In acknowledgment of his mathematical and artistic distinction, and in return for his services managing the water and street systems of Modena, Abbati was permitted in 1818 to add the name Marescotti to his own surname.
[1] He was born in Modena and received a superior education in mathematics at the university there, studying with Luigi Fantini, Paolo Cassiani and Giovan Battista Venturi.
[1] In an 1802 letter to his friend Paolo Ruffini, Abbati extended the proof to the unsolvability of equations of degree greater than five.
[1] 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.