He received his earliest education in Edinburgh, where his parents remained till he was ten or eleven years old. Then they went to a farm at Fearn, Easter Ross, and his education was continued at the Hill of Fearn Public School.
For his secondary education he went to Tain Royal Academy, whose rector, John Scott, was a mathematician. Rector and pupil worked at mathematics together. A short period followed at the Grammar School in Old Aberdeen. He entered the University of Aberdeen in 1882, and graduated in 1886 with First Class Honours in Mathematics and Natural Philosophy, winning the Simpson Mathematical and Arnott Experimental Physics Prizes and a Fullerton Scholarship.
Proceeding to Clare College, Cambridge, he graduated in 1889 as Fourth Wrangler. He became a Fellow of Clare in 189o, won the Smith's Prize in 1891 and the Adams' Prize in 1901. The Royal Society of London elected him a Fellow in 1901, and in 1916 awarded him a Royal Medal.
At Clare Macdonald was in close touch with Mr Ewbank, the College bursar, an able administrator of the College estates, and for some years had an intimate knowledge of the College property and its administration. This and his acquaintance with agriculture, as a farmer's son, were turned to good account when, in 1904, he became Professor of Mathematics in Aberdeen, and, in a few years, took over much of the administrative work of the University, especially in all matters connected with buildings.
In July 1916 Professor Macdonald joined the Ministry of Munitions and was attached to the Wages Section of the Labour Department. He soon became head of this section, to which wages disputes found their way and in which the officials were under almost constant strain. At a later date he took over additional duty as chairman of an important committee set up to regulate the demands of certain Government departments for building labour. Macdonald's knowledge of labour conditions, especially in the building trades, his unusual memory for figures, his inexhaustible patience, and his powers of physical endurance made him an invaluable member of the administration, and particularly fitted him for the work he was called upon to do. He was not infrequently required to go into the provinces and effect a settlement of some dispute. His services were of such importance that he was asked and consented to continue in the Ministry of Labour for the period of reconstruction that followed the War. He did not return to Aberdeen until September 1919.
Mountaineering was Professor Macdonald's great recreation. He climbed most of the highest peaks of the Bernese and Valaisian Alps, his favourite guide being Emmanuel Byrgener of Sass. On the march he was tireless, not given to an excess of speech any more than at other times, but a fine view or colour-effect he would recall long afterwards. He joined the Alpine Club on February 6, 1906. The Scottish Mountaineering and Cairngorm Clubs he never joined, but the Cairngorms and the Ross-shire hills he knew. Perhaps one of the last long expeditions he made was an all-night cross-country walk from Alltdourie to Inchrory by the Sneck and the summit of Ben Avon on June 30, 1934. At that time he was going quite well with his long mountaineering stride.
Though a true Highlander, he was never a fluent Gaelic speaker. His knowledge of Gaelic was gained during visits to his grandmother, and he would run into the house to ask her the meaning of Gaelic phrases used by other boys. She taught him to read the Gaelic Bible. He was a regular attender at the annual Gaelic Service in King's College Chapel, Aberdeen, and was often at students' Gaelic society meetings. His chief work for the Highlands was as Governor, from February 1916, of the Highlands and Islands Educational Trust, of which his intimate knowledge made him a most valuable member. He became Convener of the Educational Committee in 1924, and in 1930 Chairman of the Trust. His recollection of the circumstances of the various beneficiaries was remarkable.
Until the Spring of 1935 he enjoyed good health. Characteristically, when he agreed to enter a nursing home on Tuesday, May 7, for examination, he refused to let his relatives and friends know. He was elected a Fellow of this Society in 1905 and died on Thursday, May 16, 1935.
For an appreciation of Professor Macdonald's scientific work reference may be made to the Obituary Notices of Fellows of the Royal Society, No. 4, 1935, p. 551.