John Edensor Littlewood

John Edensor Littlewood

name = John Edensor Littlewood

imagesize = 150px
caption =
birth_date = birth date|1885|6|9|mf=y
birth_place = Rochester, Kent, England
death_date = death date and age|1977|9|6|1885|6|9|mf=y
death_place = Cambridge, England
residence =
nationality =
field = Mathematician
work_institution = University of Cambridge
alma_mater = University of Cambridge
doctoral_advisor = Ernest William Barnes
doctoral_students = Sarvadaman Chowla
Harold Davenport
Srinivasa Ramanujan
Stanley Skewes
Donald C. Spencer
known_for = Mathematical analysis
prizes =
religion =
footnotes =

John Edensor Littlewood (9 June 1885 – 6 September 1977) was a British mathematician, best known for his long collaboration with G. H. Hardy.


Littlewood was born in Rochester in Kent. He attended St Paul's School in London, where he was taught by F. S. Macaulay, now known for his contributions to ideal theory. He studied at Trinity College, Cambridge and was the Senior Wrangler in the Mathematical Tripos of 1905. He was elected a Fellow of Trinity College in 1908 and, apart from three years as Richardson Lecturer in the University of Manchester, his entire career was spent in the University of Cambridge. He was appointed Rouse Ball Professor of Mathematics in 1928, retiring in 1950. He was elected a Fellow of the Royal Society in 1916, awarded the Royal Medal in 1929, the Sylvester Medal in 1943 and the Copley Medal in 1958. He was president of the London Mathematical Society from 1941 to 1943, and was awarded the De Morgan Medal in 1938 and the Senior Berwick Prize in 1960.


Most of his 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.

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.

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

Among his own Ph. D. students were Sarvadaman Chowla, Harold Davenport and Donald C. Spencer.

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

He 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.'" [cite book
authorlink=Harald Bohr
title=Collected Mathematical Works
publisher=Dansk Matematisk Forening
chapter=Looking Backward
] Rp|xxvii

There is a story 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.Fact|date=September 2007

ee also

*Hardy-Littlewood circle method
*Littlewood's conjecture
*Littlewood's problem
*Littlewood's three principles of real analysis
*Littlewood-Offord problem


External links

* [ Papers of Littlewood on Number Theory]

NAME= Littlewood, John Edensor
DATE OF BIRTH= June 9 1885
PLACE OF BIRTH= Rochester, Kent, England
DATE OF DEATH= September 6 1977
PLACE OF DEATH= Cambridge, England

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