The Instituto de Matemática 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 has since maintained a national profile, aimed at:
- promoting high level scientific research in Mathematics and aplications;
- training new researchers;
- promoting the diffusion of mathematical culture and knowledge at a frontier line;
- developing projects of improvement of mathematical teaching at all levels.
These closely linked activities favor the advancement of mathematical knowledge, basic to the development of the sciences and of technology as a whole, which in itself is essential to the economic and social progress of the Nation.
Initially, IMPA initiated its activities in the premises of the Brazilian Physics Research Center (CBPF), at Praia Vermelha, Rio de Janeiro. Aside from Lélio Gama, the director, there were Leopoldo Nachbin and Maurício Peixoto as members of the research staff, a small but illustrious group.
Its academic prestige and influence became more visible with the advent of the Brazilian Mathematical Colloquiums, the first one held in 1957. These meetings have since taken place every two years, and have grown from 50 participants initially to over 1, 200 participants today. In that same year IMPA was moved to Rua São Clemente in Botafogo and Elon Lima and Paulo Ribenboim became members of the research staff.
In 1957, IMPA moved to 265 São Clemente Street, in Botafogo. The Institut used that building for ten years.
The Institute, though still not offering a formal graduate program at the time, was already focused on training researchers and on encouraging the establishment of research proups in universities across the Nation. Scientific exchange with other countries began to be encouraged as well. From the outset the library housed excellent periodic collections: they are considered of the highest international standard.
To structure somewhat more its activities in forming new researchers, Masters and Doctoral programs in Mathematics were started in 1962 by an agreement with the Federal University of Rio de Janeiro (UFRJ), which officially awarded the degrees.
Up to that time, financial resources were rather limited and the Institute had a small number of researchers. This greatly changed in 1967 when a global and much more substantial grant was offered by the National Bank for Economic Development (BNDES). In 1967, IMPA moved to Rua Luís de Camões 53, remaining in this historical building in downtown Rio de Janeiro until 1981 (now headquarters of the Hélio Oiticica Cultural Center).
Shortly before, in 1996, Lindolpho de Carvalho Dias had become director of the Institute, in place of Lélio Gama, a position which he held until 1969, and then again from 1971 to 1979, and from 1980 to 1980 Elon Lages Lima was the director on various occasions: from 1969 to 1971, from 1979 to 1980 and from 1989 to 1993. Since then, the position has been held by Jacob Palis.
In 1967, IMPA moved to 53 Luís de Camões Street, a historical building downtown Rio de Janeiro (nowadays this building is used as the Cultural Center Hélio Oiticica), remaining there until 1981.
With the support first of BNDES and later of the. Financial Agency for Studies and Projects (FINEP), and together with CNPq itself, IMPA began to enlarge its faculty in 1968 by recalling Brazilian mathematicians working or studying in distinguished institutions abroad. In 1970 it established regular masters and doctoral programs, concurrent with the extended growth in its research and researcher-training activities. Without diminishing the importance of the initial role played by its founders, this new and fundamental phase corresponds to the vision and the work of a new generation of mathematicians.
In fact, the institutional changes that took place in CNPq in the 1970’s gave rise to a qualitative jump in IMPA’s activities, by enabling the hiring of a more sizable permanent and full time research staff. Up until then its researchers had either been on fellowships or had held positions in other Brazilian or foreign institutions. This new scenario lead to a great expansion and diversification of research work, as well as the training of young researchers.
Not only research, but the masters and doctoral programs became part of the regular activities of the Institution, and IMPA became the first Mathematics Center to hold, as of 1971, a mandate from the Federal Board of Education enabling it to grant masters and doctoral degrees. It has been awarded the highest performance rates ever since by the Committee for the Advancement of University Academic Staff (CAPES). This has been recently confirmed: IMPA was one of the few institutions to achieve CAPES 1998 highest rank. The worldwide distinction that IMPA has been given stems from the quality of its scientific work and from the role it has played in the training of new researchers: about 170 doctorate and 400 master degrees up to the present time.
As of 1970, new research areas were established, such as Algebraic and Differential Geometry, Probability and Statistics, Operations Research and Mathematical Economics. Prior to this time, activities had been basically concentrated in the fields of Functional Analysis, Dynamical Systems and Differential Topology. Later on the fields of Partial Differential Equations and Fluid Dynamics and Computer Graphics would become consolidated into the program as well.
In 1979 began the construction of the permanent site of IMPA located at 110 Dona Castorina Street in Jardim Botânico. This building was inaugurated in 1981.
A fundamental factor in the consolidation of IMPA was the construction of its own headquarters in Horto Florestal, Jardim Botânico, inaugurated in July 1981, at which time an International Symposium of Dynamical Systems was held, attended by mathematicians from this and various other fields as well. The consolidation of faculty members continued throughout the decade bringing the number of researchers up to 32, all of them holding doctorate degrees. The number of areas in more applied mathematics grew in this period and now includes Computer Graphics, Fluid Dynamics, Mathematical Economics, Operations Research and Optimization. Two laboratories are now in operation, one in Computer Graphics and another in Fluid Dynamics. There are also computer facilities for researchers and students.
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 Anísio 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).