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John Edensor Littlewood
J.E. Littlewood
Born	June 9, 1885(1885-06-09) Rochester, Kent, England
Died	September 6, 1977 (aged 92) Cambridge, England
Residence	UK
Nationality	British
Field	Mathematician
Institutions	University of Cambridge
Alma mater	University of Cambridge
Academic advisor	Ernest William Barnes
Notable students	Sarvadaman Chowla Harold Davenport Srinivasa Ramanujan Stanley Skewes Donald C. Spencer
Known for	Mathematical analysis

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 went to 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.

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 reported a colleague's joke that "Nowadays, there are only three really great English mathematicians: Hardy, Littlewood, and Hardy-Littlewood." In retelling, it is often added that the latter was the greatest of the three.^{[citation needed]}

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.^{[citation needed]}

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

• O'Connor, John J; Edmund F. Robertson "John Edensor Littlewood". MacTutor History of Mathematics archive.  
• John Edensor Littlewood at the Mathematics Genealogy Project
• Papers of Littlewood on Number Theory

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