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Vito Volterra

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Vito Volterra
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|birth_place = Ancona19401105df=y}}|death_place = RomeItaly>Italian|field = Mathematics|work_institutions = University of Turin|alma_mater = University of Pisa|doctoral_advisor = Enrico BettiPaul Lévy (mathematician)>Paul LévyJoseph Pérès|known_for = Theory of integral equations The Lotka–Volterra equationsForeign Member of the Royal Society>ForMemRSWHITTAKER > FIRST1 = E. T. TITLE = VITO VOLTERRA. 1860-1940 JOURNAL = OBITUARY NOTICES OF FELLOWS OF THE ROYAL SOCIETY ISSUE = 10 YEAR = 1941 PMC =, }}Vito Volterra ({{IPAc-en|v|oʊ|l|ˈ|t|ɛr|ə}}; {{IPA-it|volˈtɛrra|lang}}; 3 May 1860 – 11 October 1940) was an Italian mathematician and physicist, known for his contributions to mathematical biology and integral equations,{{MacTutor Biography|id=Volterra}}{{MathGenealogy|id=33908}} being one of the founders of functional analysis.According to {{harvtxt|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.

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).WEB, International Congress of Mathematicians,weblink BOOK,weblink 43–57, 1902, Tome 2, Compte rendu du deuxième Congrès international des mathématiciens tenu à Paris du 6 au 12 Aout 1900, Betti, Brioschi, Casorati, trois analystes italiens et trois manières d’envisager les questions d’analyse par Vito Volterra, 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.BOOK,weblink 81–97, 1921, Compte rendu du Congrès international des mathématiciens tenu à Strasbourg du 22 au 30 Septembre 1920, Sur l'enseignement de la physique mathématique et de quelques points d'analyse par Vito Volterra, Volterra, Vito. "La teoria dei funzionali applicata ai fenomeni ereditari." Atti Congr. intern. dei Mat. a Bologna, vol. 1 (1928), pp. 215–232In 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. His son Edoardo Volterra (1904-1984) was a famous historian of Roman lawweblink

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.JOURNAL, Weinstein, A., Alexander Weinstein, Review: Opere matematiche, by Vito Volterra, Bull. Amer. Math. Soc., 1964, 70, 3, 335–337,weblink 10.1090/s0002-9904-1964-11086-7, Vol. 1, 1954; Vol. 2, 1956; Vol. 3, 1957; Vol. 4, 1960; Vol. 5, 1962; Accademia dei Lincei.

See also

Notes

{{Reflist}}

Biographical references

  • {{citation


|last = Castelnuovo
|first = G.
|author-link = Guido Castelnuovo
|title = Vito Volterra
|journal = Rendiconti della Accademia Nazionale delle Scienze detta dei XL, Memorie di Matematica e Applicazioni
|series = Serie 3,
|volume = XXV
|issue = 70
|year = 1943
|language = Italian
|pages = 87–95
|url =weblink
|id =
|mr = 0021530
|zbl = 0061.00605
|access-date = 23 June 2014
|archive-url =weblink" title="web.archive.org/web/20160305032850weblink">weblink
|archive-date = 5 March 2016
|dead-url = yes
|df = dmy-all
}}.
  • {{Citation| last =Fichera| first =Gaetano| author-link =Gaetano Fichera| editor-last = Amaldi| editor-first = E.| editor-link = Edoardo Amaldi| editor2-last = Amerio| editor2-first = L.| editor2-link = Luigi Amerio| editor3-last =Fichera| editor3-first =G.| editor3-link =Gaetano Fichera| editor4-last =Gregory| editor4-first =T.| editor4-link =| editor5-last =Grioli| editor5-first =G.| editor5-link =Giuseppe Grioli| editor6-last =Martinelli| editor6-first =E.| editor6-link =Enzo Martinelli| editor7-last =Montalenti| editor7-first =G.| editor8-last =Pignedoli| editor8-first =A.| editor8-link =Antonio Pignedoli| editor9-last =Salvini| editor9-first =Giorgio| editor9-link =Giorgio Salvini| editor10-last =Scorza Dragoni| editor10-first =Giuseppe| editor10-link =Giuseppe Scorza Dragoni| contribution =La figura di Vito Volterra a cinquanta anni dalla morte| contribution-url = | title = Convegno internazionale in memoria di Vito Volterra (8–11 ottobre 1990)| url =weblink| language = Italian| series = Atti dei Convegni Lincei| volume = 92| year = 1992| pages = 25–76| place = Roma| publisher = Accademia Nazionale dei Lincei| doi = | issn = 0391-805X| mr =1783027| zbl =0973.01024
}}. "Vito Volterra fifty years after his death" is detailed biographical survey paper on Vito Volterra, dealing mainly with scientific, philosophical and moral aspects of his personality.
  • {{Citation


| last = Gemelli
| first = Agostino
| author-link = Agostino Gemelli
| title = La relazione del presidente|trans-title=The president's relation
| journal = Acta Pontificia Academia Scientarum
| volume = 6
| year =1942
| pages = XI–XXIV
| url =weblink
| doi =
| id = }}. The commemorative address pronounced by Agostino Gemelli on the occasion of the first seance of the fourth academic year of Pontificial Academy of Sciences: it includes his commemoration of various deceased members.
  • {{Citation| last = Goodstein| first = Judith R.| author-link = Judith R. Goodstein| title = The Volterra Chronicles: The Life and Times of an Extraordinary Mathematician 1860–1940| place = Providence, RI-London| series = History of Mathematics| volume = 31| publisher = American Mathematical Society/London Mathematical Society| year = 2007| id = | mr = 2287463| zbl = 1123.01016| isbn = 0-8218-3969-1
}}. See also the review in American Scientist.
  • {{Citation


| last =Pancaldi
| first =Giuliano
| author-link =
| title =Vito volterra: Cosmopolitan Ideals and Nationality in the Italian Scientific Community between the Belle époque and the First World War
| journal =Minerva
| volume =31
| issue =1
| pages =21–37
| year =1993
| url =https://link.springer.com/article/10.1007%2FBF01096170
| issn =0026-4695
| doi =10.1007/BF01096170
}}.
  • {{Citation


| author = Pontifical Academy of Sciences
| author-link = Pontifical Academy of Sciences
| editor-last =
| editor-first =
| editor2-last =
| editor2-first =
| contribution = Vito Volterra
| contribution-url =weblink
| title = Annuario della Pontificia Accademia delle Scienze I. 1936–37
| series = Extra Series
| volume = 1
| year = 1937
| pages = 758–775
| place = Città del Vaticano
| publisher = Pontificia Academia Scientiarum
| url =weblink
| doi =
| id = }}.
  • {{Citation


| last = Somigliana
| first = Carlo
| author-link = Carlo Somigliana
| title = Vito Volterra. Discorso commemorativo pronunciato nella Prima Tornata Ordinaria del Sesto Anno Accademico, il 30 novembre 1941 (cum 2 tab.)|trans-title=Commemorative address pronounced on the occasion of the first seance of the sixth academic year, on 30 November 1941
| journal = Acta Pontificia Academia Scientarum
| volume = 6
| year =1942
| pages = 57–86
| url =weblink
| jfm =68.0018.15
| mr =0026620
| zbl =0060.01808}}. The commemorative address by Carlo Somigliana, colleague and friend of Vito Volterra.

General references

  • {{Citation| first = Luigi| last = Accardi| author-link = Luigi Accardi| editor-last = Amaldi| editor-first = E.| editor-link = Edoardo Amaldi| editor2-last =Amerio| editor2-first =L.| editor2-link =Luigi Amerio| editor3-last =Fichera| editor3-first =G.| editor3-link =Gaetano Fichera| editor4-last =Gregory| editor4-first =T.| editor4-link =| editor5-last =Grioli| editor5-first =G.| editor5-link =Giuseppe Grioli| editor6-last =Martinelli| editor6-first =E.| editor6-link =Enzo Martinelli| editor7-last =Montalenti| editor7-first =G.| editor8-last =Pignedoli| editor8-first =A.| editor8-link =Antonio Pignedoli| editor9-last =Salvini| editor9-first =Giorgio| editor9-link =Giorgio Salvini| editor10-last =Scorza Dragoni| editor10-first =Giuseppe| editor10-link =Giuseppe Scorza Dragoni| contribution = Vito Volterra and the development of functional analysis| contribution-url = | title = Convegno internazionale in memoria di Vito Volterra (8–11 ottobre 1990)|trans-title= International congress in memory of Vito Volterra (October 8–11, 1990)| url =weblink| series = Atti dei Convegni Lincei| volume = 92| year = 1992| pages = 151–181| place = Roma| publisher = Accademia Nazionale dei Lincei| doi = | issn = 0391-805X| mr =1783028| zbl =0980.01016
}}. In this paper Luigi Accardi describes the early research work of Vito Volterra on functionals, leading to the creation of functional analysis.
  • {{Citation| editor-last = Amaldi| editor-first = E.| editor-link = Edoardo Amaldi| editor2-last = Amerio| editor2-first = L.| editor2-link = Luigi Amerio| editor3-last =Fichera| editor3-first =G.| editor3-link =Gaetano Fichera| editor4-last =Gregory| editor4-first =T.| editor4-link =| editor5-last =Grioli| editor5-first =G.| editor5-link =Giuseppe Grioli| editor6-last =Martinelli| editor6-first =E.| editor6-link =Enzo Martinelli| editor7-last =Montalenti| editor7-first =G.| editor8-last =Pignedoli| editor8-first =A.| editor8-link =Antonio Pignedoli| editor9-last =Salvini| editor9-first =Giorgio| editor9-link =Giorgio Salvini| editor10-last =Scorza Dragoni| editor10-first =Giuseppe| editor10-link =Giuseppe Scorza Dragoni| contribution =| contribution-url = | title = Convegno internazionale in memoria di Vito Volterra (8–11 ottobre 1990)|trans-title= International congress in memory of Vito Volterra (October 8–11, 1990)| url =weblink| language = English, French, Italian| series = Atti dei Convegni Lincei| volume = 92| year = 1992| pages = 346| place = Roma| publisher = Accademia Nazionale dei Lincei| doi = | issn = 0391-805X
}}.
  • {{Citation| first = Dario| last = Graffi| author-link = Dario Graffi| editor-last = Amaldi| editor-first = E.| editor-link = Edoardo Amaldi| editor2-last = Amerio| editor2-first = L.| editor2-link = Luigi Amerio| editor3-last =Fichera| editor3-first =G.| editor3-link =Gaetano Fichera| editor4-last =Gregory| editor4-first =T.| editor4-link =| editor5-last =Grioli| editor5-first =G.| editor5-link =Giuseppe Grioli| editor6-last =Martinelli| editor6-first =E.| editor6-link =Enzo Martinelli| editor7-last =Montalenti| editor7-first =G.| editor8-last =Pignedoli| editor8-first =A.| editor8-link =Antonio Pignedoli| editor9-last =Salvini| editor9-first =Giorgio| editor9-link =Giorgio Salvini| editor10-last =Scorza Dragoni| editor10-first =Giuseppe| editor10-link =Giuseppe Scorza Dragoni| contribution = L'opera di Vito Volterra sui fenomeni ereditari e alcune sue conseguenze| contribution-url = | title = Convegno internazionale in memoria di Vito Volterra (8–11 ottobre 1990)|trans-title= International congress in memory of Vito Volterra (October 8–11, 1990)| url =weblink| language = Italian| series = Atti dei Convegni Lincei| volume = 92| year = 1992| pages = 39–76| place = Roma| publisher = Accademia Nazionale dei Lincei| doi = | issn = 0391-805X| mr =1783028| zbl =0977.01022
}}. "The work of Vito Volterra on hereditary phenomena and some of their consequences" is an ample technical survey paper on the research work of Vito Volterra on hereditary phenomena in mathematical physics.
  • {{Citation| first = G.| last = Israel| author-link = | editor-last = Grattan-Guinness| editor-first = I.| editor-link = Ivor Grattan-Guinness| contribution = Book on mathematical biology| contribution-url = | title = Landmark Writings in Western Mathematics, 1640–1940| year = 2005| pages = xxvi+310| place = Amsterdam| publisher = Elsevier| url = | doi = | isbn = 0-444-50871-6| id = | mr = 0408866| zbl = 1090.01002
}}
  • JOURNAL
FIRST1 = G., On the contribution of Volterra and Lotka to the development of modern biomathematics, History and philosophy of the life sciences, 10, 1, 37–49, 1988, 3045853,
  • JOURNAL, Scudo, F., Vito Volterra and theoretical ecology, 10.1016/0040-5809(71)90002-5, Theoretical Population Biology, 2, 1, 1–23, 1971, 4950157, .
  • {{Citation| first = Francesco M.| last = Scudo| author-link =| editor-last = Amaldi| editor-first = E.| editor-link = Edoardo Amaldi| editor2-last =Amerio| editor2-first =L.| editor2-link =Luigi Amerio| editor3-last =Fichera| editor3-first =G.| editor3-link =Gaetano Fichera| editor4-last =Gregory| editor4-first =T.| editor4-link =| editor5-last =Grioli| editor5-first =G.| editor5-link =Giuseppe Grioli| editor6-last =Martinelli| editor6-first =E.| editor6-link =Enzo Martinelli| editor7-last =Montalenti| editor7-first =G.| editor8-last =Pignedoli| editor8-first =A.| editor8-link =Antonio Pignedoli| editor9-last =Salvini| editor9-first =Giorgio| editor9-link =Giorgio Salvini| editor10-last =Scorza Dragoni| editor10-first =Giuseppe| editor10-link =Giuseppe Scorza Dragoni| contribution = Vito Volterra, “Ecology” and the quantification of “Darwinism”| contribution-url = | title = Convegno internazionale in memoria di Vito Volterra (8–11 ottobre 1990)|trans-title= International congress in memory of Vito Volterra (October 8–11, 1990)| url =weblink| series = Atti dei Convegni Lincei| volume = 92| year = 1992| pages = 313–333| place = Roma| publisher = Accademia Nazionale dei Lincei| doi = | issn = 0391-805X| mr =1783041| zbl =0978.01026
}}.

External links

{{commons category}}
  • weblink" title="web.archive.org/web/20100327051138weblink">Gustavo Colonnetti e le origini dell'ingegneria in Italia, Fausto Giovannardi
  • {{Gutenberg author | id=Volterra,+Vito }}
  • {{Internet Archive author |sname=Vito Volterra}}
{{Authority control}}

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