Robert Ferguson's family moved from Airdrie to Edinburgh when Robert was three years old. He was a pupil at the school attached to the Free Church Training College at Moray House, becoming an assistant master and then a lecturer at the Training College. During this period, beginning in 1843, he studied at the University of Edinburgh and at New College. After being awarded an M.A. with First Class Honours in Mathematics, Natural Philosophy and Philosophy by the University of Edinburgh, he studied under Bunsen in Heidelberg and was awarded a Ph.D. from the University of Heidelberg in 1855.
In 1858, in partnership with a Mr Bickerton, he took over running the Edinburgh Institution at 8 Queen Street, Edinburgh. He was a Partner and Joint Headmaster from 1858 to 1875, then Headmaster until he retired in 1898.
Ferguson married Janet Margaret Monteith on 13 August 1864 in Edinburgh and they had two children: Duncan (born 1872) and James (born 1876). After Janet's death he married Mary Leslie (or Marjoribanks) in Edinburgh in 1896.
Further details of his life are given in two obituaries which we present at THIS LINK and THIS LINK
Let us note that Ferguson was a founder member of the Edinburgh Mathematical Society, joining the Society at its first meeting in February 1883. He was elected President of the Society for session 1885-86. He gave his presidential address to the Society on leaving office on Friday 12 November 1886:-
On the occasion of demitting his office, Dr Ferguson delivered an address in which he congratulated the Society on its vigorous growth and encouraging prospects. He contrasted the state of mathematical education at the universities now with that which prevailed thirty years ago, and expressed a hope for the further improvement of these institutions by an increased staff of extra and infra-mural lecturers. In adverting to the position of mathematical masters in secondary schools, he thought that they should more frequently be entrusted with the highest authority. After a few remarks on the methods of mathematical tuition, he pointed out the desirability of continuing to widen the work of the Society in the interests of such professions as those of the engineer and the actuary.Robert Ferguson was elected to the Royal Society of Edinburgh on 6 January 1868, his proposers included Philip Kelland. An obituary, written by Andrew E Scougal, appears in Proc. Roy. Soc. Edinb. 33 (1912-13), 342-5.
Article by: J J O'Connor and E F Robertson