
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, climateweather 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 postdocs. 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 juniorhigh school
to graduate school. The expertise in this direction already exists by
members of the present project in the level of juniorhigh 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 PesquisasRNP) to the proposed Institute in such a way as
to give countrywide coverage of the activities. This will include videoconferencing
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 allencompassing
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 worldwide recognition.
From the economical viewpoint, 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.
