Among the research results obtained by researchers from the Institute that have so far had the greatest impact, it is worth mentioning the solution to the Nash problem in Singularity Theory by Javier Fernández de Bobadilla and María Pe;[2] the [solution to the Sidon problem in Number Theory by Javier Cilleruelo and Carlos Vinuesa;[3] the solution to the Arnold conjecture in Hydrodynamics by Daniel Peralta[4] Salas and Alberto Enciso and the construction of the mathematical model for explaining how water waves break by the research team led by Diego Córdoba.

In 2011 the ICMAT was chosen as one of the eight centers of excellence in the Severo Ochoa Program call for submissions issued by the then Spanish Ministry of Science and Technology (MICYT).

Furthermore, the ICMAT has launched the Matemáticas en la Residencia program[6] (in collaboration with the Residencia de Estudiantes and the CSIC) in which international figures for the public understanding of science such as Marcus du Sautoy, Jesús María Sanz-Serna, Pierre Cartier, Guillermo Martínez, Edward Frenkel, Christiane Rousseau, Antonio Durán and John Allen Paulos have taken part, as well as the Graffiti and Maths competition,[7] which is aimed at secondary school students.

The blog Mathematics and its Frontiers[8] has an annual readership of 150,000, in addition to the presence of the Institute in social networks: Facebook [9] and Twitter.

[10] In March, 2013, the ICMAT officially became a Scientific Culture Unit recognized by the FECYT (Spanish Foundation for Science and Technology), and is the only mathematical institution to enjoy this distinction.