**Pietro Marescotti** was an Italian mathematician who did research in the areas of algebraic equations, probability and group theory.

- We shall explain below when and why the name Marescotti was added to his given name.
- Pietro Abbati was brought up in Modena where he attended the university, studying mathematics with teachers Luigi Fantini, Paolo Cassiani and Giovanni Battista Venturi.
- Abbati was three years younger than Paolo Ruffini but they met when both were students at the University of Modena; they became friends and mathematical collaborators.
- It certainly proved advantageous to both Abbati and Ruffini that they could discuss mathematics together, particularly given that both were very talented.
- Although Abbati had no official position in mathematics after he graduated from the University of Modena, nevertheless, he was encouraged to undertake research in mathematics by Ruffini which he did very successfully.
- During the Napoleonic period, Abbati was member of the Society of Mechanical Arts (Società di Arti Meccaniche) and the Agricultural Society in the Department of Panaro (Società Agraria del Dipartimento del Panaro).
- Abbati became, therefore, a member of this combined Society which was renamed the Royal Academy of Sciences, Arts and Letters of Modena (Accademia di Scienze Lettere e Arti di Modena).
- Both Abbati and his friend Ruffini became involved in the administration of the new Republic.
- It appears that Abbati did this with more enthusiasm than Ruffini.
- This may have been due to Ruffini holding academic positions unlike Abbati who, although continuing to work on mathematics, had no teaching posts.
- First Abbati was nominated as a consultant to the Ministry of Public Economy and Education of the Republic, and in 1807 he was employed as an advisor to this Ministry.
- At this time Francis IV, Duke of Modena, appointed Abbati to continue to deal with problems relating to the water and road systems of the Duchy.
- For his outstanding contributions in this area, as well as for his scientific and artistic contributions, a decree of 10 July 1818 allowed Abbati to add Marescotti to his own name.
- Some of Marescotti's works that survive, all of mathematical interest, are:
- Letter of P Abbati of Modena to the member Paolo Ruffini, in Memoires of mathematics and physics of the Italian society of sciences, X, 2 (1803), p. 467-486, in Mathematical works of Paolo Ruffini, edited by E Bortolotti, Rome 1953);
- Reflections of P Abbati Marescotti of Modena on the method of J-L Lagrange for the solution of numerical equations, Modena 1805;
- On the computation of rational functions of the roots of any algebraic equation of the form f(x′,x′′,x′′′,...,x(m)); f (x', x'', x''', ...* 8-23;
- Letter of P Abbati to Sir Abbate Francesco Venini (the letter is dated 1806);
- On a problem of Daniel Bernoulli and Lagrange, in Memoires, cit., XIX, 2 (1824)
- The 1824 memoir [Sopra un problema dei signori Daniele Bernoulli, e De La Grange, memoria del signor conte Pietro Abbati Marescotti socio onorario inserita nel tomo 19. degli atti della Società italiana delle scienze residente in Modena Ⓣ(On a problem of Daniel Bernoulli, and de Lagrange, memoir of the Count Pietro Abbati Marescotti, Honorary member: inserted in Volume 19.

- Of particular importance is the first one, where Marescotti gives the first correct proof of the algebraic insolubility of general equations of degree greater than five, after having discovered that the proof given by Paolo Ruffini was correct for equations of the fifth degree, but not for those of higher degree.
- The letter from Abbati to Ruffini in which he extended Ruffini's proof that quintic equations were not, in general, soluble by radicals was written from Modena and dated 30 September 1802.
- In fact, more than thirty letters between Abbati and Ruffini have survived and are now in the Biblioteca Estense in Modena.
- For example, they discussed the relation between the roots of an equation and its coefficients, the number of imaginary roots that an equation possesses, particularly discussing the results of Pietro Paoli.
- Abbati and Ruffini also discussed results concerning permutations of the roots of algebraic equations of degree 4 and also of algebraic equation of degree 5 and above.
- Certainly some of the ideas of group theory introduced by Ruffini were originally ideas coming from Abbati.
- In addition to the academies and societies mentioned above, Abbati was elected a member of the National Academy of Sciences of Italy (the "Academy of Forty") in 1826 and elected to the Accademia di Scienze e Belle Lettere di Palermo.
- We should also mention that Abbati made contributions to the arts, establishing the Abbati Marescotti theatre in Modena in 1833.

Born 1 September 1768, Modena, Duchy of Modena and Reggio (now Italy). Died 7 May 1842, Modena, Duchy of Modena and Reggio (now Italy).

View full biography at MacTutor

Origin Italy

**O’Connor, John J; Robertson, Edmund F**: MacTutor History of Mathematics Archive