DR A. C. AITKEN

Evening Star, Issue 21503, 30 August 1933, Page 7

DR A. C. AITKEN

HONOURED IN EDINBURGH At a meeti/ig of the Session of the Royal Society of Edinburgh, held last month, the Makdougall-Brisbane Prize was presented to Dr A. C. Aitken (formerly of Dunedin). Principal Sir Thomas Holland, who presided, said that in the last ten years Dr Aitken had published over thirty original! papers, which had effected considerable advances in three branches of mathematical science—namely, numerical mathematics, the theory of matrices and determinants, and the mathematical theory of statistics. The earlier; papers related chiefly to numerical mathematics, including interpolation, numerical integration, and differentiation,; and the solution of algebraic and simultaneous equations. The original impetus towards this field of work doubtless came from his own extraordinary powers in mental arithmetic; for the benefit of those of them who were not gifted in this way he had devised methods by which most of the problems with which the practical mathematician was confronted could be reduced to repetitions of a process peculiarly suited to an arithnometer—namely, a_ crossmultiplication followed by a division.As a by-product of his interest in' interpolation, finite differences, and operational methods, he discovered in 1929 a remarkable and powerful general theorem which comprehended in one formula Taylor’s Theorem and the other expansion theorems of the ‘ Differential Calculus,’ all “ single-line ”• difference interpolation formulas, and a’ multitude of other possibilities. A 1 paper which he published in the ‘ Proceedings ’ in 1926, on Bernoulli’s method of solving algebraic equations and extensions of it ? led him by_ way of symmetric functions to the wider field of algebra. In 1927 he discovered a dual theorem on determinantal symmetric functions which contained theorems of Jacobi and MacMabou _aa special cases, and joined the determine autal theory of symmetric functions to the combinatory theory. Regarding algebraic equations from another point of view—namely, _ as the characteristic equations of matrices, he made many original contributions to the general theory of matrices, particularly in regard to matrices with multiple latent roots. Much of this work had appeared in the book on * Canonical Matrices ’ which he published in collaboration with Professor Turnbull last’ year, and which was recognised by, mathematicians as opening a new era iii tlio history of the subject, Lastly, mention had to be made of his researches on mathematical statistics and frequency functions. In 1930,working with Dr Oppenheim, he showed that though the frequency function of Type A in Heirite polynomials had terms of irregular order of magnitude* the logarithm of the function, so expanded, had terms regularly descending. In 1931 he proved the analogous result for Type B and its logarithm,with the appropriate polynominals. In his most recently published paper ha had examined the fitting of polynominals to data by least squares with' Tchebychef polynominals, finding new forms for the polynominals and new and rapid methods based thereon. The admiration with which mathematicians regarded the formal beauty and architectural elegance of Dr Aitkcn’s work in algebra was reinforced by the gratitude they felt for the many new practical methods which he had placed at tho •disposal of the computers