in Chemical Engineering from the Federal University of Rio de Janeiro (UFRJ), Brazil, in 1968 and then got his doctorate from the Brazilian Center for Research in Physics (CBPF), advised by Leopoldo Nachbin in 1977.
His most prolific period spawned from his collaboration with Newton da Costa,[1] a Brazilian logician and one of the founders of paraconsistent logic, which began in 1985.
[2] His main achievement (with Brazilian logician and philosopher Newton da Costa) is the proof that chaos theory is undecidable (published in 1991), and when properly axiomatized within classical set theory, is incomplete in the sense of Gödel.
The decision problem for chaotic dynamical systems had been formulated by mathematician Morris Hirsch.
More recently da Costa and Dória introduced a formalization for the P = NP hypothesis that they called the “exotic formalization,” and showed in a series of papers that axiomatic set theory together with exotic P = NP is consistent if set theory is consistent.