Pietro Abbati Marescotti (1 September 1768 – 7 May 1842) was an Italian

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change. History On ...

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 The ''Dizionario Biografico degli Italiani'' ( en, Biographical Dictionary of the Italians) is a biographical dictionary published by the Istituto dell'Enciclopedia Italiana, started in 1925 and completed in 2020. It includes about 40,000 biograp ...

, 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 ...

prime number A prime number (or a prime) is a natural number greater than 1 that is not a product of two smaller natural numbers. A natural number greater than 1 that is not prime is called a composite number. For example, 5 is prime because the only ways ...

s, 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 In algebra, a quintic function is a function of the form :g(x)=ax^5+bx^4+cx^3+dx^2+ex+f,\, where , , , , and are members of a field, typically the rational numbers, the real numbers or the complex numbers, and is nonzero. In other words, a q ...

equations, the equation of differences, rational functions of roots, resolution by approximation, and the related

Lagrange multipliers In mathematical optimization, the method of Lagrange multipliers is a strategy for finding the local maxima and minima of a function subject to equality constraints (i.e., subject to the condition that one or more equations have to be satisfied ex ...

. The thirty letters which Abbati wrote to Ruffini are now housed in the Ruffini Archive of the

Biblioteca Estense The Biblioteca Estense ('' Estense Library''), was the family library of the marquis and dukes of Este. The exact date of the library's birth is still under speculation, however it is known for certain that the library was in use during the fourte ...

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