John Edensor Littlewood

John Edensor Littlewood (9 June 1885 – 6 September 1977)^[1] was a British mathematician, best known for the results achieved in collaboration with G. H. Hardy.

Life [edit]

Littlewood was born in Rochester in Kent. He lived in Wynberg in Cape Town from 1892 to 1900 where his father (a 9th wrangler) was a headmaster. He then attended St Paul's School in London for three years, 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.

John Edensor Littlewood was born in 1885, the son of Edward Thornton Littlewood and Sylvia Ackland. His unusual middle name came about as it was the maiden name of his great-great-grandmother Sarah Edensor, who married Thomas Littlewood.

Work [edit]

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. However, the link between the Riemann hypothesis and the Prime Number Theorem had been known before in Continental Europe, and Littlewood also wrote later in his book A mathematician’s miscellany that his actually only rediscovered result did not shed a bright light on the isolated state 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.

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. 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).

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 on Littlewood–Paley theory 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 [edit]

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.'" ^{[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.^{[citation needed]} 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 [edit]

• Critical line theorem
• Hardy–Littlewood circle method
• Hardy–Littlewood zeta-function conjectures
• Littlewood's conjecture
• Littlewood polynomial
• Littlewood's three principles of real analysis
• Littlewood–Offord problem
• Hardy–Littlewood tauberian theorem
• Hardy–Littlewood maximal function
• Littlewood subordination theorem

Notes [edit]

Further reading [edit]

• Littlewood's Miscellany, edited by B. Bollobás, Cambridge University Press; 1986. ISBN 0-521-33702-X (alternative title for A Mathematician's Miscellany)

External links [edit]

Wikiquote has a collection of quotations related to: John Edensor Littlewood

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