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Vito Volterra

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Vito Volterra
Born(1860-05-03)3 May 1860
Ancona, Papal States
Died11 October 1940(1940-10-11) (aged 80)
Rome, Kingdom of Italy
Alma materUniversity of Pisa
Scuola Normale Superiore di Pisa
Known forVolterra integral equation
Volterra operator
Lotka–Volterra equations
Volterra lattice
Scientific career
InstitutionsUniversity of Pisa
University of Turin
Sapienza University of Rome
Doctoral advisorEnrico Betti
Doctoral studentsPaul Lévy
Joseph Pérès
Cornelia Fabri

Vito Volterra KBE FRS(For) HFRSE (/vlˈtɛrə/, Italian: [ˈviːto volˈtɛrra]; 3 May 1860 – 11 October 1940) was an Italian mathematician and physicist, known for his contributions to mathematical biology and integral equations,[2][3] being one of the founders of functional analysis.[4]


Born in Ancona, then part of the Papal States, into a very poor Jewish family: his father was Abramo Volterra and his mother, Angelica Almagià. Abramo Volterra died in 1862 when Vito was two years old. The family moved to Turin, and then to Florence, where he studied at the Dante Alighieri Technical School and the Galileo Galilei Technical Institute. [5]

Volterra showed early promise in mathematics before attending the University of Pisa, where he fell under the influence of Enrico Betti, and where he became professor of rational mechanics in 1883. He immediately started work developing his theory of functionals which led to his interest and later contributions in integral and integro-differential equations. His work is summarised in his book Theory of functionals and of Integral and Integro-Differential Equations (1930).

In 1892, he became professor of mechanics at the University of Turin and then, in 1900, professor of mathematical physics at the University of Rome La Sapienza. Volterra had grown up during the final stages of the Risorgimento when the Papal States were finally annexed by Italy and, like his mentor Betti, he was an enthusiastic patriot, being named by the king Victor Emmanuel III as a senator of the Kingdom of Italy in 1905. In the same year, he began to develop the theory of dislocations in crystals that was later to become important in the understanding of the behaviour of ductile materials. On the outbreak of World War I, already well into his 50s, he joined the Italian Army and worked on the development of airships under Giulio Douhet. He originated the idea of using inert helium rather than flammable hydrogen and made use of his leadership abilities in organising its manufacture. [citation needed]

After World War I, Volterra turned his attention to the application of his mathematical ideas to biology, principally reiterating and developing the work of Pierre François Verhulst. An outcome of this period is the Lotka–Volterra equations.

Volterra is the only person who was a plenary speaker in the International Congress of Mathematicians four times (1900, 1908, 1920, 1928).[6][7][8][9][10]

Volterra was an International Member of the United States National Academy of Sciences and the American Philosophical Society.[11][12]

In 1922, he joined the opposition to the Fascist regime of Benito Mussolini and in 1931 he was one of only 12 out of 1,250 professors who refused to take a mandatory oath of loyalty. His political philosophy can be seen from a postcard he sent in the 1930s, on which he wrote what can be seen as an epitaph for Mussolini's Italy: Empires die, but Euclid’s theorems keep their youth forever. However, Volterra was no radical firebrand; he might have been equally appalled if the leftist opposition to Mussolini had come to power, since he was a lifelong royalist and nationalist. As a result of his refusal to sign the oath of allegiance to the fascist government he was compelled to resign his university post and his membership of scientific academies, and, during the following years, he lived largely abroad, returning to Rome just before his death.

In 1936, he had been appointed a member of the Pontifical Academy of Sciences, on the initiative of founder Agostino Gemelli.

He died in Rome on 11 October 1940. He is buried in the Ariccia Cemetery. The Academy organised his funeral.


In 1900 he married Virginia Almagia, a cousin.[13] Their son Edoardo Volterra (1904–1984) was a famous historian of Roman law.[14]

Volterra also had a daughter, Luisa Volterra, who married Umberto d'Ancona. D'Ancona piqued his father-in-law's interest in biomathematics when he showed Vito a set of data regarding populations of different species of fish in the Adriatic Sea, where decreased fishing activity from the war had led to an increase in the populations of predatory fish species. Vito published an analysis of the dynamics of interacting species of fish the next year.

Selected writings by Volterra[edit]

  • 1912. The theory of permutable functions. Princeton University Press.
  • 1913. Leçons sur les fonctions de lignes. Paris: Gauthier-Villars.[15]
  • 1912. Sur quelques progrès récents de la physique mathématique. Clark University.[16]
  • 1913. Leçons sur les équations intégrales et les équations intégro-différentielles. Paris: Gauthier-Villars.[17]
  • 1926, "Variazioni e fluttuazioni del numero d'individui in specie animali conviventi," Mem. R. Accad. Naz. dei Lincei 2: 31–113.
  • 1926, "Fluctuations in the abundance of a species considered mathematically," Nature 118: 558–60.
  • 1930. Theory of functionals and of integral and integro-differential equations. Blackie & Son.[18]
  • 1931. Leçons sur la théorie mathématique de la lutte pour la vie. Paris: Gauthier-Villars.[19] Reissued 1990, Gabay, J., ed.
  • 1936. with Joseph Pérès: Théorie générale des fonctionnelles. Paris: Gauthier-Villars.[20]
  • 1938. with Bohuslav Hostinský: Opérations infinitésimales linéaires. Paris: Gauthier-Villars.[21]
  • 1960. Sur les Distorsions des corps élastiques (with Enrico Volterra). Paris: Gauthier-Villars.
  • 1954-1962. Opere matematiche. Memorie e note.[22] Vol. 1, 1954; Vol. 2, 1956; Vol. 3, 1957; Vol. 4, 1960; Vol. 5, 1962; Accademia dei Lincei.

See also[edit]


  1. ^ Whittaker, E. T. (1941). "Vito Volterra. 1860-1940". Obituary Notices of Fellows of the Royal Society. 3 (10): 690–729. doi:10.1098/rsbm.1941.0029.
  2. ^ Borsellino, A. [in Italian] (1980). "Vito Volterra and Contemporary Mathematical Biology". In Barigozzi, Claudio (ed.). Vito Volterra Symposium on Mathematical Models in Biology. New York: Springer. pp. 410–417. ISBN 0-387-10279-5.
  3. ^ O'Connor, John J.; Robertson, Edmund F., "Vito Volterra", MacTutor History of Mathematics Archive, University of St Andrews
  4. ^ According to Accardi (1992, p. 150). Precisely, Accardi's analysis of the contribution of Volterra to the founding of functional analysis is aimed to show that he was the sole founder of the field, and to stimulate the readers to read Volterra's original papers.
  5. ^ Biographical Index of Former Fellows of the Royal Society of Edinburgh 1783–2002 (PDF). The Royal Society of Edinburgh. July 2006. ISBN 0-902-198-84-X.
  6. ^ "International Congress of Mathematicians".
  7. ^ "Betti, Brioschi, Casorati, trois analystes italiens et trois manières d'envisager les questions d'analyse par Vito Volterra". Compte rendu du deuxième Congrès international des mathématiciens tenu à Paris du 6 au 12 Aout 1900. Vol. Tome 2. 1902. pp. 43–57.
  8. ^ Volterra, Vito. "Le matematiche in Italia nella seconda metà del secolo XIX." In Atti del IV Congresso Internazionale dei Matematici (Roma 1908), vol. 1, pp. 55-65. 1909.
  9. ^ "Sur l'enseignement de la physique mathématique et de quelques points d'analyse par Vito Volterra" (PDF). Compte rendu du Congrès international des mathématiciens tenu à Strasbourg du 22 au 30 Septembre 1920. 1921. pp. 81–97.
  10. ^ Volterra, Vito. "La teoria dei funzionali applicata ai fenomeni ereditari." Atti Congr. intern. dei Mat. a Bologna, vol. 1 (1928), pp. 215–232
  11. ^ "Vito Volterra". www.nasonline.org. Retrieved 9 November 2023.
  12. ^ "APS Member History". search.amphilsoc.org. Retrieved 9 November 2023.
  13. ^ Biographical Index of Former Fellows of the Royal Society of Edinburgh 1783–2002 (PDF). The Royal Society of Edinburgh. July 2006. ISBN 0-902-198-84-X.
  14. ^ Sturm, Fritz (1987). "Edoardo Volterra (1904–1984)". Zeitschrift der Savigny-Stiftung für Rechtsgeschichte: Romanistische Abteilung (in German). 104 (1): 918‐926. doi:10.7767/zrgra.1987.104.1.918. S2CID 180699084.
  15. ^ Bliss, G. A. (1915). "Book Review: Leçons sur les Fonctions des Lignes". Bulletin of the American Mathematical Society. 21 (7): 345–355. doi:10.1090/S0002-9904-1915-02656-X. MR 1559651.
  16. ^ Shaw, James Byrnie (1915). "Book Review: Sur quelques Progrès récents de la Physique mathématique". Bulletin of the American Mathematical Society. 21 (4): 192–200. doi:10.1090/S0002-9904-1915-02600-5.
  17. ^ Westlund, Jacob (1914). "Book Review: Leçons sur les Equations intégrales et les Equations intégro-différentielles". Bulletin of the American Mathematical Society. 20 (5): 259–263. doi:10.1090/S0002-9904-1914-02481-4.
  18. ^ Langer, R. E. (1932). "Book Review: Theory of Functionals and of Integral and Integro-differential Equations". Bulletin of the American Mathematical Society. 38 (9): 623–624. doi:10.1090/S0002-9904-1932-05479-9.
  19. ^ Doob, J. L. (1936). "Book Review: Leçons sur la Théorie Mathématique de la Lutte pour la Vie". Bulletin of the American Mathematical Society. 42 (5): 304–306. doi:10.1090/S0002-9904-1936-06292-0.
  20. ^ Hestenes, M. R. (1938). "Book Review: Théorie Générale des Fonctionnelles". Bulletin of the American Mathematical Society. 44 (5): 311–313. doi:10.1090/S0002-9904-1938-06719-5.
  21. ^ Birkhoff, Garrett (1938). "Book Review: Opérations Infinitésimales Linéaires". Bulletin of the American Mathematical Society. 44 (11): 759–762. doi:10.1090/S0002-9904-1938-06869-3.
  22. ^ Weinstein, A. (1964). "Review: Opere matematiche, by Vito Volterra". Bulletin of the American Mathematical Society. 70 (3): 335–337. doi:10.1090/s0002-9904-1964-11086-7.

Biographical references[edit]

General references[edit]

External links[edit]