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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 equation]]s.
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 equation]]s.


Volterra is the only person who was a [[list of International Congresses of Mathematicians Plenary and Invited Speakers|plenary speaker in the International Congress of Mathematicians]] four times (1900, 1908, 1920, 1928).<ref>{{cite web|title=International Congress of Mathematicians|url=http://www.mathunion.org/db/ICM/Speakers/SortedBySection.php}}</ref><ref>{{cite book|chapter-url=https://books.google.com/books?id=cF1tAAAAMAAJ&pg=PA43|pages=43–57|year=1902|volume=Tome 2|title=Compte rendu du deuxième Congrès international des mathématiciens tenu à Paris du 6 au 12 Aout 1900|chapter=''Betti, Brioschi, Casorati, trois analystes italiens et trois manières d’envisager les questions d’analyse'' by Vito Volterra}}</ref><ref>Volterra, Vito. [https://www.liberliber.it/mediateca/libri/v/volterra/la_teoria_dei_funzionali/pdf/volterra_la_teoria.pdf "La teoria dei funzionali applicata ai fenomeni ereditari."] Atti Congr. intern. dei Mat. a Bologna, vol. 1 (1928), pp. 215–232</ref>
Volterra is the only person who was a [[list of International Congresses of Mathematicians Plenary and Invited Speakers|plenary speaker in the International Congress of Mathematicians]] four times (1900, 1908, 1920, 1928).<ref>{{cite web|title=International Congress of Mathematicians|url=http://www.mathunion.org/db/ICM/Speakers/SortedBySection.php}}</ref><ref>{{cite book|chapter-url=https://books.google.com/books?id=cF1tAAAAMAAJ&pg=PA43|pages=43–57|year=1902|volume=Tome 2|title=Compte rendu du deuxième Congrès international des mathématiciens tenu à Paris du 6 au 12 Aout 1900|chapter=''Betti, Brioschi, Casorati, trois analystes italiens et trois manières d’envisager les questions d’analyse'' par Vito Volterra}}</ref><ref>Volterra, Vito. [http://media.accademiaxl.it/pubblicazioni/Matematica/link/Volterra_1908.pdf "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.</ref><ref>Volterra, Vito. [https://www.liberliber.it/mediateca/libri/v/volterra/la_teoria_dei_funzionali/pdf/volterra_la_teoria.pdf "La teoria dei funzionali applicata ai fenomeni ereditari."] Atti Congr. intern. dei Mat. a Bologna, vol. 1 (1928), pp. 215–232</ref>


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 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.

Revision as of 12:01, 26 October 2017

Vito Volterra
Vito Volterra
Born(1860-05-03)3 May 1860
Ancona
Died11 October 1940(1940-10-11) (aged 80)
Rome
NationalityItalian
Alma materUniversity of Pisa
Known forTheory of integral equations
The Lotka–Volterra equations
AwardsForMemRS[1]
Scientific career
FieldsMathematics
InstitutionsUniversity of Turin
Doctoral advisorEnrico Betti
Doctoral studentsPaul Lévy
Joseph Pérès

Vito Volterra (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]

Biography

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. 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).[5][6][7][8]

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. The Academy organised, in 1940, his funeral, which could be attended by his family.

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.[9] Vol. 1, 1954; Vol. 2, 1956; Vol. 3, 1957; Vol. 4, 1960; Vol. 5, 1962; Accademia dei Lincei.

See also

Notes

  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. ^ O'Connor, John J.; Robertson, Edmund F., "Vito Volterra", MacTutor History of Mathematics Archive, University of St Andrews
  3. ^ Vito Volterra at the Mathematics Genealogy Project
  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. ^ "International Congress of Mathematicians".
  6. ^ "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.
  7. ^ 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.
  8. ^ Volterra, Vito. "La teoria dei funzionali applicata ai fenomeni ereditari." Atti Congr. intern. dei Mat. a Bologna, vol. 1 (1928), pp. 215–232
  9. ^ Weinstein, A. (1964). "Review: Opere matematiche, by Vito Volterra". Bull. Amer. Math. Soc. 70 (3): 335–337. doi:10.1090/s0002-9904-1964-11086-7.

Biographical references

General references

External links

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