However the Edinburgh Mathematical Society was rather different from the other societies since it was founded by school teachers rather than by university teachers. The initial idea came from two mathematics teachers at George Watson's College in Edinburgh, namely A Y Fraser and A J G Barclay. Together with Cargill G Knott, assistant to the professor of physics at the University of Edinburgh P G Tait, they sent out a letter dated 23 January 1883:-
... to gentlemen in Edinburgh, in Cambridge, and throughout Scotland generally whom we deem likely to take an interest in such a Society...The letter asked for support for their project:-
It is proposed to establish, primarily in connection with the University, a Society for the mutual improvement of its members in the Mathematical Sciences, pure and applied.The first meeting took place at 8 p.m. on Friday 2 February 1883 in the Mathematics Classroom of Edinburgh University. The first president, elected at the meeting, was J S Mackay, the head mathematics master at The Edinburgh Academy. George Chrystal, the professor of mathematics at Edinburgh University, and Peter Guthrie Tait, the professor of natural philosophy, were elected honorary members of the Society at this first meeting. Of the first ten presidents, seven were school teachers indicating that in its early days the Society was more school based than university based.
Amongst the methods by which this object might be attained may be mentioned: Reviews of works both British and Foreign, historical notes, discussions of new problems or new solutions, a comparison of the various systems of teaching in different countries, or any other means tending to the promotion of mathematical Education.
At the first ordinary meeting of the Society in March 1883, 51 members joining the Society. Professor Chrystal addressed the Society on Present fields of mathematical research. In 1884 the Society began publication of the Proceedings of the Edinburgh Mathematical Society.
Although initially an Edinburgh Society, it very soon extended its remit to cover Scotland. The Society held its first meeting outside Edinburgh when it met in Glasgow in March 1900. It continued to meet regularly in Glasgow, adding St Andrews as a meeting venue in 1922, Dundee in 1930, and Aberdeen in 1937.
George Chrystal, one of the Society's first honorary members, died in 1911 and in the following year Edmund Whittaker took up Chrystal's chair in Edinburgh. Almost immediately he encouraged the Edinburgh Mathematical Society to hold a mathematical colloquium which it did in Edinburgh in 1913. A second colloquium was held in Edinburgh in the following year, prior to the outbreak of World War I, but the series had to be discontinued for the duration of the War. Turnbull was appointed Regius Professor of Mathematics in the United College of St Salvator and St Leonard at the University of St Andrews in 1921 and he was enthusiastic that the Edinburgh Mathematical Society should resume its Colloquium but that the venue should be St Andrews. This was accepted by the Society and in 1926 the first of the St Andrews Colloquia was held. Colloquia have been held roughly every four years since.