Littlewood, Dudley Ernest

(1903-1979), mathematician

by A. O. Morris

© Oxford University Press 2004 All rights reserved

Littlewood, Dudley Ernest (1903-1979), mathematician, was born on 7 September 1903 at 289 Kennington Road, London, the only child of Harry Bramley Littlewood, a solicitor's clerk, and his wife, Ada Piper. He was educated at Tottenham county school, Middlesex, and Trinity College, Cambridge, supported by a state scholarship and a major open entrance scholarship. He was in the first class in part one, and graduated in 1925 as a wrangler with distinction, having earlier been awarded college prizes and a share of the Yeats prize. After one unproductive year of research in Cambridge working in analysis, he was forced, mainly for financial reasons, to seek employment. After a number of temporary positions as a schoolteacher he was appointed in 1928 as a temporary part-time lecturer at University College, Swansea. Except for a short period as an assistant at University College, Dundee, he remained at Swansea until 1947, first as assistant lecturer (from 1930) and as lecturer from 1934. He was then appointed university lecturer at Cambridge, but after a short period returned to Wales, in 1948, to the chair of mathematics at the University College of North Wales, Bangor, where he remained until his retirement in 1970. In 1930 he married Muriel Doris Dyson (1901-1989); their only son was born in 1935.

At Swansea Littlewood found that Archibald Read Richardson (1881-1954), the professor of mathematics, who had a considerable reputation as an algebraist, was 'bursting with problems' (Barker and Brown); he immediately set to work on these, producing a series of papers, but this early work did not truly fire his imagination--indeed, it had little long term impact. In the meantime, again at the instigation of Richardson, Littlewood studied the work of the leading German algebraists Ferdinand Georg Frobenius (1849-1917) and Issai Schur (1875-1941). This resulted in his joint paper with Richardson, 'Group characters and algebras' (PTRS, 233A, 1934, 99-141), which laid the foundation for his life's work. In it they introduced the 'immanant' of a matrix (a generalization of the determinant and permanent) and its relationship with a class of symmetric functions, which they christened S-functions (or Schur functions). Above all, this paper is renowned for its statement of a rule for multiplying S-functions, now universally called the Littlewood-Richardson rule (this had to wait a further thirty-five years for a rigorous proof). There followed in quick succession a number of papers in which Littlewood developed these ideas and discovered a number of fascinating combinatorial formulae involving S-functions. This led to his monograph, The Theory of Group Characters and Matrix Representations of Groups (1940). He continued to be a prolific author, applying S-functions skilfully to classical invariant theory. As a by-product he obtained a new purely combinatorial definition of S-functions in terms of tableaux and introduced his new multiplication of S-functions which he called 'plethysm'. His many original ideas had to wait for almost half a century before they were taken up in the modern area of algebraic combinatorics.

There were other major contributions; for example, Littlewood introduced some of the basic combinatorial ideas on the modular representations of the symmetric groups. His last major acknowledged contribution was a generalization of his beloved S-functions, now called the Hall-Littlewood functions (named after him and Phillip Hall, his Trinity contemporary). His elegant combinatorial definition of these laid the foundation for a new area of research with applications on a broad front.

Littlewood also had a passionate interest in the fundamental problems of theoretical physics with a belief that S-functions could be used profitably in this context. In the early sixties he was left bitter and despondent when his proposed unified field theory was rejected by the Royal Society. His Trinity tutor J. E. Littlewood's comment that 'his has always been an unusual type of mind' (private information) was truly perceptive and could explain the lack of recognition during his lifetime. His style was reminiscent of an earlier generation but in some respects he could be regarded as a man before his time.

Littlewood did not appreciate mathematical rigour--he had a strong intuitive grasp of formal mathematics--and when he felt a result to be true he could be perfunctory about its proof. He had little direct contact with his contemporaries, felt isolated, and later became quite depressed by the absence of interest in his work. Towards the end of his life he was gratified with the growing interest in his ideas; he would have been overwhelmed by their impact later--he has come to be regarded as a master of the usable formula.

Littlewood also had a profound interest in philosophy and religion, which he regarded as 'subjects far more worthy of investigation than mathematics' (private information). On his retirement in 1970 he wrote up his ideas in an unpublished manuscript, 'In search of wisdom'. He was an avid reader of science fiction, shy and retiring by nature, always with a friendly smile; kind, caring, and supportive in an unobtrusive way. Littlewood died suddenly at his home, Melrose, Queens Road, Llandudno, on 6 October 1979, a few weeks after breaking a leg. He was buried in Llan-rhos, Llandudno.

A. O. MORRIS

Sources  
A. O. Morris and C. C. H. Barker, Bulletin of the London Mathematical Society, 15 (1983), 56-9
C. C. H. Barker and R. Brown, University College of North Wales, Bangor, Gazette, 19 (1980), 11-12
personal knowledge (2004)
private information (2004)
b. cert.
d. cert.
m. cert.

Likenesses  
photograph, repro. in Morris and Barker, Bulletin of the London Mathematical Society, 57

Wealth at death  
£73,750: probate, 8 Jan 1980, CGPLA Eng. & Wales


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