Pietro Abbati Marescotti
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, 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.
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 (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.
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.
The thirty letters which Abbati wrote to Ruffini are now housed in the Ruffini Archive of the Biblioteca Estense in Modena. All the letters remain unpublished except one published by E. Bortolotti in an edition of Ruffini's correspondence.
The chief known events of Abbati's life were:
- 1802: "Letter to my colleague Paolo Ruffini" (written September 30 in Modena): Ruffini had already written about the unsolvability of equations up to the fifth degree. In this letter Abbati extended the proof to the unsolvability of equations of degree greater than five.
- 1807? Named as an advisor to Francis IV, Duke of Modena
- 1810? Appointed by Francis IV to the ministry of state economics and education, with particular responsibility for waterworks and streets
- 1818: In recognition of his contributions to science, art and infrastructure, Abbati was granted permission to add the name Marescotti to his surname and was granted the title of count.
- 1824: Publication of On a problem of Daniel Bernoulli and Lagrange – an essay by earl Pietro Abbati Marescotti
- 1826: Named a member of the Accademia nazionale delle scienze detta dei XL (‘National Association of the Sciences’ known as ‘Academy of the Forty’), a learned society composed of the forty most eminent Italian scientists
- 1833: Opening of the Abbati Marescotti Theater (which closed in 1866)
In addition to the honors listed above, Abbati was also a member of the:
- Società di Arti Meccaniche (Society of Mechanical Arts)
- Società Agraria delle Panaro (Agrarian Society of the Panaro)
- Accademia dei Dissonanti, which evolved into the Accademia di Scienze Lettere e Arti di Modena (Modena Academy of Arts and Sciences)
- Accademia di Scienze e Belle Lettere di Palermo (Palermo Academy of Arts and Sciences)