Problems and justifications

One of Brazil's greatest challenges is to improve upon the economical development model that was constructed during the last decades. Such model brought the country to a privileged position "vis à vis" other developing nations, and possibly side by side with China and India.

Throughout this improvement process, science and technology receive a special importance in the consolidation of a modern economy and its insertion in a global context. The main goal being always the construction and strengthening of a more just and balanced society.

It is well accepted nowadays that the performance of a competitive and integrated economy in the international panorama depends crucially upon its effective capacity of using its existing bases of technological and scientific knowledge, among which one finds Mathematics and Scientific Computation. Indeed, the extraordinary scientific and technological advances of the last decades were only possible because of the corresponding development of Mathematics and Scientific Computation.

New avenues are being opened by the advancement of natural and social sciences, requiring a strong interaction with Mathematics and Computation. The new fields of interdisciplinary research will be the most important characteristic of the XXI century science.

Quoting from biologist Rita Colwell, presently president of the National Science Foundation in a recent speech "I cannot stress too strongly how vital mathematics is to keeping our R&D enterprise strong. Nurturing the discipline of mathematics itself is the foundation of this broader role. We see mathematics as fundamental for progress in science and engineering. ... as our world and economy change more quickly than ever, lifelong learning becomes a survival skill. Mathematical literacy will become an even more vital ingredient in this scenario."

Along these lines, one should stress that UNESCO has declared 2000 as International Mathematical Year.

Indeed, the high demand for competent mathematicians in its different specialties has poignantly manifested itself throughout the world in several different fronts, especially in Brazil and in Latin America.

• Therefore, it is imperative an even more expressive development of Computational as well as Fundamental Mathematics. The progress of the latter being the basis for present and future applications of the former. It is also of fundamental importance to vigorously foster the integration of Mathematics with other scientific disciplines opening new avenues to knowledge. This will doubtless benefit society as a whole in areas such as climate prediction, applications to medicine and biology (e.g. tomography, image reconstruction, blood flow modeling ), mathematical and computational modeling of natural phenomena (e.g. population dynamics, ecological modeling). We also emphasize in this project high impact areas in mathematical physics such as phase transitions and linguistics.
• Another area of primary importance concerns the integration of mathematicians with the productive sector. As examples we have the study of models for oil prospection and extraction, finances, and electrical energy optimization.

Some of the aforementioned research areas are already in full development, both as far as the interdisciplinary character is concerned and as far as the integration with the productive sector. Examples of the former are, climate-weather studies and applications to medicine, whereas examples of the latter are ongoing projects in oil and electric energy.

• The preparation of new generations of researchers is a key issue that was taken into account in the present project. This includes both the process of training and developing young researchers and Ph.D.s, stimulating and interacting with young post-docs. In this respect, the capacity and excellence of the principal investigators involved in the present project is well established and proven by their experience and enthusiasm. One of the central objectives of our project is to expand considerably the number of young researchers working in interdisciplinary lines and applied to the productive sector, including in finances and other areas of economy.

In all the above aspects the already existing international cooperation is extraordinary, as the participation in the project of five Field Medalists, together with several other renowned scientists and research centers indicates.

• The Institute shall also give a relevant contribution to the teaching of Mathematics in levels ranging from junior-high school to graduate school. The expertise in this direction already exists by members of the present project in the level of junior-high school, high school, and college mathematical teaching. In this sense we have also secured a formal agreement with the National Research Network (Rede Nacional de Pesquisas-RNP) to the proposed Institute in such a way as to give country-wide coverage of the activities. This will include video-conferencing both at the level of teaching as well as research development and exchange.
• Another fundamental aspect shall be the support to emerging research centers such as the Universities of Amazonas, Paraiba, Alagoas, Bahia, Espirito Santo, Goias, e Parana.
• At the same time, the exchange with other centers in Latin America, along the lines of the Millennium Institutes will certainly be very profitable. This is corroborated by the already existing intense scientific exchanges between the researchers in the proposed Institute and the most active research communities in the region, such as those in Argentina, Chile, Peru, Mexico, Venezuela, and Uruguay.
• The Institute shall also emphasize in nurturing the mathematical interest of youth in the range of 10 through 17 years old as well as the search for new young talents. This will be done by the strengthening of the already well structure "Olimpiadas Brasileiras de Matematica" both at the regional level as well as at the national level.

The potential and economical contributions of the project are significant. They involve applications to vital sectors of the country including basic research, the integration with other knowledge areas, computational and applied mathematical modeling, teaching in different levels, and the production of highly competent human resources.

• At the regional level, the Institute will contribute to a strong presence of Brazil in fostering and realizing scientific research and applications throughout Latin America, as well as in the preparaiton of highly skilled human resources.
• As for the potential interest that the project will bring to society, we remark that teaching and preparation of well qualified scientific personnel has a fundamental and all-encompassing importance. Among some of the impact areas we may cite the applications to climate and weather prediction, to medicine, and potentially to ecology. In the latter case by using techniques from dynamical systems and differential equations, which are areas where Brazil has a world-wide recognition.

From the economical view-point, besides the aforementioned items, it is relevant to remark the contribution that the Institute will bring to oil prospection and extraction, as well as to mathematical economy and finances.

Finally, by not tackling in one way or another the central questions of this Institute's project, one would be delaying in several of the above mentioned fronts the social and economical progress of our country.