Dudley Ernest Littlewood
Born: 7 Sept 1903 in London, England
Died: 6 Oct 1979 in Bangor, Wales
Dudley Littlewood was educated at Trinity College, Cambridge where his undergraduate tutor was Littlewood (J E) who was not related. He graduated in 1925, the same year as Hall and Hodge also graduated from Cambridge. He began research in analysis at Cambridge but it appears that he was neither sufficiently good or interested in analysis and, lacking financial support, decided to give up research.
Dudley's first appointment was as a school teacher, but, in 1928, he found a post as a 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.
Dudley was keen to return to Cambridge and, when the chance came in 1947, he accepted a post as College 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 soon he was appointed to the chair of mathematics at Bangor in 1948.
Until Littlewood's appointment to Swansea he had no definite research interests. However at Swansea the professor, A R Richardson, was an algebraist 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 when he began an investigation of group characters, in particular the characters of the symmetric group. He examined S-functions (named after Schur) and applied these to invariant theory. He also studied quantum mechanics and some of the problems in representation theory he considered were motivated from 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 [1] 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.