The Society was founded in 1883 by a group of Edinburgh school teachers and academics, on the initiative of Alexander Yule Fraser FRSE and Andrew Jeffrey Gunion Barclay FRSE,[1][2] both maths teachers at George Watson's College, and Cargill Gilston Knott, the assistant of Peter Guthrie Tait, professor of physics at the University of Edinburgh.

[4] This was due to an increase in the number of academic positions available and the new requirement for teachers to undergo an additional year of vocational training.

[6] Every four years it awards the Sir Edmund Whittaker Memorial Prize to an outstanding mathematician with a Scottish connection.

)[9] The Proceedings were first published in 1884, and are issued three times a year, covering a range of pure and applied mathematics subjects.

[6] Between 1909 and 1961, the Society also published the Edinburgh Mathematical Notes, on the suggestion of George Alexander Gibson, a professor at the University of Glasgow, who wished to remove the more elementary or pedagogical articles from the Proceedings.