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Biography of Vico Volterra

Dates of Birth and Death:() 3 May 1860 in Ancona, then Papal States, now Italy() 11 October 1940 in Rome, Italy

Family Data:Volterras family was very poor. The father died when Vito was two yearsold.

In 1905, Volterra became a Senator. During World War I, he joined theItalian Air Force. When in 1922 Fascism came to power in Italy, Volterrafought it in the Italian Parliament. It was abolished in 1930, but Volterrarefused to take an oath of allegiance to the Fascist regime and had to leavethe University of Rome. During the subsequent years he mostly lived abroad,mainly in Paris and Spain.

Education:Volterra had a great mathematical talent. At his eleven, he studied Adrien-Marie Legendres (1752-1833) geometry, with 13 years he dealt with the

Three Body Problem. After having attended courses in Florence, he startedto study at the University of Pisa under Enrico Betti (1823-1892) in 1878. In1882, he finished his doctoral dissertation in Physics about hydrodynamics.His thesis contained some results discovered by Stokes, but Volterra hadfound them independently.

Professional Career:In 1883, Volterra became professor of Mechanics at the University of Pisaand after Bettis death, he occupied his chair of Mathematical Physics. Afterserving as the chair for Mechanics at the University of Turin, he became

professor for Mathematical Physics in Rome in 1900. After World War I, hedealt with Mathematical Biology.

Volterra worked on the theory of functions (functional analysis, partial dif-ferential and integral equations (integral equation of Volterra type).
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Publications:

Opere matematiche, memorie e note, 5. vols. (Roma: Accademia deiLincei 1881-1955-1962).

Giorgio Israel, Ana Millan Gasca (eds.), The biology of numbers: thecorrspondence of Vito Volterra on mathematical biology(Basel 2002).

Sopra alcuni problemi della teoria del potenziale(Pisa 1983) (Habil.schrift).

Sui fondamenti della teoria della equazione differentiali lineari, 2 vols.

(Napoli, Roma 1887-1889). Sui tentativi d applicazione delle matematiche alle scien ze biologiche e

sociali, Discorso inaugurale,Annuario della reale Universita di Roma(1901) pp. 3-28, repr: Giornale degli economisti 23, pp. 436-458;Archivio di Fisiologia 3 (1906) pp. 175-191, and in: Opere, vol. 3,pp. 14-29, French: La revue du mois (1906) pp. 1-20.

Sur lequiblibre des corps elastiques multiplement connexes(Paris 1907).

Lecons sur lintegration des equations differentel les aux derivees par-tielles: professees a Stockholm(Paris 1912).

Lectures delivered at the celebration of the twentieth anniversary of thefoundation of Clark University..., Worcester, Mass., September 7-11,1909(Worcester, Mass. 1912).

Henri Poincare(Paris ca. 1912).

The theory of permutable functions(Princeton 1912).

Lecons sur les fonctions de lignes: professees a la Sorbonne en 1912(Paris 1913).

Lecons sur les equations integrales et les equations integro-differentielles:lecons professees a la Faculte des sciences de Rome en 1910 (Paris1913).

Drei Vorlesungen uber neuere Fortschritte der mathematischen Physik:gehalten 1909 an der Clark-Universit at von Vito Volterra (Leipzig,Berlin 1914).

The theory of permutable function(London 1915).
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Saggi scientifici(Bologna 1920, 1994).

Flow of electricity in a magnetic field(Berkeley 1921; New York 1966).

Together with Joseph Peres: Lecons sur la composition et es fonctionspermutables(Paris 1924).

Variazioni e fluttuazioni del numero dindividui in specie animali con-viventi,Memorie della Reale Aaccademia dei Lince2 (1926) pp. 31-113, repr. Opere, vol. 5, pp. 1-111.

Together with S.J. Lotka: Fluctuations in the abundance of a species

considered mathematically,Nature118 (1926) pp. 558-560; 119 (1927)pp. 12-13.

Theory of functionals and of integral and integro-differential equations(London 1930; New York 1959; Mineola, NY 2005), Spanish: Teoriade las funcionales y de las ecuaciones integrales e integro-diferenciales(Madrid 1927), French: Theorie generale des fonctionel les(Paris 1936).

Lecons sur la theorie mathematique de la lutte pour la vie(Paris 1931),repr. Paris 1990, deutsch: Der Kampf ums Dasein. Eine biologisch-mathematische Darstellung der Lebensgemeinschaften und biologischen

Gleichgewichte(Berlin 1939), englisch:The struggle for existence(Lei-den 1954).

Le calcul des variations, son evolution et ses progres, son role dans laphysique mathematique(Praha-Brno 1932).

Together with U. DAncona: Les associations biologiques au point devue mathematique(Paris 1935).

Principes de biologie mathematique, Acta biotheoretica3 (1937) pp.6-39, repr. Opere, vol. 5, pp. 414-447.

Conferences sur quelques questions de mecanique et de physique mathematique:rotation des corps dans lesquels existent des mouvements internes(Paris1938).

Fluctuations dans la lutte pour la vie, leurs lois fondamentales et dereciprocite(Paris 1938).

Operations infinitesimales lineaires: applications aux equations differentielleset fonctionelles(Paris 1938).


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Sur les distorsions des corps elastiques (theorie et applications) (Paris

1960).

Francesco M. Scudo (ed.), The golden age of theoretical ecology: 1923-1940; a collection of works by V. Volterra, V.A. Kostitzin, A.J. Lotkaand A.N. Kolmogoroff(Berlin 1978).

The biology of numbers: the Correspondence of Vito Volterra on math-ematical biology(Basel 2002).

Scientific Awards:

In 1938 the University of St Andrew offered Volterra an honorary degree buthis doctor did not permit him to travel to Scotland to receive it.

Bibliography: Charles Coulston Gillespie (ed.), Dictionary of scientific biography, vol.XIV (New York 1976) pp. 85-88. U. DAncona, Dellinfluenza della stasi peschereccia nel periodo 1914-18sul patrimonio ittico dellAlto Adriatico, Memorie del Regio Comitato Ta-lassografico Italiano126 (1926). U. DAncona, Der Kampf ums Dasein. Eine biologisch-mathematische

Darstellung der Lebensgemeinschaften und biologischen Gleichgewichte(Berlin1939), englisch: The struggle for existence(Leiden 1954). Claudio Barigozzi, Vito Volterra Symposium on Mathematical Models inBiology..., Rome, Dec. 17-21, 1979(Berlin 1980). Elart von Collani (ed.), Defining the Science of Stochastics(Lemgo 2004).Convegno internazionale in memoria di Vito Volterra (Roma, 8-11 ottobre1990)(Roma 1992). Alan Feldstein, Volterra centennial: selected papers. Second InternationalConference on the numerical solution of Volterra and Delay Equations, May1996(Amsterdam 1997).

G. Fichera, Vito Volterra and the brht of functional analysis, Develop-ment of mathematics 1900-1950(Basel 1994) pp. 171-183.G.F. Gause,Verifications experimentales de la theorie mathematique de lalutte pour la vie(Paris 1935). Judith Goodstein, The Volterra chronicles: the life and times of an ex-traordinary mathematician, 1860-1940(Providence, RI 2007). Angelo Guarraggio, Le memorie di Volterra e Peano sul movimento deipoli,Archive for History of Exact Sciences31 (1984) pp. 97-126. Angelo Guerraggio, Giovanni Paolini, Vito Volterra(Roma 2008).


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G. Israel, Volterra Archive at the Accademia Nazionale dei Lincei, His-

toria Mathematica9 (1982) pp. 229-238.G. Israel, Volterras analytical mechanics of biological associations,ArchivesInternationales dHistoire des Sciences41 (1991) pp. 57-104, 307-352. G. Israel, Volterra Archive at the Accademia dei Lincei, Historia Math-ematica9 (1982) pp. 229-238. G. Israel, The emergence of biomathematics and the case of populationdynamics: a revival of mechanical reductionism and Darwinism, Science inContext6 (1993) pp. 469-509. G. Israel, Millan Gasca, The biology of numbers. The correspondence ofVito Volterra on mathematical biology(Basel 2002).

G. Israel, Vito Volterra, Book on Mathematical Biology (1931), in: I.Grattan-Guiness (ed.),Landmark. Writings in Western Mathematics 1640-1940(Amsterdam, Boston 2005) pp. 936-944.S.E. Kingsland,Modeling nature: episodes in the history of population ecol-ogy(Chicago 1985). V.A. Kostitzin, Symbiose, parasitisme et evolution (etude mathematique)(Paris 1934). V.A. Kostitzin, Biologie mathematique(Paris 1937). G. Krall, Vito Volterra: La matematica e la scienza del suo tempo,Civilta delle Macchine3 (1955) pp. 64-77.

Sandra Linguerri, Vito Volterra e il Comitato Talassografico Italiano: im-prese per aria e per mare nellItalia Unita (1883-1930) (Firenze 2005). A. Lotka,Elements of physical biology(New York 1925). Arnaldo Masotti, Bibliografie di Tullio Levi-Civita e Vito Volterra, Mi-lan Journal of Mathematics17 (1946) pp. 16-61.Giovanni Paolini,Vito Volterra e il suo tempo 1860-1940: mostra storico-documentaria(Roma 1990).Pico Mauro, Vito Volterra,La ricerca scientifica26 (1956) pp. 3277-3289.Henri Poincare,Loeuvre scientifique, Loeuvre philosophique par Vito Volterra,Prof. Jacques Hadamard, Paul Langevin, Prof. Pierre Boutroux(Paris 1914). F.M. Scudo, The Golden Age of theoretical ecology: a conceptual ap-praisal, Revue Europeenne des sciences sociales22 (1984) pp. 11-64. Raffaella Simili, Alberto Conte (eds.), Scienta, tecnologia e istituzioni inEuropa: Vito Volterra e lorigine del CNR (Bari 1993). L. Tanzi Cattabianchi, I contributi di Vito Volterra alla balistica di aero-mobili, Rivista di Matematica dellUniversita di Parma 14 (1988) pp. 87-105. Luciano de Vito, Sulla equazione integro-differenziale di tipo ellitico diVolterra(Torino 1961).E.T. Whittacker, Vito Volterra, Obituary notices of Fellows of the Royal


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Society of London3 (1941) pp. 619-729.

J.J. OConnor, E.F. Robertson, http://www-groups.dcs.st-and.ac.uk/ his-tory/Mathematician/Volterra.html (20 February 2006). J.J. OConnor, E.F. Robertson, http://www-groups.dcs.st-and.ac.uk/ his-tory/References/Volterra.html (20 February 2006). http://de.wikipedia.org/wiki/Vito Volterra (05 Otober 2005).

Author(s) of this contribution:Claudia von Collani

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