Mackay was appointed as a Mathematics Master at Perth Academy in 1863, spending three years in this post while he attended the Theological Hall with the intention of entering the United Presbyterian Church. However, he decided that he would make teaching his career and in 1866 he was appointed as a Mathematics Master at the Edinburgh Academy; he held this post until he retired in 1904.
He was elected a Fellow of the Royal Society of Edinburgh on 6 February 1882 having been proposed by Peter Guthrie Tait, George Chrystal, H C Fleeming Jenkin, Alexander Dickson. He served the Royal Society of Edinburgh as a Councillor from 1895 to 1898, and again from 1900 to 1903.
Mackay was an active member of the Edinburgh Mathematical Society. He is famed as the first President of the Society in 1883.
His obituary, written by George A Gibson, was published in the Proceedings of the Edinburgh Mathematical Society. You can see it at THIS LINK.
He was also a member of the Franco-Scottish Society. He was honoured by the University of St Andrews when he was awarded an honorary LL.D. in 1884.
Mackay was unmarried. He lived at 69 Northumberland Street, Edinburgh, where he died at the age of 70.
Article by: J J O'Connor and E F Robertson