Shortly thereafter he began lecturing in philosophy and psychology at the Institute of Education of the University of Chile in Valparaíso.

Torretti was professor emeritus of the University of Puerto Rico, and a member of the Institut International de Philosophie.

[2] In September 2011 Cordua and Torretti were jointly awarded the National Prize for Humanities and Social Sciences by the Republic of Chile.

Much of Torretti's work dealt with physics and mathematics, with a major focus on relativity theory and 19th-century geometry.

[5] He devoted the book El Paraíso de Cantor to the set-theoretical tradition in logic and philosophy of mathematics.