by T. Chaundy, rev. Karen Hunger Parshall

© Oxford University Press 2004 All rights reserved

**Elliott, Edwin Bailey** (1851-1937), mathematician, was born on 1 June 1851 at 35 Cornmarket Street, Oxford, the eldest son of Edwin Litchfield Elliott, shoemaker, and his wife, Matilda Bailey. He was educated at Magdalen College School, Oxford, and in 1869 went up to Magdalen College with a demyship. He graduated in 1873 after having earned first classes both in moderations (1872) and in the final school (1873). The following year, he won the senior university mathematical scholarship and was elected fellow and mathematical tutor of Queen's College. He held this post until 1892, when he was appointed the first Waynflete professor of pure mathematics, a chair that carried with it a fellowship at Magdalen College. He would hold both until his retirement as professor emeritus in 1921. From 1884 to 1893, he also served as a lecturer in mathematics at Corpus Christi College. On 29 June 1893 Charlotte Amelia Mawer *(d.* 1937), the daughter of John William Mawer, a hosier, married Elliott in an Anglican ceremony. The couple had no children and spent their married life in Oxford, principally at 4 Bardwell Road.

Elliott was an active member of the university and of the British mathematical communities. At Oxford he served as member of the hebdomadal council, visitor of the observatory, curator of the university chest, and delegate of the common university fund. His work with the last involved the influential task of appointing professors and lecturers at Oxford in fields that did not have permanent endowments. His opinion was also regularly sought on financial matters, where his strength lay more in exactness of detail than in boldness of conception. He put this talent to use in a broader civic context through his service as a trustee of the Oxford city charities and as a treasurer of the Oxford Eye Hospital. Beyond Oxford, Elliott played an active role in the London Mathematical Society, joining in 1875, serving on the organization's governing council, and assuming its presidency for the two-year term 1896-8. He was elected FRS in 1891.

Elliott's mathematical life thus circulated around the twin foci of Oxford and London. Besides his work in formal teaching and lecturing at Oxford he was one of the founders (1888) of the Oxford Mathematical Society, its first secretary, and later its president.

Elliott wrote some sixty articles and notes during his mathematical career which appeared almost exclusively in English mathematical publications. Of note among these was his paper entitled 'The interchange of the variables in certain linear differential operators' *(Philosophical Transactions of the Royal Society of London,* 181, 1890, 19-51). There he continued the algebraical research he had begun in 1886 on reciprocants, that is, differential forms which remain invariant under the action of a linear transformation of their variables. J. J. Sylvester had sparked the interest of the Oxford mathematical community in this topic in 1885 when he introduced the new theory, in the context of binary forms only, in his inaugural lecture as Savilian professor of geometry. A flurry of research ensued, including Elliott's paper of 1890 which extended Sylvester's work to forms in more than two variables. As Elliott came to recognize in 1898, however, his research on reciprocants represented but a special case of the theory of continuous groups developed on the continent by the Norwegian mathematician, Sophus Lie, and others.

Elliott's mathematical interests extended beyond differential invariant theory to the theory of elliptic functions, number theory, geometry, and the theories of convergence and integral equations. He made his most influential contribution in the theory of algebraic invariants, however, in the form of his book *An Introduction to the Algebra of Quantics* (1895; 2nd edn, 1913). Arthur Cayley, J. J. Sylvester, and others, both in Great Britain and on the continent, had developed algebraic invariant theory, that is, the study of homogeneous expressions in the coefficients of algebraic forms in *n* variables (or n-ary quantics) which remain essentially unchanged under the action of a linear transformation of non-zero determinant. In his book Elliott gave a readable and self-contained account of this area as it had developed, particularly in Britain. This text served to introduce a generation of English-speaking mathematicians to the subject and remains a valuable resource for penetrating the work of its late nineteenth-century British practitioners. In his presentation, Elliott largely eschewed the purely symbolic methods that characterized the continental approach to the theory, preferring instead the more direct, more immediately constructive techniques devised principally by his own countrymen.

Elliott made his final noteworthy mathematical contribution to the theory of integral equations. In his 1926 paper, 'A simple exposition of some recently proved facts as to convergency' *(Journal of the London Mathematical Society),* he gave a new, simple, and intrinsic demonstration of a key inequality in the area. His method of proof, which had eluded the efforts of such mathematicians as Issai Schur, Edmund Landau, G. H. Hardy, and J. E. Littlewood, attests to his powers as a mathematician.

Elliott's other interests lay in music, natural history, and literature. As evidence of the latter, he and a colleague founded the Addison Society, the oldest literary society at Queen's College. In 1916, Queen's acknowledged Elliott's achievements by electing him to an honorary fellowship.

In demeanour Elliott was modest and retiring, hesitant in speech, and always willing to help others. He was conservative in university as well as in national politics, deploring many of the changes that he had seen both in the city and in the university. Though he published well into the twentieth century, he persisted in doing mathematics in a largely late nineteenth-century style. As his independent discovery in 1898 of Lie's earlier and more general researches on differential invariants exemplifies, he tended to work in relative isolation at a time when mathematics was becoming increasingly international.

Elliott's wife died in May 1937. Elliott himself died of pulmonary congestion and the complications of surgery for a strangulated hernia at the Acland Nursing Home, Banbury Road, Oxford on 21 July 1937. He was buried three days later, on 24 July, at the Holywell cemetery in Oxford.

T. CHAUNDY, *rev.* KAREN HUNGER PARSHALL

**Sources **

H. W. Turnbull, *Obits. FRS,* 2 (1936-8), 425-31

*The Times* (23 July 1937)

K. H. Parshall, 'Towards a history of nineteenth-century invariant theory', *The history of modern mathematics,* ed. D. E. Rowe and J. McCleary, 1: *Ideas and their reception* (1989), 157-206

b. cert.

m. cert.

d. cert.

**Archives **

Magd. Oxf., MSS

**Likenesses **

photograph, repro. in Turnbull, *Obits. FRS*

**Wealth at death **

£25,646 17s. *1d.:* probate, 19 Aug 1937, *CGPLA Eng. & Wales*

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