Vito Volterra

Vito Volterra's interest in mathematics started at the age of 11 when he began to study Legendre's Geometry. At the age of 13 he began to study the Three Body Problem and made some progress by partitioning the time into small intervals over which he could consider the force constant.

His family were extremely poor (his father had died when Vito was two years old) but after attending lectures at Florence he was able to proceed to Pisa in 1878. At Pisa he studied under Betti, graduating Doctor of Physics in 1882. His thesis on hydrodynamics included some results of Stokes, discovered later but independently by Volterra.

He became Professor of Mechanics at Pisa in 1883 and, after Betti's death, he occupied the Chair of Mathematical Physics. After being appointed to the Chair of Mechanics at Turin he was appointed to the Chair of Mathematical Physics at Rome in 1900.

Volterra conceived the idea of a theory of functions which depend on a continuous set of values of another function in 1883. Hadamard was later to introduce the word 'functional' which replaced Volterra's original terminology. In 1890 Volterra showed by means of his functional calculus that the theory of Hamilton for the integration of the differential equations of dynamics could be extended to other problems of mathematical physics.

During the years 1892 to 1894 Volterra published papers on partial differential equations, particularly the equation of cylindrical waves.

His most famous work was done on integral equations. He began this study in 1884 and in 1896 he published papers on what is now called 'an integral equation of Volterra type'. He continued to study functional analysis applications to integral equations producing a large number of papers on composition and permutable functions.

During the First World War Volterra joined the Air Force. He made many journeys to France and England to promote scientific collaboration. After the War he returned to the University of Rome and his interests moved to mathematical biology. He studied the Verhulst equation and the logistic curve. He also wrote on predator-prey equations.

In 1922 Fascism siezed Italy and Volterra fought against it in the Italian Parliament. However by 1930 the Parliament was abolished and when Volterra refused to take an oath of allegience to the Fascist Government in 1931 he was forced to leave the University of Rome. From the following year he lived mostly abroad, mainly in Paris but also Spain and other countries.

Volterra was offered an honorary degree by the University of St Andrews in 1938 but his doctor did not allow him to travel to Scotland to receive it.

1. Biography in Dictionary of Scientific Biography (New York 1970-1990).
2. Biography in Encyclopaedia Britannica.

Books:


3. E M Polishchuk, Vito Vol'terra 1860-1940 (Russian), Nauchno-Biograficheskaya Literatura, Izdat. "Nauka" Leningrad. Otdel. (Leningrad, 1977).
4. R Simili (ed.), Scienza, tecnologia e istituzioni in Europa : Vito Volterra e l'origine del Cnr (Rome, 1993).

Articles:


5. E S Allen, The scientific work of Vito Volterra, Amer. Math. Monthly 48 (1941), 516-519.
6. Anonymous, Vito Volterra, Archimede 10 (1958), 29-32.
7. G Armellini, Vito Volterra e la sua opera scientifica, Ricerca Sci. 21 (1951), 3-12.
8. A Borsellino, Vito Volterra and contemporary mathematical biology, Vito Volterra Symposium on Mathematical Models in Biology, Lecture Notes in Biomath. 39 (Berlin-New York, 1980), 410-417.
9. G Castelnuovo, Obituary: Vito Volterra, Mem. Soc. Ital. Sci. (3) 25 (1943), 87-95.
10. G Colonnetti, Nel cinquantesimo anniversario di una memoria di Vito Volterra che ha aperta vie nuove alla moderna scienza delle costruzioni, Univ. e Politec. Torino. Rend. Sem. Mat. 16 (1956-57), 95-100.
11. D'Arcy W Thompson and S Chapman, Obituary: Prof. Vito Volterra, For. Mem. R S, Nature 147 (1941), 349-350.
12. L Dell'Aglio and G Israel, The themes of stability and qualitative analysis in the works of Levi-Civita and Volterra (Italian), Italian mathematics between the two world wars (Bologna, 1987), 125-141.
13. W Dunham, A historical gem from Vito Volterra, Math. Mag. 63 (4) (1990), 234-237.
14. G Fichera, Vito Volterra and the birth of functional analysis, Development of mathematics 1900-1950 (Basel, 1994), 171-183.
15. V Gavagna, From the theory of functions to functional analysis: the Arzelà-Volterra correspondence (Italian), Boll. Storia Sci. Mat. 14 (1) (1994), 3-89.
16. A Guerraggio, Memoirs of Volterra and Peano on the motion of the poles (Italian), Archive for History of Exact Science 31 (2) (1984), 97-126.
17. G Israel, Volterra Archive at the Accademia Nazionale dei Lincei, Historia Mathematica 9 (2) (1982), 229-238.
18. G Israel, On Vito Volterra's proposals to confer the Nobel Prize in physics on Henri Poincaré (Italian), Proceedings of the fifth national congress on the history of physics, Rend. Accad. Naz. Sci. XL Mem. Sci. Fis. Natur. (5) 9 (1985), 227-229.
19. G Krall, Vito Volterra: La matematica e la scienza del suo tempo, Civiltà delle Macchine 3 (1) (1955), 64-77.
20. B Levi, The personality of Vito Volterra (Spanish), Publ. Inst. Mat. Univ. Nac. Litoral 3 (1941), 25-36.
21. A Masotti, Bibliografie di Tullio Levi-Civita e Vito Volterra, Rend. Sem. Mat. Fis. Milano 17 (1946), 16-61.
22. A F Monna, Volterra et les fonctions de lignes: un centenaire, Nieuw Arch. Wisk. (3) 30 (3) (1982), 247-257.
23. A Pérard, Obituary: Vito Volterra (1860-1940), Cahiers de Physique 1941 (3) (1941), 51-58.
24. E Picard, Obituary: Vito Volterra, C. R. Acad. Sci. Paris 211 (1940), 309-312.
25. M Picone, Vito Volterra, Ricerca Sci. 26 (1956), 3277-3289.
26. E M Poliscuk, Vito Volterra (Russian), Istor.-Mat. Issled. Vyp. 21 (1976), 183-213.
27. Publications of Vito Volterra, Publ. Inst. Mat. Univ. Nac. Litoral 3 (1941), 37-48.
28. A Rosenblatt, Obituary: Vito Volterra. (Spanish), Revista Ci., Lima 44 (1942), 423-442.
29. C Somigliana, Obituary: Tullio Levi-Civita e Vito Volterra, Rend. Sem. Mat. Fis. Milano 17 (1946), 1-15.
30. C Somigliana, Obituary: Vito Volterra, Pont. Acad. Sci. Acta 6 (1942), 57-85.
31. L Tanzi Cattabianchi, The contributions of Vito Volterra to air ballistics (Italian), Riv. Mat. Univ. Parma (4) 14 (1988), 87-105.
32. R Wavre, Obituary: Vito Volterra, 1860-1940, Enseignement Math. 38 (1942), 347-348.
33. E T Whittacker, Vito Volterra, Obituary Notices of Fellows of the Royal Society of London 3 (1941), 619-729.
34. E T Whittacker, Vito Volterra, J. London Math. Soc. 16 (1941), 131-139.