The Instituto de Matemаtica Pura e Aplicada (IMPA) was the first research unit to be established by the Brazilian National Research Council — CNPq, presently the Brazilian Council for the Development of Science and Technology, just one year after CNPq itself was founded in 1951, becoming the foremost agency to promote and support research in Brazil.

IMPA is working today at a high research and training capacity, with a staff of about 34 researchers, including long-term associate fellows. As mentioned above, research work currently takes place in the fields of Algebra and Algebraic Geometry, Partial Differential Equations and Fluid Dynamics, Computer Graphics, Mathematical Economics, Differential Geometry, Operations Research and Optimization, Probability and Dynamical Systems. Students in the doctorate program come from all over Latin America and some from Europe, Asia and Africa. Furthermore, IMPA has been acknowledged as being a Post-Doctoral Center of Excellence on an international level by the Third World Academy of Sciences (TWAS). It is the permanent headquarters of the Brazilian Mathematical Society, founded in 1969, and of the International Mathematical Union for the period 1990–1998.

From the start, research has been associated to the formation of new researchers and has focused on supporting national universities, and later other Latin American institutions, in an effort to help these centers to develop similar high level activities of their own. Aside from training programs forming new researchers (masters and doctorates), incentives for bringing visiting researchers, including those from abroad, have been of prime importance, as well as the organization of scientific conferences, and of the Brazilian Mathematics Colloquia, combined with the regular running of the long term Post-Doctoral and the Summer Graduate and Post-Doctoral Programs. The Post-Doctoral program includes long-term activities (ranging from six months to one year), and short-term activities (one to three months), the latter generally held during the Summer. Various advanced research activities are offered at this time. Every year, an average of 70 mathematicians come to IMPA for post-doctoral training. Much joint research work has been accomplished in co-authorship by members of geographically-distant universities, thanks to contacts made during Summer Programs. In addition, about 80 undergraduate and graduate students from universities in just about every state in the federation attend Mathematics courses in the Post-Graduate Summer Program offered by the Institute. For several years now IMPA has offered retraining courses for high school teachers. This activity has grown in importance and is now being incorporated into the regular program. For an even longer period, IMPA has given ample support to the Brazilian Mathematics Society, in particular to its Olympic Mathematics Program, not only on a nationwide level but also in terms of Brazil's participation in international contests. Another main activity that has flourished at IMPA, besides research activities and human resources training, has been the publication of educational materials. Various series of IMPA publications are utilized by universities as reference material for graduate and post-graduate courses. This is especially true of the Euclid Project and the University Mathematics Collection. The existence of Brazilian mathematical literature is not only an important teaching asset but also serves as a powerful incentive for young people to develop their research skills. IMPA has also produced, in collaboration with the Vitae Foundation, a collection of books especially designed for high school mathematical teachers, in conjunction with a retraining program for them.

As a consequence of such successful and comprehensive set of activities, IMPA is now very visible and praised both in Brazil and abroad. Its faculty members have earned numerous national and international prizes, such as the Moinho Santista Prize, the National Prize for Science and Technology, the Bernardo Houssay Interamerican Prize for Science, the Third World Academy of Sciences Prize and the Ansio Teixeira Prize. Many of them are members of the Brazilian Academy of Sciences as well as foreign academies of sciences and hold honorific degrees at several universities. In addition, more than 90 percent of the research staff hold research fellowships from CNPq and almost as many are involved in long-term research projects sponsored by the Brazilian Government (PRONEX).