约翰·恩瑟·李特尔伍德1885—1977

生平

利特尔伍德出生在肯特郡的罗彻斯特。他在伦敦的圣保罗学校上学，并在那里受到了F·S·麦考利的教育，现在因为他对理想理论的贡献而出名。利特尔伍德在剑桥大学三一学院学习，并在1905年的数学Tripos考试中成为Senior Wrangler。在1908年他被选为三一学院的研究员，除了在曼彻斯特大学担任理查德讲师的三年外，在他的职业生涯中，他都在剑桥大学度过。

1928年，李特尔伍德获得劳斯·鲍尔数学教授席位，直到1950年。

工作

他的大部分工作都是在数学分析领域中。他在欧内斯特·巴恩斯的指导下开始研究，巴恩斯说利特尔伍德曾经尝试过证明黎曼猜想：利特尔伍德证明了如果黎曼猜想是正确的，那么素数定理成立，并可得到误差项。这项工作使他成为了三一学院的一位研究员。

John Edensor Littlewood (9 June 1885 – 6 September 1977) was a British mathematician. He worked on topics relating to analysis, number theory, and differential equations and had lengthy collaborations with G. H. Hardy, Srinivasa Ramanujan and Mary Cartwright.

Biography

Littlewood was born on the 9th of June 1885 in Rochester, Kent, the eldest son of Edward Thornton Littlewood and Sylvia Maud (née Ackland). In 1892, his father accepted the headmastership of a school in Wynberg, Cape Town, in South Africa, taking his family there. Littlewood returned to Britain in 1900 to attend St Paul's School in London, studying under Francis Sowerby Macaulay, an influential algebraic geometer.

In 1903, Littlewood entered the University of Cambridge, studying in Trinity College. He spent his first two years preparing for the Tripos examinations which qualify undergraduates for a bachelor's degree where he emerged in 1905 as Senior Wrangler bracketed with James Mercer (Mercer had already graduated from the University of Manchester before attending Cambridge). In 1906, after completing the second part of the Tripos, he started his research under Ernest Barnes. One of the problems that Barnes suggested to Littlewood was to prove the Riemann hypothesis, an assignment at which he did not succeed. He was elected a Fellow of Trinity College in 1908. From October 1907 to June 1910, he worked as a Richardson Lecturer in the School of Mathematics at the University of Manchester.

Work

Most of Littlewood's 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 wrote later in his book, A Mathematician's Miscellany that his rediscovery of the result did not shed a positive light on the isolated nature of British mathematics at the time.

Theory of the distribution of prime numbers

In 1914, Littlewood published his first result in the field of analytic number theory concerning the error term of the prime-counting function. If π (x) denotes the number of primes up x, then the prime number theorem implies that π (x) Li (x), where Li (x) is the offset logarithmic integral.

Numerical evidence seemed to suggest that π (x)<Li (x) for all x. Littlewood, however proved that the difference π (x)-Li (x) changes sign infinitely often.

Military service WWI – ballistics work

During the Great War, Littlewood served in the Royal Garrison Artillery as a second lieutenant. He made highly significant contributions in the field of ballistics.

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

Cultural references

John Littlewood is depicted in two films covering the life of Ramanujan – Ramanujan in 2014 portrayed by Michael Lieber and The Man Who Knew Infinity in 2015 portrayed by Toby Jones.