardy

Littlewood collaborated for many years with G. H. Hardy. Together they devised the first Hardy–Littlewood conjecture, a strong form of the twin prime conjecture, and the second Hardy–Littlewood conjecture.

In a 1947 lecture, the Danish mathematician Harald 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.'" [2] :xxvii

There is a story (related in the Miscellany) that at a conference Littlewood met a German mathematician who said he was most interested to discover that Littlewood really existed, as he had always assumed that Littlewood was a name used by Hardy for lesser work which he did not want to put out under his own name; Littlewood apparently roared with laughter. There are versions of this story involving both Norbert Wiener and Edmund Landau, who, it is claimed, "so doubted the existence of Littlewood that he made a special trip to Great Britain to see the man with his own eyes".[3]

See also


  1. ^ Burkill, J. C. (1978). "John Edensor Littlewood. 9 June 1885–6 September 1977". Biographical Memoirs of Fellows of the Royal Society 24: 322–326.  
  2. ^  
  3. ^  
  4. ^ Phillips, Keith L. (1967). "The Maximal Theorems of Hardy and Littlewood". Amer. Math. Monthly 74: 648–660.  

Further reading

External links

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