Aitken, Alexander Craig

(1895-1967), mathematician

by J. M. Whittaker, rev. Anita McConnell

© Oxford University Press 2004 All rights reserved

Aitken, Alexander Craig (1895-1967), mathematician, was born at Dunedin, New Zealand, on 1 April 1895, the eldest of the seven children of William Aitken and his wife, Elizabeth Towers. His grandfather Alexander Aitken had emigrated from Lanarkshire to Otago in 1868 and farmed in the neighbourhood of Dunedin. Aitken's father, one of fourteen children, left the farm to work as a grocer in Dunedin, and subsequently acquired the business. Aitken's mother was born in Wolverhampton and went to New Zealand at the age of eight.

Aitken became head boy of Otago Boys' High School in 1912 and won first place in the entrance scholarship examination to Otago University. His most striking characteristic at this stage was a phenomenal memory, and he had not shown any special bent for mathematics. He decided on a course combining languages with mathematics, but this was soon interrupted by the outbreak of war in 1914. He enlisted as a private soldier in the New Zealand expeditionary force and reached Gallipoli in November 1915 with the 6th infantry reinforcements, five weeks before the evacuation. Subsequently he served in France and was commissioned on the field of battle. He was badly wounded in a raid during the battle of the Somme and in March 1917 was invalided home to New Zealand. Before resuming his interrupted university career he wrote an account of his wartime experiences. His continuing anguish about those experiences caused him, forty-five years later with but little revision, to publish the work as Gallipoli to the Somme: Recollections of a New Zealand Infantryman (1963), which won the Hawthornden prize. In 1920 Aitken married Mary Winifred, daughter of Alfred Betts, of Nelson, New Zealand. She was a lecturer in botany at Otago University from 1916 to 1923. They had two children, a boy and a girl.

Mathematics was at a low ebb in Otago because there was no professor until R. J. T. Bell arrived from Glasgow in 1920. This may explain why in 1920 Aitken gained only a second-class degree in mathematics, although he achieved a first class in languages and literature (Latin and French). Nevertheless he decided to pursue mathematics: after three years as a master at his old school, in 1923 he was awarded a postgraduate scholarship and went to Edinburgh University to work under E. T. Whittaker, who was greatly interested in numerical mathematics and in 1913 had founded the only mathematical laboratory in the country. Since one of Whittaker's closest friends was G. J. Lidstone, the leading actuary of his time, Aitken was given a problem of actuarial interest as his doctoral subject: the graduation or the fitting of a smooth curve to a set of points subject to statistical error. Whittaker had taken the first step towards providing the subject with a rational basis but his formula was unsuited to numerical calculation. Aitken overcame the difficulty, an achievement for which he was awarded a DSc in 1926. The rest of his life, all of which was spent in Edinburgh, was devoted to the closely linked disciplines of numerical mathematics, statistics, and the algebra of matrices.

Numerical mathematics is a difficult subject to appraise since it is dependent on the characteristics of the machines or tables in use at the time. Mechanical calculating machines were in common use in industry and commerce but their cost, and not less their noise, precluded their use in a class of fifty students. Whittaker considered that a properly trained student could do nearly as well with tables. It was on this basis that Aitken took over the conduct of the laboratory. He discovered two new devices which have passed into general use: 'Aitken's d-process', by which a sequence may be transformed into one more rapidly convergent; and the Neville-Aitken method in finite difference theory, by which the values of the interpolating polynomial at a series of equidistant points can be discovered without having to find the polynomial explicitly.

In 1925 Aitken was appointed as lecturer in actuarial mathematics at Edinburgh and in 1936 he became a reader in statistics. Much of his later work belongs to statistics, and the mathematics to which it gives rise. Aitken was also interested in decimal coinage, and broadcast on the subject. He succeeded Whittaker in the Edinburgh chair of mathematics when the latter retired in 1946. He himself retired in 1965.

Aitken was renowned for his powers of mental calculation. They were the subject of a paper by the psychologist I. M. L. Hunter, who concluded that his skill possibly exceeded that of any other person for whom precise authenticated records existed. Aitken, a violinist and close friend of the musician Sir D. F. Tovey, said that he gave roughly four times as much thought to music as to mathematics. Physically he was short and slight; he was a leading high-jumper in his youth and a keen hill walker in his Edinburgh days.

Aitken was elected FRS in 1936 and for several terms was a vice-president of the Royal Society of Edinburgh, to which he had been elected in 1925. The universities of Glasgow and New Zealand awarded him honorary degrees. He was also a fellow of the Royal Society of Literature, and an honorary fellow of the Royal Society of New Zealand and of the Faculty of Actuaries. Aitken died at 153 Morningside Drive, Edinburgh, on 3 November 1967. He was survived by his wife.

J. M. WHITTAKER, rev. ANITA MCCONNELL

Sources  
J. M. Whittaker and M. S. Bartlett, Memoirs FRS, 14 (1968), 1-14
Proceedings of the Edinburgh Mathematical Society, 16 (1968), 151-76
The Times (6 Nov 1967), 10g
The Times (7 Nov 1967), 12h
The Times (22 Nov 1967), 12h
I. M. L. Hunter, 'An exceptional talent for calculative thinking', British Journal of Psychology, 53 (1962), 243-58
d. cert.

Archives  
Trinity Cam., corresp. with Harold Davenport
U. Edin. L., letters to I. Hunter
U. St Andr. L., corresp. with Sir D'Arcy Thompson

Likenesses  
P. Shillabeer, photograph, 1925, RS; repro. in Whittaker and Bartlett, Memoirs FRS
W. Stoneman, photograph, 1945, NPG [see illus.]
photograph, repro. in Proceedings of the Royal Edinburgh Mathematical Society

Wealth at death  
£34,124 17s.: confirmation, 13 Dec 1967, CCI


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