# A.C. AITKEN (1895 -- 1967)

## P.C. Fenton

Alexander Craig Aitken was born 100 years ago, on 1 April 1895, in Dunedin, New Zealand. His work in actuarial mathematics and statistics has been widely influential, and he made important contributions to linear algebra. E.T. Whittaker's comment that Aitken was the best algebraist since Cayley has undertones of British insularity, but conveys the sense of Aitken's eminence. A conference marking the centenary of Aitken's birth and representing the main themes of his work is to be held at his alma mater, the University of Otago in Dunedin from 28 August to 1 September 1995.

Setting aside a period of service in the Middle East and France during the Great War, Aitken spent his first twenty eight years in Dunedin. All the main threads of his life have their origins there, though it would be an affront both to Aitken and to those of us currently traversing the undulations of middle and later age to neglect subsequent influences, some of which are critical to an understanding of him. Nevertheless in the late 1950s Aitken wrote:

[J]ust as the first part of my academic career, up to my arrival in Edinburgh, was quite chaotic and unorthodox, so the second half has been conventional, and could be easily reconstructed by anyone with the indications in Who's Who.

The tone is as usual self-deprecatory but also reflects a certain weariness that periodically took possession of him.

Aitken was the eldest of seven children of William Aitken, a grocer, and his wife, the former Elizabeth Towers. William had been born of intelligent, rural Scots parents at Maungatua, a small settlement twenty miles from Dunedin. Elizabeth had arrived in New Zealand at the age of 7 from Wolverhampton, though her parents too were Scots. The Aitken household was materially poor but not deprived. William's gentle simplicity and indifference to worldly attainment was absorbed by the children, and is the source of the same qualities so often remarked upon in Aitken. Aitken's memory and calculative power, both of which are legendary - he could recite the first 1000 decimal places of $\pi$ and was considered the most impressive mental calculator for whom reliable records exist - were present early, and his first years at school were remarkable, without necessarily suggesting the extent of his later achievement. He took off'' as he put it, in middle adolescence, under the influence of his mathematics master at Otago Boys' High School, the extraordinary W.J. Martyn. He began to exercise his calculative ability and to build up an immense arithmetic landscape. One has the sense that in many calculations Aitken was able to avoid large computational steps by drawing on memory, with the same kind of intuitive certainty with which a navigator might draw on subconscious representations of known topographical features to determine a course. A much-quoted example illustrates the point. Aitken was asked by his children to multiply 123456789 by 987654321.

I saw in a flash that 987654321 by 81 equals 80000000001; and so I multiplied 123456789 by this, a simple matter, and divided the answer by 81. Answer: 121932631112635269. The whole thing could hardly have taken more than half a minute.

His memory developed in other directions: as a boy he knew the Aeneid by heart. During school holidays Aitken stayed with his grandparents on their farm on the Otago Peninsula, an area that abuts the outer suburbs of Dunedin while keeping its own, quite separate identity. Out of his wanderings over the Peninsula developed his profound love of the natural world, one of the romantic elements that, in combination with certain classical tendencies - mathematics of course, athletics and music, and classical art and literature - produced the vibrance of the mature Aitken. Music was central to his life. Eric Fenby, Delius's amanuensis, who described Aitken as the most accomplished amateur musician he had known, wrote to him:

At our first meeting it was evident to me that I had not met a man like you before, and it has been my privilege to know several men of most outstanding power, but not one of their several occupations called for the sustained effort of brain and memory imperative in yours. ... I thank God that you have your Bach. No composer could possibly appeal to and satisfy your whole complicated nature as he.

Aitken entered the University of Otago in 1913, enrolled in mathematics, French and Latin. The effect of the Mathematics Department in the person of Professor D.J. Richards, a temperamental, eccentric Welshman, who seemed to lack the power to communicate his knowledge to his students'', was to turn Aitken's interests, hitherto balanced between mathematics and languages, distinctly towards the latter. With the war in Europe, Aitken volunteered on his twentieth birthday, in time to participate in the latter stages of the Gallipoli debacle. He was commissioned in the field in northern France, and was wounded in one of the countless raids that filled gaps between bombardments and helped to make up the Battle of the Somme. Invalided home in 1917, he passed a year of recuperative inactivity in Dunedin during which he wrote a draft of the memoir published later as Gallipoli to the Somme (1967). For this work he was elected a fellow of the Royal Society of Literature.

Aitken resumed his studies in 1918. In 1919 he was elected President of the Students' Association and became one of their most effective presidents, bringing order to the Association's slapdash procedures and straightening out a financial mess that threatened scandal. In his final examinations Aitken and other colonial mathematics students were undone by a paper of impossible difficulty, set from the splendid isolation of Home. He graduated with first class honours in languages but only a second in mathematics. Bitterly disappointed, he abandoned the idea of a career in mathematics and took a job teaching, mainly languages and geography, at his old high school.

Aitken was married in 1920 to Winifred Betts, a brilliant student of botany who became the first female lecturer at the University of Otago. When R.J.T. Bell, Richards's successor to the chair of Mathematics, required an assistant he called on Aitken, and with Bell's encouragement Aitken's mathematical ambitions revived. He applied for and was awarded a University of New Zealand scholarship to study under E.T. Whittaker at Edinburgh. Aitken left New Zealand in July 1923, Winifred joining him at the conclusion of the academic year.

Aitken's thesis, on the graduation of observational data, was completed in 1925, but at great personal cost. He suffered a severe breakdown in 1927 which permanently altered his outlook, though not entirely for ill. He wrote:

[S]ince that time, there is not a tree, not a turn in the road, not a hill-top, not even a swaying reed, but speaks of the beauty, the terrible beauty and mystery of the world.

Aitken was appointed to the staff at Edinburgh as Lecturer in Actuarial Mathematics in 1925, was promoted to Reader following his FRS in 1936, and was invited to take up the chair of Pure Mathematics, my real line'' as he put it, on Whittaker's retirement in 1948.

To an unusual extent Aitken was able to incorporate his extraordinary abilities into a view of humanity that gave primacy to pure being. Despite recurrent illness, his simplicity and natural grace were refined by age. He died on 3 November 1967.

University of Otago
Dunedin, New Zealand

# The A.C. AITKEN CENTENARY CONFERENCE

The conference will be held at the University of Otago in Dunedin over the period 28 August-1 September 1995, to celebrate the life and work of this famous New Zealand mathematician who was born 1 April 1895. The conference is sponsored by the Australasian Region of the Biometrics Society, the New Zealand Statistical Association, and the Statistical Society of Australia. In keeping with A.C. Aitken's own interests, the themes of the conference will be actuarial mathematics, numerical analysis, linear algebra and statistics.

Further details are given conference list .

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