Brazil produces 2.4% of all mathematical research worldwide.

* The text below was part of Brazil's application dossier for Group 5, the elite of world mathematics, of the International Mathematical Union.

Analysis and dynamical systems were the first areas of mathematical research developed in Brazil. Differential geometry and the calculus of variations soon followed, naturally leading to partial differential equations, algebra, and algebraic geometry. Statistics, control, optimization, and probability theory followed. More recent additions include discrete mathematics, especially combinatorics, and various applications: numerical analysis, fluid dynamics, computer vision, and inverse problems, to mention just a few.

Among the most interesting recent developments are the emergence of a new generation of mathematicians interested in modern trends in geometry (symplectic, complex, etc.), algebra (non-commutative, non-associative, etc.) and discrete mathematics, as well as the creation of important research groups in operator algebras, Lie theory, and certain areas of mathematical physics, including gauge theory and string theory.

IMPA (Rio de Janeiro), the state universities of São Paulo (São Paulo and São Carlos) and Campinas, the federal universities of Rio de Janeiro, Brasília, Minas Gerais (Belo Horizonte) and Ceará (Fortaleza), and the Pontifical Catholic University of Rio de Janeiro are considered the main national centers for mathematical research. High-standard research groups also exist at the federal universities of Pernambuco (Recife), Paraíba (João Pessoa, Campina Grande), Paraná (Curitiba), Rio Grande do Sul (Porto Alegre) and Fluminense (Niterói), and at the state universities of Maringá and São Paulo in Rio Preto. Especially since the late 1990s, smaller but very productive groups have been established at the federal universities of Pará (Belém), Bahia (Salvador), Alagoas (Maceió), Goiás (Goiânia), Santa Catarina (Florianópolis), ABC (Santo André) and São Carlos.

All of these institutions offer doctoral programs in mathematics and/or statistics for Brazilian and international students. Thus, research in mathematics is now quite well distributed throughout Brazil.

One consequence of this growth is that Brazil's contribution to global mathematical production has been increasing rapidly, both in absolute terms and as a percentage. In 2006, for example, shortly after Brazil reached Group IV of the IMU, it represented 1.53% of global production (1043 research papers). By 2016, it had grown to 2.35% (2076 papers). By comparison, both Brazil's gross domestic product (GDP) and population represent approximately 2.9% of the corresponding world totals.

In 2016, a total of 2,349 research papers were written by Brazilian mathematicians, up from 253 in 1986, 530 in 1996, and 1,155 in 2006 (source: MathSciNet).

From a more qualitative point of view, research papers by Brazilian mathematicians regularly appear in most of the most important scientific publications and journals. Certainly, not only has the number of these high-level publications increased substantially over the last two decades, but the list of journals where Brazilian authors regularly publish is also expanding, reflecting the growing diversity of mathematics being produced in the country.

In 2016, the percentage of mathematical research papers by Brazilian authors reached 2.35% of the total world output, compared to 0.70% in 1986, 1.06% in 1996, and 1.53% in 2006 (source: MathSciNet).

This was also reflected in an increasing presence of Brazilian guest speakers and plenary sessions at the International Congress of Mathematicians:

Several of the people on this list are originally from other countries: it is worth noting that Brazilian universities and research institutes regularly hire faculty members from around the world, without citizenship restrictions. Brazilian mathematicians have been distinguished with prestigious international awards, including the 2010 Balzan Prize (Fondazione Internazionale Prix Balzan, Italy) for Jacob Palis and the 2016 Grand Prix Scientifique Louis D. (Institut de France) for Marcelo Viana. Furthermore, the Ramanujan Prize (IMU and ICTP) has been awarded four times to Brazilian mathematicians: Marcelo Viana (2005), Enrique Pujals (2008), Fernando Codá Marques (2012), and Eduardo Teixeira (2017).

A small sample of mathematics meetings held in Brazil.
International Congress of Mathematical Physics, 2006
International Congress on Minimal and Constant Mean Curvatures Surfaces, 2007
Workshop on Partial Differential Equations: Theory, Computation and Applications, 2007
First Indo-Brazilian Symposium on Mathematics, 2008
International Conference on the Analysis of Algorithms, 2008
Mathematical Methods and Modeling of Biophysical Phenomena, 2009
Workshop on Conservative Dynamics and Symplectic Geometry, 2009
Clay Mathematics Institute Summer School, 2010
Poisson 2010 – Poisson geometry in Mathematics and Physics, 2010
Mathematical Modeling and Calibration in Commodities and Energy, 2011
Arithmetic of Modular forms and Elliptic Curves, 2011
Quantum Groups and 3-Manifold Invariants, 2012
Arithmetic and Geometry of Picard-Fuchs Differential Equations, 2012
International Conference on Dynamical Systems, 2013
Symmetries in Mathematics and Physics II, 2013
International Symposium on Generalized Convexity and Monotonicity, 2014
Discrete Markov Chains: mixing times and beyond, 2014
Latin American School of Algebraic Geometry and Applications, 2015
International Conference in Number Theory and Physics, 2015
SAET Conference on Current Trends in Economics, 2016
International Conference on Stochastic Programming, 2016
International Mathematical Olympiad, 2017