Pietro Abbati Marescotti (1 September 1768 – 7 May 1842) was an Italian mathematician who taught in

Modena Modena (, , ; egl, label=Emilian language#Dialects, Modenese, Mòdna ; ett, Mutna; la, Mutina) is a city and ''comune'' (municipality) on the south side of the Po Valley, in the Province of Modena in the Emilia-Romagna region of northern I ...

.Abbati Marescotti, Pietro
Dizionario Biografico degli Italiani, Vol. I, 1960, retrieved 2014-06-27.

Biography

Born in

, Pietro Abbati descended from a 16th-century noble family who were related to the Marescotti local family. 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. In an 1802 letter to his friend

Paolo Ruffini Paolo Ruffini (Valentano, 22 September 1765 – Modena, 10 May 1822) was an Italian mathematician and philosopher. Education and Career By 1788 he had earned university degrees in philosophy, medicine/surgery and mathematics. His works inclu ...

, Abbati extended the proof to the unsolvability of equations of degree greater than five. In 1807, he was named as an advisor to

Francis IV, Duke of Modena Francis IV Joseph Charles Ambrose Stanislaus (Italian: ''Francesco IV Giuseppe Carlo Ambrogio Stanislao d'Asburgo-Este''; 6 October 1779 – 21 January 1846) was Duke of Modena, Reggio, and Mirandola (from 1815), Duke of Massa and Prince of Carr ...

. Three years later, he became ministry of state economics and education, with particular responsibility for waterworks and streets. In 1824, he published ''On a problem of Daniel Bernoulli and Lagrange''. In 1826, he was named a member of the

Accademia nazionale delle scienze detta dei XL The Accademia Nazionale delle Scienze (), or more formally L'Accademia Nazionale delle Scienze detta dei XL, and also called the Accademia dei XL (), is Italy's national academy of science. Its offices are located within the Villino Rosso, at the co ...

("National Association of the Sciences", also known as "Academy of the Forty"), a learned society composed of forty eminent Italian scientists.

Mathematics

He was friends with

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 equation In mathematics, a Diophantine equation is an equation, typically a polynomial equation in two or more unknowns with integer coefficients, such that the only solutions of interest are the integer ones. A linear Diophantine equation equates to a c ...

s, 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.

References

{{DEFAULTSORT:Abbati, Pietro 1768 births 1842 deaths Scientists from Modena 18th-century Italian mathematicians 19th-century Italian mathematicians