# Dudley Ernest Littlewood

### Born: 7 September 1903 in London, England

Died: 6 October 1979 in Llandudno, Wales

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**Dudley Littlewood**'s mother was Ada Piper and his father was Harry Bramley Littlewood who worked as a solicitor's clerk in London. Dudley was an only child, brought up in London through the years of World War I, and he attended Tottenham county school in Middlesex. In his final year at school he won a state scholarship and an open entrance scholarship to Trinity College, Cambridge. He entered Trinity College where his undergraduate tutor was J E Littlewood (who was not related to Dudley). Littlewood was a very successful mathematics undergraduate being awarded College prizes and the Yeats prize. He graduated in 1925, the same year as Hall and Hodge also graduated from Cambridge, being a wrangler (first class student) in the Mathematical Tripos. He remained at Cambridge, where he began research in analysis, but it appears that he was neither sufficiently good or interested in analysis and, lacking financial support, decided to give up research and look for a job.

Littlewood's first appointment was as a school teacher, but, in 1928, he found a post as a temporary part-time lecturer at University College Swansea. He worked for a short time at Queen's College, Dundee (at that time part of the University of St Andrews) but returned to Swansea where he worked until 1947. He married Muriel Doris Dyson in 1930 and they had one child, a son born in 1935. His part-time position became an assistant lectureship in 1930 and a lectureship in 1934. Although his research flourished in Swansea, Littlewood was keen to return to Cambridge and, when the chance came in 1947, he accepted a post as university lecturer. It was not a College appointment so he only had an office through the kindness of Hodge. Littlewood's family were not happy with the move to Cambridge but he did not remain there long for in 1948 he was appointed to the chair of mathematics at the University College of North Wales, Bangor.

Until Littlewood's appointment to Swansea he had no definite research interests. However at Swansea the professor, Archibald Read Richardson, was an algebraist who, according to [2], was 'bursting with problems', and he introduced Littlewood to research in algebra. His first work was on quaternion algebras and some of his first papers were written jointly with A R Richardson. During this period, developments of his first papers led to further work in which he laid the foundations of invariant theory of forms in non-commutative algebra.

Invariant theory was at its height in the 19

^{th}century with the work of Cayley, Sylvester, Clebsch, Gordan and others. Littlewood claimed that:-

Another reason was certainly the work of Hilbert, but Littlewood tried to remedy the "tensor reason" in a series of papers on tensors and invariant theory.... interest in invariant theory had flagged somewhat, one reason for this being the introduction of tensors.

Littlewood's main work, however, began in 1934 after Richardson had suggested that Littlewood study papers by Frobenius and Schur. The two Swansea mathematicians then collaborated on

*Group characters and algebras*which was published in the

*Philosophical transactions of The Royal Society*in 1934 [1]:-

This marks the beginning of Littlewood's investigation of group characters, in particular the characters of the symmetric group. He examinedIn 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).

*S*-functions and applied these to invariant theory. He also studied quantum mechanics and some of the problems in representation theory he considered were motivated by this. He published three books perhaps the first

*The theory of group characters and matrix representations of groups*(1940) being the most famous.

J A Green, a student of Littlewood's, summed up his approach to mathematics writing:-

In [3] the authors write:-Littlewood's mathematical strength lay in his extraordinary insight into the way certain algebraic processes worked.

Morris writes in [2]:-He clearly had a strong intuitive grasp of formal mathematics and when he felt a result to be true he could be perfunctory about its proof. Littlewood had a great love for the works of Frobenius, Schur and Weyl - these were mathematicians who produced the kind of usable formulae which he could and did appreciate. But he did not appreciate their mathematical rigour, he grasped their methods and results and he proceeded to develop them in his own fashion.

In 1970 Littlewood retired from the chair at Bangor, but he continued to live at Llandudno on the North Wales coast. Around the time of his 76Littlewood also had a profound interest in philosophy and religion, which he regarded as 'subjects far more worthy of investigation than mathematics' ... . On his retirement in1970he 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.

^{th}birthday, Littlewood fell and broke a leg. He died suddenly a few weeks later at his home. He was buried at Llanrhos, just south of Llandudno, where parts of the ancient church date back to the 6

^{th}century. His wife Muriel died ten years later.

**Article by:** *J J O'Connor* and *E F Robertson*

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