ICMS was created in December 1989 by Edinburgh and Heriot-Watt Universities in response to a challenge laid down by Nobel Prize winner Abdus Salam in his Edinburgh Medal address of that year. The creation of ICMS would have been impossible without early support from the International Centre for Theoretical Physics, the City of Edinburgh District Council and the Scottish Development Agency. Since then it has also benefited from support from Standard Life, Scottish Provident, the Scottish Higher Education Funding Council, Engineering and Physical Sciences Research Council, the London and Edinburgh Mathematical Societies, and the Royal Society of Edinburgh.

Robin Knops, a past vice-principal of Heriot-Watt, has written an interesting brief history of the early development of ICMS which can be found here. 

Our core activity began in 1991 with a workshop on Geometry and Physics at Newbattle Abbey College, Edinburgh and continued with workshops and symposia covering all aspects of mathematical sciences. In April 1994, the Centre moved to 14 India Street, the birth place of James Clerk Maxwell, which was rented from the James Clerk Maxwell Foundation. This historic address housed the administrative staff and provided space for seminars, lectures and workshops for 16 years. The building also contains a small collection of Maxwell's papers and memorabilia which was always popular with visiting mathematicians.

2010 saw ICMS move to a new home at 15 South College Street. This building located just of South Bridge in the centre of Edinburgh, this building was a converted church that worked well as a conference centre. Further expansion of ICMS activity meant that we outgrew our South College Street home and moved in the summer of 2018 to the Bayes Centre. ICMS occupies the top floor of the building, along with the Maxwell Institute Graduate School, and has purpose-built accommodation that more closely matches the needs of ICMS activity. In 2021 ICMS once again rented space from the James Clerk Maxwell Foundation at 14 India Street and use the offices on the top floor of Maxwell's birthplace for our Research-in-Groups visitors.