Pia Nalli

Pia Maria Nalli (February 10, 1886 – September 27, 1964) was an Italian mathematician known for her work on the summability of Fourier series, on Morera's theorem for analytic functions of several variables and for finding the solution to the Fredholm integral equation of the third kind for the first time.[3] Her research interests ranged from algebraic geometry to functional analysis and tensor analysis; she was a speaker at the 1928 International Congress of Mathematicians.

Pia Nalli
Pia Nalli
Born(1886-02-10)10 February 1886
Palermo
DiedSeptember 27, 1964(1964-09-27) (aged 78)
Catania
Alma materUniversity of Palermo
Scientific career
Fields
Institutions
Theses
  • Riduzione di un fascio di curve piane di genere uno, corrispondente a sé stesso in una trasformazione birazionale involutoria del piano[1] (1911)
  • Esposizione e confronto critico delle diverse definizioni proposte per l'integrale definito[2] (1914)
Doctoral advisorGiuseppe Bagnera
Notable studentsGaetano Fichera

She is also remembered for her struggles against discrimination against women in the Italian university hiring system.[4] A street in Rome is named after her.

Life and academic career

Early life and education

Nalli was born on February 10, 1886, in Palermo, to a middle-class family with seven children.[5] She studied at the University of Palermo, where she obtained a laurea in 1910 under the supervision of Giuseppe Bagnera,[6] with a thesis concerning algebraic geometry, and in the same year joined the Circolo Matematico di Palermo.[5]

After finishing her studies, Nalli assisted Bagnera in Palermo in 1911, and then began working as a school teacher. She completed a habilitation thesis in 1914 on the theory of integrals, and continued to work on Fourier analysis and Dirichlet series for the next several years.[5]

Academic career

Nalli served as assistant to Giuseppe Bagnera at the University of Palermo from 1 April 1911 to 16 November 1911. She then taught at a number of secondary schools, first in the girls' school at Avellino, then in Trapani, and from 16 November 1912 in the girls' technical school in Palermo. During this time Nalli continued her research, completing her thesis "Esposizione e confronto critico delle diverse definizioni proposte per l'integrale definito di una funzione limitata o no",[2] a study of the theory of the integral based on recent work on the subject by Émile Borel, Henri Lebesgue Charles de la Vallée Poussin, Giuseppe Vitali and Arnaud Denjoy.[5]

In 1921, Nalli became extraordinary professor at the University of Cagliari. She had been ranked second to Mauro Picone in the competition for the position, possibly in part because she was female, but Picone chose to stay at the University of Catania and become head of mathematics there, so the Cagliari position fell to Nalli. In 1923, she was listed first in a search for a position at the University of Pavia, but not offered the position. Finally, after similar mistreatment from several other universities, she moved to the University of Catania as a full professor in 1927. At around this time, perhaps encouraged by Tullio Levi-Civita, she switched her research focus from functional analysis to tensor calculus.[5]

She was an invited speaker at the International Congress of Mathematicians in 1928.[7]

Death and legacy

Nalli died on September 27, 1964, in Catania. A street in Rome, the Via Pia Nalli,[8] is named after her.[5]

Selected works

Pia Nalli published 61 mathematical works, including the monograph (Nalli 1914) and a textbook.[9] Her "Selected works" (Nalli 1976) include this monograph plus eleven articles on topics mainly belonging to functional and mathematical analysis: the following list includes also her doctoral thesis (Nalli 1911) and other works on tensor calculus

  • Nalli, Pia (1911), "Riduzione di un fascio di curve piane di genere uno, corrispondente a sé stesso in una trasformazione birazionale involutoria del piano" [Reduction of a bundle of genus one planar curves, corresponding to itself in a birational involutive transformation of the plane] (PDF), Rendiconti del Circolo Matematico di Palermo (in Italian), 31 (1): 92–108, doi:10.1007/BF03018796, JFM 42.0604.02.
  • Nalli, Pia (1914), Esposizione e confronto critico delle diverse definizioni proposte per l'integrale definito di una funzione limitata o no [Exposition and critical comparison of the different definitions proposed for the definite integral of a bounded or not function] (in Italian), Palermo: Stabilimento tipografico Virzì, p. 163, JFM 45.1282.01.
  • Nalli, Pia (1922), "Sulle operazioni funzionali lineari" [On linear functional operations], Rendiconti del Circolo Matematico di Palermo (in Italian), 46 (1): 49–90, doi:10.1007/BF03018259, JFM 48.1247.01.
  • Nalli, Pia (1928), "Sulla metrica superficiale di una varietà" [On the surface metric of a manifold], Rendiconti del Circolo Matematico di Palermo (in Italian), 52 (1): 260–264, doi:10.1007/BF03016619, JFM 54.0769.01.
  • Nalli, Pia (1937), "Trasporti rigidi di vettori nelle varietà metriche" [Rigid transport of vectors in metric manifolds], Rendiconti del Circolo Matematico di Palermo (in Italian), 61 (2): 314–338, doi:10.1007/BF03014120, JFM 65.0796.06, Zbl 0020.26002.
  • Nalli, Pia (1976), Fichera, Gaetano; Guglielmino, Francesco (eds.), Opere scelte [Selected works], Opere dei Grandi Matematici Italiani (in Italian), Milano: Litografia D. Cislaghi per conto dell'Unione Matematica Italiana e dell'Università di Catania, p. 364, Zbl 1308.01004.

Notes
  1. (Nalli 1911).
  2. (Nalli 1914).
  3. See (Fichera 1999, pp. 288–290).
  4. See (Fichera 1978, pp. 55–58).
  5. O'Connor, John J.; Robertson, Edmund F., "Pia Maria Nalli", MacTutor History of Mathematics archive, University of St Andrews..
  6. Pia Nalli at the Mathematics Genealogy Project
  7. ICM Plenary and Invited Speakers since 1897, International Mathematical Union, retrieved 2015-10-07.
  8. 41.79050°N 12.48765°E / 41.79050; 12.48765
  9. According to the list of her works included in (Nalli 1976, pp. 361–364).
gollark: And copper's cost is barely below silver.
gollark: Huh, apparently golds are quite cheap now on the market and silvers are barely above aeons.
gollark: Apparently I also won a raffle for a 4G SAltkin today. This has been a day of very low probability.
gollark: Well, I'm hatchling-locked for the next 4 hours anyway, so no more for a while.
gollark: ... I just got *another* thunder. This is ridiculous.

References

Biographical and general references

  • Fichera, Gaetano (1965), "Necrologio di Pia Nalli" [Obituary of Pia Nalli], Bollettino dell'Unione Matematica Italiana, Serie III (in Italian), 20 (4): 544–549, Zbl 0132.24406.
  • Fichera, Gaetano (1978), "Il contributo femminile al progresso della matematica" [Women's contribution to the advancement of mathematics], Memorie e Rendiconti della Accademia di scienze, lettere e belle arti degli Zelanti e dei Dafnici, Serie II (in Italian), VIII: 41–58.
  • Marino, Mario (2014), "Ricordo di Francesco Guglielmino, matematico" [Recollection of Francesco Guglielmino, mathematician] (PDF), Bollettino dell'Accademia Gioenia (in Italian), 47 (377): 437–444, ISSN 0393-7143.

Scientific references

  • Fichera, Gaetano (1993), "Il calcolo infinitesimale alle soglie del Duemila" [Infinitesimal calculus at the threshold to the year 2000], Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Supplemento, Serie IX, 4 (1): 69–86, MR 1286793, Zbl 0876.01032. A survey paper describing the development of infinitesimal calculus during the twentieth century and trying to trace possible scenarios for its future evolution.
  • Fichera, Gaetano (1999), "L'analisi matematica in Italia fra le due guerre" [Mathematical analysis in Italy between the two world wars], Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni, Serie IX, 10 (4): 279–312, MR 1286793, Zbl 0876.01032. A survey paper describing the development of mathematical analysis in Italy during the two world wars, describing the contributions of several Italian scientists who worked during that period.
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