3 May 1860|
|Died||11 October 1940
|Institutions||University of Turin|
|Alma mater||University of Pisa|
|Doctoral advisor||Enrico Betti|
|Doctoral students||Paul Lévy
|Known for||Theory of integral equations
The Lotka–Volterra equations
Born in Ancona, then part of the Papal States, into a very poor Jewish family, 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.
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. The most famous outcome of this period is the Lotka–Volterra equations.
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.
Selected writings by Volterra 
- 1910. Leçons sur les fonctions de lignes. Paris: Gauthier-Villars.
- 1912. The theory of permutable functions. Princeton University Press.
- 1913. Leçons sur les équations intégrales et les équations intégro-différentielles. Paris: Gauthier-Villars.
- 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.
- 1960. Sur les Distorsions des corps élastiques (with Enrico Volterra). Paris: Gauthier-Villars.
- 1930. Theory of functionals and of integral and integro-differential equations. Blackie & Son.
- 1931. Leçons sur la théorie mathématique de la lutte pour la vie. Paris: Gauthier-Villars. Reissued 1990, Gabay, J., ed.
- 1954-1962. Opere matematiche. Memorie e note. Vol. 1, 1954; Vol. 2, 1956; Vol. 3, 1957; Vol. 4, 1960; Vol. 5, 1962; Accademia dei Lincei.
See also 
- Volterra (crater)
- Volterra's function
- Lotka–Volterra equation
- Smith–Volterra–Cantor set
- Volterra integral equation
- Volterra series
- Product integral
- Volterra operator
- Volterra space
- Volterra Semiconductor
- Poincaré lemma
- Whittaker, E. T. (1941). "Vito Volterra. 1860-1940". Obituary Notices of Fellows of the Royal Society 3 (10): 690–626. doi:10.1098/rsbm.1941.0029.
- O'Connor, John J.; Robertson, Edmund F., "Vito Volterra", MacTutor History of Mathematics archive, University of St Andrews.
- Vito Volterra at the Mathematics Genealogy Project
- Weinstein, A. (1964). "Review: Opere matematiche, by Vito Volterra". Bull. Amer. Math. Soc. 70 (3): 335–337.
- Castelnuovo, G. (1943), "Vito Volterra", Rendiconti della Accademia Nazionale delle Scienze detta dei XL, Memorie di Matematica e Applicazioni, Serie 3, (in Italian) XXV (70): 87–95, MR 0021530, Zbl 0061.00605.
- Goodstein, Judith R. (2007), The Volterra Chronicles: The Life and Times of an Extraordinary Mathematician 1860–1940, History of Mathematics 31, Providence, RI-London: American Mathematical Society/London Mathematical Society, ISBN 0-8218-3969-1, MR 2287463, Zbl 1123.01016. See also the review in American Scientist.
- Israel, G. (2005), "Book on mathematical biology", in Grattan-Guinness, I., Landmark Writings in Western Mathematics, 1640–1940, Amsterdam: Elsevier, pp. xxvi+310, ISBN 0-444-50871-6, MR 0408866, Zbl 1090.01002
- Israel, G. (1988). "On the contribution of Volterra and Lotka to the development of modern biomathematics". History and philosophy of the life sciences 10 (1): 37–49. PMID 3045853.
- Scudo, F. (1971). "Vito Volterra and theoretical ecology". Theoretical Population Biology 2 (1): 1–23. doi:10.1016/0040-5809(71)90002-5. PMID 4950157.
- Pancaldi, G. (1993) ‟Vito Volterra: Cosmopolitan Ideals and Nationality in the Italian Scientific Community between the “Belle époque” and the First World War.” in «Minerva», 31: 21-37.