**Pietro Paoli** was an Italian mathematician. He worked mainly in calculus and its applications to optics and mechanics.

- Paoli continued to hold the chair of algebra at Pisa until 1798 when he was appointed to the chair of higher mathematics.
- The University became an Imperial Academy in 1803 and at this time Paoli was named as an Honorary Inspector.
- The University of Pisa became a Normal School in 1813 and Paoli was one of the commissioners appointed to draft new regulations for the University.
- Among Paoli's publications we mention Liburnensis Opuscula analytica Ⓣ(Works on analysis from Livorno) (1780), Ricerche sulle serie Ⓣ(Research on series) (1788) which corrects an error in a 1779 paper by Laplace on series, Della integrazione dell'equazioni a differenze parziali finite ed infinitesime Ⓣ(On integration of the equations of partial finite and infinitesimal differences) (1800), Sulle oscillazioni di un corpo pendente da un filo estendibile memoria Ⓣ(Memoir on the oscillations of a body hanging from an expandable wire)(1815), and Sull'uso del calcolo delle differenze finite nella dottrina degl'integrali definiti memoria Ⓣ(Memoir on the use of the calculation of finite differences in definite integrals) (1828).
- Paoli was most famed for Elementi di algebra finita ed infinitesimale Ⓣ(Introduction to finite and infinitesimal algebra) (1794) which became a classic text used in Italy for many years.
- Paoli, who corresponded and exchanged books with Lagrange, sent a copy of the first edition of his Elements of algebra to Lagrange who replied with a note of thanks in September 1798.
- We see from the Preface that Paoli wanted to write the book because he was unhappy with the standard of mathematics teaching in Italy at this time.
- Of course, as well as Ruffini, Paoli was thinking of Lagrange, with whom he corresponded, as an Italian.
- Perhaps Paoli's most famous student was Vincenzo Brunacci (1768-1818) who studied with him at Pisa, graduated in 1788, and published the two volume Elementi di algebra e di Geometria Ⓣ(Introduction to algebra and geometry) in 1809.
- In addition to Brunacci, Paoli's students included Giovanni Taddeo Farini (1778-1822) and Antonio Bordoni.
- Paoli received many honours including election to the academies of Bologna, Naples, and Mantua, and to the Mathematical Circle of Palermo.

Born 2 March 1759, Livorno (now Italy). Died 21 February 1839, Florence (now Italy).

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Origin Italy

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