he began his career as a high school teacher in fortaleza, ceará. lima graduated with a bachelor's degree in mathematics from the universidade do brasil (today ufrj) in 1953. he obtained his doctorate in 1958 from the university of chicago with edwin henry spanier as advisor. he is a former guggenheim fellow, and holds memberships in the "academia brasileira de ciências" (brazilian academy of sciences) and the twas, the academy of sciences for the developing world. he is a professor honoris causa of the universidade federal do ceará and of the university of brasília. he was a member of the upper board of faperj from 1987 to 1991. he was also a member of the national board of education.