He was born on 13th June 1883, in the schoolhouse of Dunmore on West Loch Tarbert at which his father, Daniel McArthur, was schoolmaster. After primary education at Dunmore he received his higher grade training at Whitehill School in Glasgow. He matriculated at the University of Glasgow in 1900 and graduated Master of Arts, with First Class Honours in Mathematics and Natural Philosophy, in 1905, thereafter taking the Degree of Bachelor of Science.
In 1906 Mr McArthur was appointed an Assistant on the staff of the Professor of Mathematics in the University of Glasgow. He was promoted to a Lectureship in 1908, and became Senior Lecturer in the Department in 1920. From 1906 until his retirement in 1948 his service in the Department was broken only by military service during the First World War. As an Argyll man he enlisted in the Argyll and Sutherland Highlanders, with whom he had a distinguished career on active service in France, gaining the Military Medal. He was twice wounded in action. Later he was transferred to the Sound-ranging Section of the Royal Engineers in a somewhat belated attempt to make use of his mathematical ability. During the Second World War he gave part-time service as an Intelligence Officer on the staff of the District Commissioner for Civil Defence in the West of Scotland, and in the Home Guard.
Mr McArthur served for a time as Editor of the Proceedings of this Society and was President in Session 1919-20. He was President of the Glasgow Mathematical Association in 1946-47. He published papers in the journals of both these societies. In conjunction with Mr Alexander Keith he wrote a text-book on Algebra which has found great acceptance. After his retirement he became an external examiner in Mathematics for the University of Glasgow.
Mr McArthur rendered notable service to his university both within and without the Department of Mathematics. He was one of the first members of the non-professorial staff to be appointed to the Senate, and his colleagues did him the honour of electing him Chairman of the Association of Lecturers and Assistants for his last session on the staff.
The many students to whom Mr McArthur lectured during his long teaching career will remember him with gratitude as a gifted teacher with a gracious personality. He earned their respect and their affection.
His interests were wide. He was a keen naturalist, well versed in the fine arts, a painter in water colours, an enthusiastic photographer. Broad and varied reading produced in him a well-stored mind which made his conversation a delight.
His closest friends will remember Neil McArthur for what he was, a gentleman, in the noblest sense of that much-abused word.