Pietro Abbati Marescotti

Who was Pietro Abbati Marescotti?

Pietro Abbati Marescotti was an Italian mathematician who taught in Modena.

Pietro Abbati was descended from the 16th-century noble family of Abbati, who were related to the Marescotti family of Modena. In acknowledgment of his mathematical and artistic distinction, Abbati was permitted to add the name Marescotti to his own surname.

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. He was friends with Paolo Ruffini his entire life, and engaged in mathematical research with him, 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.

Abbati's investigations and exchanges with Ruffini also examined diophantine equations, prime numbers, the specification of the number of imaginary roots as compared with the results of P. Paoli, the relation among the roots and the coefficients of an equation, the Cartesian rule for incomplete equations, the properties of permutations of the roots of quartic and quintic equations, the equation of differences, rational functions of roots, resolution by approximation and the related Lagrange multipliers.