Mr McArthur was born at Dunmore Schoolhouse, West Loch Tarbert, Argyll, on June 13, 1883. He was the son of Mr Daniel McArthur, schoolmaster at Dunmore and later at St Catherines, Argyll, to which place the family moved in 1906. Mr McArthur completed his schooling at Whitehill School, Glasgow, and thence proceeded in 1900 to Glasgow University, where he graduated with First-Class Honours in Mathematics and Natural Philosophy in 1905. In the following year he was appointed Assistant to the Professor of Mathematics at Glasgow University, and thus began the long teaching career there which was to be his life-work. In 1908 he became a Lecturer and in 1920 Senior Lecturer; and after his retirement in 1948 he continued his connection with the Glasgow Mathematics Department as External Examiner, a position which he held at the time of his death.
Mr McArthur's career at Glasgow was interrupted by his period of service in the First World War. Early in the war he joined the Argyll and Sutherland Highlanders, served with distinction in France, was twice wounded, and was awarded the Military Medal. In the latter part of the war his mathematical abilities were recognised and he was transferred to the Sound Ranging Section of the Royal Engineers. In the Second World War he served as an Intelligence Officer with the District Commissioner in Glasgow.
Mr McArthur's quality as a mathematician was recognised outside his own Department. He was for a time Editor of the Proceedings of the Edinburgh Mathematical Society and was President of the Society in 1919-20. In 1946-47 he was President of the Glasgow Mathematical Association. He published papers under the auspices of both these societies, and was joint author, with Mr Alexander Keith, of a well-known textbook, Intermediate Algebra. In Glasgow University Mr McArthur gave devoted service not only in the administration of the Mathematics Department but also in wider spheres of university life. He was one of the first of the non-professorial staff to serve on the Senate, and in his last year on the staff he was Chairman of the Association of Lecturers and Assistants.
Mr McArthur will be remembered with respect and affection as a very able lecturer by all those who attended his classes. He was extremely interested in teaching, and was always devising new ways of presenting his subject. His range of interests extended far beyond the confines of mathematics. Widely read in general literature, he was especially attracted by all pertaining to the fine arts, especially painting, and he himself spent many happy hours sketching in water-colours. He was also a keen photographer.
Those who knew him well will remember his modest and retiring disposition, his upright character, and the wisdom, generosity and kindliness which marked all his actions. He always saw the best in people and never spoke uncharitably of anyone.
Mr McArthur was unmarried.
He was elected a Fellow of the Society in 1921.