Its membership is international, but it mainly represents mathematicians in universities and other third level institutes in Ireland.

[2] The society was founded on 14 April 1976 at a meeting in Trinity College, Dublin when a constitution drafted by D McQuillan, John T. Lewis and Trevor West was accepted.

Since 2020, it has been the adhering organization for Ireland's membership of the International Mathematical Union.

[5] The logo was designed by Irish mathematician Desmond MacHale.

[7] It accepts articles that are of interest to both Society members and the wider mathematical community.