Editing John Edensor Littlewood (section)

==Later life==

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 PhD 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]]).

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 transform|Fourier theory]], and with [[Cyril Offord]] in combinatorial work on random sums, in developments that opened up fields that are still intensively studied.

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.'{{thin space}}"<ref>
{{cite book
|last=Bohr
|first=Harald
|author-link=Harald Bohr
|title=Collected Mathematical Works
|volume=1
|year=1952
|publisher=Dansk Matematisk Forening
|location=Copenhagen
|oclc=3172542
|pages=xiii–xxxiv
|chapter=Looking Backward
|no-pp=true
}}
</ref> {{Rp|xxvii}}

The German mathematician [[Edmund Landau]] supposed that Littlewood was a pseudonym that Hardy used for his lesser work and "so doubted the existence of Littlewood that he made a special trip to Great Britain to see the man with his own eyes".<ref name="Krantz 1990 pp. 32–38">{{cite journal | last=Krantz | first=Steven G. | title=Mathematical anecdotes | journal=The Mathematical Intelligencer | volume=12 | issue=4 | date=1990 | issn=0343-6993 | doi=10.1007/BF03024029 | pages=32–38}}</ref>  He visited Cambridge where he saw much of Hardy but nothing of Littlewood and so considered his conjecture to be proven.  A similar story was told about [[Norbert Wiener]], who vehemently denied it in his autobiography.<ref>{{citation |journal=The American Mathematical Monthly |volume=96 |year=1989 |number=2 |title=Littlewood's Miscellany |author=Ralph P. Boas |pages=167–169 |doi=10.1080/00029890.1989.11972165}}</ref>  

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