John Edensor Littlewood produced fundamental contributions to analysis, number theory, and the theory of differential equations throughout a career primarily centered at the University of Cambridge. Between 1903 and 1950, he occupied various academic roles at Trinity College, ultimately serving as the Rouse Ball Professor of Mathematics for over two decades while establishing far-reaching research partnerships.
Academic Formation and Early Research
Educated at St Paul's School and Trinity College, Cambridge, Littlewood emerged as Senior Wrangler in 1905. His early research, conducted under the supervision of Ernest Barnes, focused on the Riemann hypothesis. Although he did not prove the hypothesis, his work on the error term of the prime-counting function earned him a Trinity fellowship in 1908. He briefly taught at the Victoria University of Manchester before returning to Cambridge in 1910.
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Littlewood maintained a significant, multi-decade collaboration with G. H. Hardy, focusing on Diophantine approximation and Waring's problem. Their joint output includes the Hardy–Littlewood circle method, the Hardy–Littlewood maximal function, and the Hardy–Littlewood tauberian theorem. Together with Hardy, he championed the work of Srinivasa Ramanujan. Additionally, he worked with Raymond Paley on Fourier theory and Cyril Offord on random sums.
Differential Equations and Dynamical Systems
In the late 1930s, Littlewood collaborated with Mary Cartwright on the properties of non-linear differential equations, research spurred by developments in radar technology. Their findings concerning these equations provided a precursor to the modern theory of dynamical systems. His mathematical contributions also extend to the Littlewood polynomial, Littlewood's three principles of real analysis, and the 4/3 inequality on bilinear forms.
Professional Recognition and Legacy
His accolades include the 1938 De Morgan Medal, the 1943 Sylvester Medal, the 1958 Copley Medal, and the 1960 Senior Berwick Prize. He documented his career in A Mathematician's Miscellany.
Fast facts
- Born: 1885, Rochester
- Died: 1977, Cambridge
- Education: St Paul's School, Trinity College
- Fellow of the Royal Society: 1916
- Rouse Ball Professor of Mathematics: 1928-1950
- Notable awards: Copley Medal, Sylvester Medal, De Morgan Medal
- Primary research fields: Number theory, mathematical analysis
Questions readers ask
What is the Hardy–Littlewood circle method?
It is a central technique in analytical number theory developed by Littlewood and G. H. Hardy to approach problems like Waring's problem.
Did Littlewood work exclusively on pure mathematics?
No, he also contributed to applied mathematics, particularly through his significant work in ballistics and his research on non-linear differential equations.
Achievements
- Fellow of the Royal Society — 1916
- Copley Medal — 1958
- Royal Medal — 1929
- De Morgan Medal — 1938
- Senior Berwick Prize — 1960
- Notable work: First Hardy–Littlewood conjecture
- Notable work: Second Hardy–Littlewood conjecture
- Notable work: Hardy–Littlewood circle method
- Notable work: Hardy–Littlewood inequality
- Held posts at Victoria University of Manchester, Trinity College and University of Cambridge
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