**Vincenzo Flauti** was an Italian mathematician who was a leader of the synthetic school of mathematics.

- Before looking at Flauti's life let us understand a little of the background.
- We have to look at Flauti's life and work against this background.
- Flauti was educated in Naples and greatly benefited from the educational institutions of that city, the schools and the university.
- Flauti was educated at Fergola's school along with other fellow students, Giuseppe Scorza (1781-1843) and Ferdinando De Luca (1783-1869), all of whom as well as being Fergola's students would become his followers.
- Giuseppe Scorza was born in a small town in Calabria in 1781 and so was a year older that Flauti.
- He moved to Naples for his education and he and Flauti studied philosophy with Giuseppe Caposale, and elementary geometry with Macello Cecere.
- However, the greatest influence on Flauti and his two contemporaries, was Nicola Fergola who taught mathematics in the rigorous style of the ancient Greek geometers.
- He taught rigorous mathematics with a tenderness and passion which determined how Flauti would approach both research and teaching mathematics for the rest of his life.
- Flauti had started to study medicine but largely due to Fergola's influence, he turned to mathematics.
- In 1801, Flauti took over the management, together with Felice Giannattasio (1759-1849), of the private high school that Fergola had founded about thirty years earlier but had been closed during the fighting of 1799.
- Shortly after taking over management of the school, Flauti began his career at the University of Naples, benefiting from the favours bestowed by Ferdinand IV to his loyal supporters after his restoration.
- The teachings of Flauti should not lead one into thinking that, on his side, he inclines towards analytical methods.
- In 1806, the commission established by the government to choose the texts to be adopted in Neapolitan schools approved Fergola's proposal to assign to Flauti the task of dictating which criteria a course of mathematics should follow.
- The criteria inspiring Flauti's work are described by him in Del metodo in matematiche, della maniera d'ordinare gli elementi di queste scienze e dell'insegnamento dei medesimi con un'esposizione del corso di matematiche del professor Flauti, dissertazioni lette alla Reale Accademia delle scienze di Napoli l'anno 1821 e che ora si pubblicano per la seconda volta Ⓣ(On the method in mathematics, of the way of ordering the elements of these sciences and of their teaching with an exposition of the course of mathematics by Professor Flauti, dissertations read to the Royal Academy of Sciences of Naples in 1821 and which now are published for the second time), Naples 1822.
- The ideal course of mathematics - according to Flauti - should have geometry as a starting point and should propose in an historical sequence a sort of anthology that, starting from Euclid's Elements and passing through conic sections, would arrive at Archimedes and Pappus and finally at trigonometry.
- Algebra too, according to Flauti, should be taught using the Euclidean method, that is, by clearly expressing the theorems.
- In reality, the programme put forward by Flauti provided such an incoherent and schematic exposition of the main topics to be covered in the course that it is reasonable to suppose that the work was to be written up by multiple authors.
- Flauti edited editions of Euclid (The first six books and the eleventh and twelfth of Euclid, Naples, 1810) as well as a treatise on trigonometry and one on algebra, both with a long historical introduction.
- Flauti supported the idea that descriptive geometry was a complement of ancient geometry.
- The eighth booklet, edited by Flauti, dealt with the problem of the Wallis cylindroid, which was treated again in La misura del cilindroide wallisiano Ⓣ(The measure of the Wallis cylindroid), in Atti della Reale Accademia delle scienze Ⓣ(Proceedings of the Royal Academy of Sciences), IV (1839), p.
- Around 1850, Flauti contributed to differential geometry with some observations on the theory of envelopes (Observations on the methods proposed by the illustrious Lagrange for the envelope curves with other alike researches, in Memoirs of mathematics and physics of the Italian society of sciences residing in Modena, (1850), p.
- A fundamental intent of Flauti was that of claiming the role that Fergola's school had in reviving the spirit of scientific inquiry (On geometric invention, posthumous work of Nicola Fergola ordered and containing important notes of prof.
- Flauti, Naples 1842).
- 223-236), dedicated to the history of the divination of the lost books of Apollonius on the intentions and the exposition of the results obtained by him and by his pupil R Minervini, Flauti was again aiming to praise the booklets of Fergola's school published around 1810.
- Flauti had been a supporter of the defeated Bourbons and so was excluded from the Academy of Sciences of Naples when it was reconstituted as an academy within the Kingdom of Italy.
- Flauti had been elected to the Academy of Sciences of Naples on 17 July 1854 and had been a secretary of the Academy.
- As well as his mathematical texts, Flauti also published Teoria dei miracoli Ⓣ(Theory of miracles), a mathematical demonstration of the existence of God.

Born 4 April 1782, Naples, Kingdom of Naples (now Italy). Died 20 June 1863, Naples, Italy.

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Origin Italy

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