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 , 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 19th century with the work of Cayley, Sylvester, Clebsch, Gordan and others. Littlewood claimed that:-
... interest in invariant theory had flagged somewhat, one reason for this being the introduction of tensors.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.
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 :-
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).This marks the beginning of Littlewood's investigation of group characters, in particular the characters of the symmetric group. He examined 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:-
Littlewood's mathematical strength lay in his extraordinary insight into the way certain algebraic processes worked.In  the authors write:-
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.Morris writes in :-
Littlewood also had a profound interest in philosophy and religion, which he regarded as 'subjects far more worthy of investigation than mathematics' ... . 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.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 76th 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 6th century. His wife Muriel died ten years later.
Article by: J J O'Connor and E F Robertson