Abstract
In Chap. 5 and the war years, we spoke very little of mathematics. In effect, Volterra’s political and academic responsibilities amply justified the fact that he had less time for research, and so there was less mathematical work for us to discuss. The same can be said for the period between the two world wars, with the one ‘great exception’ that we will deal with in this chapter.
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Notes
- 1.
The relationship between Volterra and Tonelli was very cordial. At the beginning of the 1920s Volterra campaigned (unsuccessfully) to have Tonelli ‘called’ to the University of Rome. Tonelli left the University of Bologna in 1930, accepting Gentile’s invitation to move to Pisa.
- 2.
Theory of Functionals and of Integral and Integro-Differential Equations (Mineola, NY: Dover Publications, 1959), p. 3.
- 3.
Luigi Fantappiè (1901–1956), a student of Volterra and Severi, taught at the universities of Cagliari, Palermo, Bologna and Rome.
- 4.
Vito Volterra, “Variazioni e fluttuazioni del numero d’individui in specie animali conviventi”, Reale Commitato Talassografico Italiano, Memoria cxxxi, Venice, 1927.
- 5.
Vito Volterra, Leçons sur la théorie mathématique de la lutte pour la vie (Paris: Gauthier-Villars, 1931).
- 6.
Vito Volterra, “Applications des Mathématiques à la Biologie”, L’Enseignement mathématique, 36 (1937), pp. 297–330.
- 7.
Vito Volterra, “Una teoria matematica sulla lotta per l’esistenza”, Scientia, 41 (1927), pp. 85–102.
- 8.
Letter from Umberto D’Ancona to Vito Volterra, 10 February 1929.
- 9.
See Piero Manfredi and Giuseppe A. Micheli, “Ecologia matematica e Matematica delle popolazioni”, in La matematica italiana dopo l’Unità. Gli anni tra le due guerre mondiali (Milan: Marcos y Marcos: 1998), pp. 671–734.
- 10.
Vito Volterra, “Fluctuations in the abundance of a species considered mathematically”, Nature, 118 (1926), pp. 558–560.
- 11.
“Une thérie mathématique de la lutte pour la vie”, Scientia, 41 (1927), pp. 33–48.
- 12.
For more about Kostitzin and his contributions, see Francesco M. Scudo, “Vito Volterra, Ecology and the Quantification of Darwinism”, in Atti del Convegno internazionale in memoreia di Vito Volterra, op. cit.; see also Giorgio Israël and Ana Millán Gasca, The Biology of Numbers (Basel: Birkhäuser, 2002), which contains an interesting account of the debate that arose over Volterra’s contributions.
- 13.
Andrej Kolmogoroff, “Sulla theoria di Volterra della lotta per l’esistenza”, Giornale dell’Istituto Italiano deli Attuari, 7 (1936), pp. 74–80.
- 14.
Vito Volterra, “Variazioni e fluttuazioni del numero d’individui in specie animali conviventi”, op. cit.
- 15.
On this question, see Giorgio Israël, “Le equazioni di Volterra e Lotka: una questione di priorità”, in Atti del Convegno “La storia delle matematiche in Italia”, O. Montaldo and L. Grugnetti, ed. (Cagliari: Università di Cagliari, Istituti di Matematica della Facoltà di Scienze e Ingegneria, 1982), pp. 495–502.
- 16.
For a “modern” defence of the approach taken by Volterra, see, among others, Martin Braun, “Why the Percentage of Sharks Caught in the Mediterranean Sea Rose Dramatically During World War I”, in Differential Equation Models, Martin Braun, Courtney S. Coleman, Donald A. Drew, eds. (Berlin: Springer-Verlag, 1983).
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Guerraggio, A., Paoloni, G. (2012). After the Cats, Fish. In: Vito Volterra. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-27263-9_8
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