Nicola Fergola

Nicola Fergola (29 October 175321 June 1824) was an Italian mathematician. He was the founder of the synthetic school, whose teaching centred on pure geometry and the methods of classical mathematics.

Life and work

Fergola studied in the Jesuit school; he then went to the university of Naples in 1767, where he studied mathematics under Giuseppe Marzucco. As concerns his philosophical education, he was deeply influenced by the mathematician Nicola Antonio De Martino (1701-1769), and by the Enlightenment philosopher Antonio Genovesi. In particular, Genovesi believed that a science consisted of established, proven, and interconnected truths, and that a scientific theory had to be presented according to the method of the ancient geometers, namely the synthetic method. From Genovesi Fergola inherited his lifelong commitment to synthetic geometry.

From 1770 Fergola was teaching, by royal appointment, in the Liceo del Salvatore, a school founded in the same building where the Jesuit school had been (the Jesuit order was suppressed three years before).

Fergola founded his own private school in Naples in 1771. This school quickly gained a high reputation and many of the brightest boys of the country were sent to study there. Fergola taught and did research in both synthetic and analytic geometry, paying special attention to the physical application of calculus. The first works on the application of integral calculus to physical problems published in Naples were by him. However Fergola showed a strong preference for the synthetic methods of classical geometry.

In 1779 Fergola was made a member of the Royal Academy of Sciences. His lectures on conic sections, published anonymously in 1791, were highly successful and adopted in colleges across the kingdom.

In 1799, during the Napoleonic period, he lived in Capodimonte but, when the Borbonic monarchy was restated, he was appointed to the mathematics chair in the university of Naples. In 1821 he suffered a stroke which left him disabled for the rest of his life. Fergola died in Naples on 21 June 1824.

Work Fergola was one of the most important mathematician of the Kingdom of Naples in the late eighteenth century. A pioneer of projective geometry, his work was highly appreciated by Michel Chasles.

Fergola was one of the protagonists of an ideological quarrel among the Neapolitan scientists at the end of 18th and the first half of the 19th century. In the field of mathematics, the quarrel was about the use of synthetic or analytic methods. These polemics were coincident with the politically conservative conceptions of the former and the progressive views of the followers of the analytic method.

Fergola and his school put particular emphasis on the need for a "pure" mathematics to be taught and practised. According to them, mathematics is "pure" when not related to material reality, but only to spiritual entities. They considered mathematics a spiritual science, a powerful resource against atheism and materialism, and insisted that it should not be contaminated with practical applications.

Fergola's close ties with the Bourbon dynasty proved fatal to his legacy. After the unification of Italy his school was accused of being a reactionary and his work was virtually forgotten. He was rediscovered at the end of the nineteenth century by Gino Loria.

Fergola wrote many treatises on mathematics and mechanics. His most important work is Prelezioni sui Principi matematici della filosofia naturale del cavalier Isacco Newton (Introduction to Mathematical Principles of the Natural Philosophy of Isaac Newton), published in two volumes in 1792 and 1793. It is interesting to see the religious point of view of the Newtonian force concept.

This religious conception is seen in all of Fergola's mathematical works. Fergola's manuscript entitled Teorica de miracoli esposta con metodo dimostrativo was published in 1839, in which Fergola tried to demonstrate the possibility of the miracles in a mathematical way: proposition, demonstration, theorem, lemma, scolium, etc.

Selected works

Della invenzione geometrica opera postuma, di Nicola Fergola; ordinata, compiuta, e corredata d'importanti note dal prof. V. Flauti, aggiuntovi un esercizio di problemi geometrici risoluti con gli antichi, ed i moderni metodi, In Napoli: Nella stamperia dell'autore, 1842 (on-line).