Proceedings of the Edinburgh Mathematical Society (Series 2)

Research Article

The Contributions of E. T. Whittaker to Algebra and Numerical Analysis

A. C. Aitkena1

a1 The Mathematical Institute, The University Edinburgh

Whittaker's contributions to algebra are not numerous and are confined to special problems ; in one or two cases they are rediscoveries, of the kind that add a certain illumination to the original. His outlook on algebra was that of his time ; one might characterise it by referring to the spirit and content of Perron's Algebra, as contrasted with the Moderne Algebra of van der Waerden. Bred in the Cayley-Sylvester tradition of matrix algebra and the invariant theory of forms, he was expert also in the manipulation of continued fractions and determinants. His lectures to honours classes in Edinburgh always included a course on matrices, vector analysis and invariants, historical reference being made to Grassmann, Cayley and Sylvester; it is to such a course that the writer owes his first acquaintance with matrix algebra. In later years, from about 1925, Whittaker acquired an adequate knowledge, though never a marked taste, for those parts of modern abstract algebra, in particular the representation of groups and algebras, that serve a purpose in mathematical physics; his courses of research lectures, which he kept up until a late period in his tenure of the chair, bore witness of this.