[2] His main field of research was computability theory, a branch of mathematical logic that studies the class of functions that can be calculated automatically.

In this field he has published about thirty articles, and the two-volume book Classical Recursion Theory (North Holland Elsevier, 1989 and 1999), which has become a seminal text on the subject.

[9] He repeatedly manifested his opposition to US policies, in particular against that of George W. Bush and Israel, as indicated in his writings Non siamo tutti americani,[10] La dannata Terra Santa[11] and the controversial Intervista a Hitler,[12] in his book Il matematico impertinente.

His views on Israel "immodestly inspired" by José Saramago and Noam Chomsky caused protests, which led to the deletion of an editorial he wrote in his blog at la Repubblica in November 2012,[13] where he talked about the Israeli incursion in the Gaza Strip.

In 2014, a few days after Maryam Mirzakhani became the first female winner of the Fields Medal, Odifreddi suggested in an article for La Repubblica that biological factors were the reason why so few women had previously achieved great mathematical feats, acknowledging but ultimately dismissing the social and institutional barriers that prevent women from advancing in the discipline.