President, Academy of Sciences for the Developing World (TWAS)

Member of the IAC Board

Born in 1940 in Uberaba, in the state of Minas Gerais, Brazil. Graduated in 1962 at the Engineering School of the University of Brazil (now Federal University of Rio de Janeiro). Due to his performance, including entrance examination, he was awarded the prize University of Brazil. Still, he felt all along an attraction for Mathematics and Physics so that he would understand more profoundly the concepts and formulas he was confronted with in the Engineering disciplines. This finally led him to become a mathematician immediately after graduation. He then spent about a year and half at the Instituto de Matemática Pura e Aplicada (IMPA).

In the Fall of 1964 he initiated his Ph.D. program in Mathematics at the University of California, concluded three years later under the supervision of one of the greatest living mathematicians, Steve Smale (Fields Medal, 1966). After a short period as Assistant Professor at that University, he returned to IMPA, where he has been ever since. He thought at that time, that two great challenges were to produce in a continuous basis first rate research in Mathematics in Brazil as well as to form new high quality researchers also on a regular basis. He has since then taken active part in the development of Science, particularly in research and in advising new talents. He directed so far thirty five Ph.D. theses in Dynamical Systems of students from ten different countries, most of them in Latin America and some in Europe. This represents a main contribution to the existence of a Latin American School in Dynamical Systems internationally recognized as a high level research group. He published approximately seventy research works, that occupy more than a thousand pages of the best international periodicals in the field, like Annals of Math., Acta Math., Inventions Math. and Publications Math. Inst. Hautes Études Scient. In the sixties, he worked on questions related to the global stability of dynamic systems. The results obtained together with Smale, led them to the formulation of a basic conjecture in the modern theory of dynamical systems, corrrelating the concepts of hyperbolicity and stability. The last part of the proof of this conjecture was about twenty years later, by one of his brilliant Ph.D. students, Ricardo Mañé. In the seventies, he dedicated himself to the study of bifurcations, i.e., change of dynamic structures in systems that depend on parameters and, increasingly to the study of chaotic systems, that is, systems sensible to initial conditions. He adopted a more probabilistic point of view than the geometric-topologic one common in the sixties, that resulted in the formulation of a global conjecture for the set of all dynamical systems. According to this conjecture, the majority of the systems has their essential behavior determined by a finite number of attractors (hyperbolic/strange). This conjecture may be combined with others on evolution equations, especially those who govern turbulence of fluids, leading to a more comprehensive scenario for this difficult and important phenomenon.

He has been awarded the Prizes University of Brazil (1962), Moinho Santista (1976), Third World Academy of Sciences (1989), National Brazilian Prize for Science and Technology (1990), Brazilian National Order of Scientific Merit (1994) and the Interamerican Prize for Science (1994).