 In 1826 he was named a member of the Accademia nazionale delle scienze detta dei XL ("National Association of the Sciences", also known as "Academy of the Forty"), a learned society composed of forty eminent Italian scientists.He was friends with Paolo Ruffini his entire life, and engaged in mathematical research with him (although without any official recognition), especially in the areas of algebraic equations, probability, and group theory.Indeed, it appears that Abbati suggested the idea of group theory to Ruffini, who subsequently expanded it.