The journal was originally named Mathematical Notes, with the subtitle A Review of Elementary Mathematics and Science.
[1] Its creation was the suggestion of George Alexander Gibson, a professor at University of Glasgow, who wished to remove the more elementary or pedagogical articles from the Proceedings of the Edinburgh Mathematical Society.
[2] Is founding editor was Peter Pinkerton, who at the time headed the mathematics department of George Watson's College and later became rector of the High School of Glasgow.
In 1958 its issues began being published as issues of the Proceedings of the Edinburgh Mathematical Society, and after 1961 they became incorporated into a department of the Proceedings rather than being published separately.
[1] The archives of the journal are available online to subscribers through the Cambridge University Press.