Pietro Abbati Marescotti
Encyclopedia
Pietro Abbati Marescotti (1 September 1768 – 7 May 1842) 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 (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 appoximation 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 All the letters remain unpublished except one published by E. Bortolotti in an edition of Ruffini's correspondence.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 events of Abbati's life were:
In addition to the honors listed above, Abbati was also a member of the:
Italy
Italy , officially the Italian Republic languages]] under the European Charter for Regional or Minority Languages. In each of these, Italy's official name is as follows:;;;;;;;;), is a unitary parliamentary republic in South-Central Europe. To the north it borders France, Switzerland, Austria and...
mathematician
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
who taught in Modena
Modena
Modena is a city and comune on the south side of the Po Valley, in the Province of Modena in the Emilia-Romagna region of Italy....
.
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
Paolo Ruffini
Paolo Ruffini was an Italian mathematician and philosopher.By 1788 he had earned university degrees in philosophy, medicine/surgery, and mathematics...
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
Diophantine equation
In mathematics, a Diophantine equation is an indeterminate polynomial equation that allows the variables to be integers only. Diophantine problems have fewer equations than unknown variables and involve finding integers that work correctly for all equations...
, prime numbers
Prime number
A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. A natural number greater than 1 that is not a prime number is called a composite number. For example 5 is prime, as only 1 and 5 divide it, whereas 6 is composite, since it has the divisors 2...
, 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
Quartic function
In mathematics, a quartic function, or equation of the fourth degree, is a function of the formf=ax^4+bx^3+cx^2+dx+e \,where a is nonzero; or in other words, a polynomial of degree four...
and quintic
Quintic equation
In mathematics, a quintic function is a function of the formg=ax^5+bx^4+cx^3+dx^2+ex+f,\,where a, b, c, d, e and f are members of a field, typically the rational numbers, the real numbers or the complex numbers, and a is nonzero...
equations, the equation of differences, rational functions of roots, resolution by appoximation and the related Lagrange multipliers
Lagrange multipliers
In mathematical optimization, the method of Lagrange multipliers provides a strategy for finding the maxima and minima of a function subject to constraints.For instance , consider the optimization problem...
.
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 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 ModenaFrancis IV, Duke of ModenaFrancis IV Joseph Charles Ambrose Stanislaus was Duke of Modena, Reggio, and Mirandola , Duke of Massa and Prince of Carrara , Archduke of Austria-Este, Royal Prince of Hungary and Bohemia, Knight of the Order of the Golden Fleece...
- 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 earl.
- 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 PanaroPanaroThe Panaro is an Italian river and the final right-hand tributary to the Po, discounting the Cavo Napoleonico canal. It runs right across Emilia-Romagna in a north-easterly direction: from its source close to the Apennine watershed, where Emilia-Romagna meets Tuscany, to its outlet where the Po...
)
- 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 PalermoPalermoPalermo is a city in Southern Italy, the capital of both the autonomous region of Sicily and the Province of Palermo. The city is noted for its history, culture, architecture and gastronomy, playing an important role throughout much of its existence; it is over 2,700 years old...
(Palermo Academy of Arts and Sciences)