At the origin of CIRM's start is the decision by the community of Trent to start, under the university, a science department. The docents of the university transfered to Trent following this decision understood that the primary scope of the courses allowing receipt of a degree in mathematics or physics was that of giving the area highly qualified science teachers at the junior high school level. As time went by, the University's level of teaching increased and contacts established with well-known university researchers.

To attract high level mathematicians to Trent, it was found desirable to provide the city with an institution auxiliary to the university able to put Trent in the list of places visited by the most highly qualified researchers. For this reason CIRM was founded, and in its first 42 years of activity has carried out its task quite well.

In 1978 CIRM was founded by Istituto Trentino di Cultura (ITC) in partnership with the Italian National Council for Research (CNR) with the primary purpose of organizing seminar and meeting weeks on mathematics research.

The CIRM has continued its activities without interruption ever since and, at the moment of the transition from ITC/irst to Bruno Kessler Foundation, the Centre has enlarged its spectrum of activities. The Statutary norms which rule the CIRM were formally re-established by the Board of Directors on May 2.nd, 2011. These foresee the combination of the original purposes together with the additional aim of supporting mathematical disciplines in the perspective of an integration with scientific domains of interest of other FBK Research Centres.

Next to the traditional activity, which has seen the CIRM organize 336 international mathematical Meetings and Conferences (with 18200 participants), and next to the related editorial activity, which has seen the publication of 78 research books and journal volumes, present in the libraries of most Universities in the world, in 2008 the Comitato Direttivo set up a new range of activities, focused on the aim to have research done at the CIRM, along with scientific training.

Especially a new program was set up, encompassing four types of visiting positions, with the intention of stimulating the interaction between the mathematical research community of the Trento area and the European and international mathematical community.

In July 2017 the President of the Fondazione Bruno Kessler (FBK), the President of the Istituto Nazionale di Alta Matematica (INdAM) and the Rector of the University of Trento signed an agreement to cooperate in a joint laboratory, with the same denomination "Centro Internazionale per la Ricerca Matematica", in order to continue the activities carried out up-to now by CIRM and at the same time to achieve new synergies, developping scientific initiatives and advanced training courses.

In July 2020 the agreement was renewed for the three year period 2020-2023.