**Pia Nalli** was an Italian mathematician known for her work on algebraic geometry, functional analysis and tensor analysis.

- Pia was educated in Palermo and after graduating from the local school, entered the University of Palermo.
- While Nalli was studying at the University of Palermo, Sicily was hit with a 7.1 magnitude earthquake on 28 December 1908.
- However, one consequence of the earthquake was that Giuseppe Bagnera, who was on the staff at Messina at the time, joined the University of Palermo and was advisor to Nalli during the final stages of writing her thesis.
- Nalli joined the Mathematical Circle in 1910, after graduating from Palermo.
- At the time when Nalli joined, the Mathematical Circle had, over the preceding few years, published some of the most important mathematical papers in the world in the Rendiconti.
- Nalli submitted her first paper Riduzione di un fascio di curve piane di genere uno, corrispondente a se stesso in una trasformazione birazionale involutoria del piano Ⓣ(Reduction of a bundle of generally planar curves of genus one, corresponding to itself in a birational transformation involution) to the Mathematical Circle in May 1910.
- Her second paper Sopra una definizione di dominio piano limitato da una curva continua, senza punti multipli Ⓣ(On a plane domain definition limited by a continuous curve without multiple points) was submitted to the Mathematical Circle in September 1911, read at a meeting of the society on 12 November 1911 and printed on 25 November 1911.
- Nalli was Giuseppe Bagnera's assistant at the University of Palermo from 1 April 1911 to 16 November 1911.
- Despite a very heavy teaching load, Nalli was able to carry out high quality research during her time as a school teacher.
- Between 1915 and 1918, Nalli concentrated her efforts on extending the theorem of de la Vallee Poussin to functions fff that are integrable using the restricted Denjoy integral.
- Nalli published Sulle serie di Fourier delle funzione non assolutamente integrabili Ⓣ(On the Fourier series of the absolutely integrable function) in 1915.
- Progress along these lines came to a stop at that point and Nalli's result was the high point in this area for a long time.
- In the year 1919 Nalli started to work on issues related to the theory of linear integral equations and the study of integral operators.
- Already, at this time, Nalli was a university lecturer being appointed as an extraordinary professor of analysis at the University of Cagliari in 1921.
- The panel examining the candidates put Picone first and Nalli second.
- It is now widely believed that Nalli was actually ranked first but pushed down the list because she was a woman.
- Cagliari then gave Nalli an extraordinary professorship of analysis.
- Although she was a professor at Cagliari, Nalli continued to enter competitions for professorships at other universities.
- However, despite being ranked first, Pavia did not appoint Nalli to the chair and she wrote a strong letter of complaint to the rector of the university as well as writing to Tullio Levi-Civita complaining bitterly about the injustice.
- However, the greatest indication of the reply Nalli must have received is seen from the fact that at this time she changed her research topic and after this worked on tensor calculus, the topic for which Levi-Civita is famed.
- Nalli carried on and took part in the competition for the chair at Florence, and she was again ranked second (as we noted above) while the local candidate, whom the faculty at Florence had been expecting would be appointed, was not ranked at all.
- The University of Catania claimed that Nalli had not responded quickly enough to their proposal of 4 August 1926 so withdrew their offer to her.
- Nalli was not going to accept this sort of treatment, so she wrote to the Minister of Education, Pietro Fedele (1873-1943), who was a modern historian at Turin before being made Education Minister in 1925.
- Despite some time having now elapsed, no appointment had been made to the chair at the University of Catania and, after Pietro Fedele intervened, they offered Nalli a permanent chair of analysis starting on 16 February 1927.
- The professorship at Catania did not suit Nalli, partly because she felt that her colleagues resented her being there, having only accepted her at Fedele's insistence, partly because she would have preferred to be in Palermo where she felt much more at home.
- Let us indicate some of Nalli's publications after she moved to Catania.
- But in the national scene, Pia Nalli was left in complete obscurity.
- Despite the lack of honours given to Nalli in her lifetime, we note that she has been honoured with the naming of a street Via Pia Nalli in Rome.

Born 10 February 1886, Palermo, Sicily, Italy. Died 27 September 1964, Catania, Sicily, Italy.

View full biography at MacTutor

Origin Italy, Women

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