Vito Volterra
Encyclopedia
Vito Volterra was an Italian
mathematician
and physicist
, known for his contributions to mathematical biology
and integral equations.
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 functional
s 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 dislocation
s in crystal
s 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 airship
s 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
. The most famous outcome of this period is the Lotka–Volterra equations.
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.
Italy
Italy , officially the Italian Republic languages]] under the European Charter for Regional or Minority Languages. In each of these, Italy's official name is as follows:;;;;;;;;), is a unitary parliamentary republic in South-Central Europe. To the north it borders France, Switzerland, Austria and...
mathematician
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
and physicist
Physicist
A physicist is a scientist who studies or practices physics. Physicists study a wide range of physical phenomena in many branches of physics spanning all length scales: from sub-atomic particles of which all ordinary matter is made to the behavior of the material Universe as a whole...
, known for his contributions to mathematical biology
Mathematical biology
Mathematical and theoretical biology is an interdisciplinary scientific research field with a range of applications in biology, medicine and biotechnology...
and integral equations.
Born in Ancona
Ancona
Ancona is a city and a seaport in the Marche region, in central Italy, with a population of 101,909 . Ancona is the capital of the province of Ancona and of the region....
, then part of the Papal States
Papal States
The Papal State, State of the Church, or Pontifical States were among the major historical states of Italy from roughly the 6th century until the Italian peninsula was unified in 1861 by the Kingdom of Piedmont-Sardinia .The Papal States comprised territories under...
, into a very poor Jewish family, Volterra showed early promise in mathematics
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
before attending the University of Pisa
University of Pisa
The University of Pisa , located in Pisa, Tuscany, is one of the oldest universities in Italy. It was formally founded on September 3, 1343 by an edict of Pope Clement VI, although there had been lectures on law in Pisa since the 11th century...
, where he fell under the influence of Enrico Betti
Enrico Betti
-External links:...
, and where he became professor of rational mechanics in 1883. He immediately started work developing his theory of functional
Functional (mathematics)
In mathematics, and particularly in functional analysis, a functional is a map from a vector space into its underlying scalar field. In other words, it is a function that takes a vector as its input argument, and returns a scalar...
s which led to his interest and later contributions in integral
Integral equation
In mathematics, an integral equation is an equation in which an unknown function appears under an integral sign. There is a close connection between differential and integral equations, and some problems may be formulated either way...
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
University of Turin
The University of Turin is a university in the city of Turin in the Piedmont region of north-western Italy...
and then, in 1900, professor of mathematical physics at the University of Rome La Sapienza
University of Rome La Sapienza
The Sapienza University of Rome, officially Sapienza – Università di Roma, formerly known as Università degli studi di Roma "La Sapienza", is a coeducational, autonomous state university in Rome, Italy...
. Volterra had grown up during the final stages of the Risorgimento when the Papal States were finally annexed by Italy
Italy
Italy , officially the Italian Republic languages]] under the European Charter for Regional or Minority Languages. In each of these, Italy's official name is as follows:;;;;;;;;), is a unitary parliamentary republic in South-Central Europe. To the north it borders France, Switzerland, Austria and...
and, like his mentor Betti, he was an enthusiastic patriot, being named by the king Victor Emmanuel III as a senator
Italian Senate
The Senate of the Republic is the upper house of the Italian Parliament. It was established in its current form on 8 May 1948, but previously existed during the Kingdom of Italy as Senato del Regno , itself a continuation of the Senato Subalpino of Sardinia-Piedmont established on 8 May 1848...
of the Kingdom of Italy in 1905. In the same year, he began to develop the theory of dislocation
Dislocation
In materials science, a dislocation is a crystallographic defect, or irregularity, within a crystal structure. The presence of dislocations strongly influences many of the properties of materials...
s in crystal
Crystal
A crystal or crystalline solid is a solid material whose constituent atoms, molecules, or ions are arranged in an orderly repeating pattern extending in all three spatial dimensions. The scientific study of crystals and crystal formation is known as crystallography...
s that was later to become important in the understanding of the behaviour of ductile materials. On the outbreak of World War I
World War I
World War I , which was predominantly called the World War or the Great War from its occurrence until 1939, and the First World War or World War I thereafter, was a major war centred in Europe that began on 28 July 1914 and lasted until 11 November 1918...
, already well into his 50s, he joined the Italian Army
Military of Italy
The Italian armed forces are the military of Italy, they are under the command of the Italian Supreme Council of Defence, presided over by the President of the Italian Republic. The total number of active military personnel is 293,202...
and worked on the development of airship
Airship
An airship or dirigible is a type of aerostat or "lighter-than-air aircraft" that can be steered and propelled through the air using rudders and propellers or other thrust mechanisms...
s under Giulio Douhet
Giulio Douhet
General Giulio Douhet was an Italian general and air power theorist. He was a key proponent of strategic bombing in aerial warfare...
. He originated the idea of using inert helium
Helium
Helium is the chemical element with atomic number 2 and an atomic weight of 4.002602, which is represented by the symbol He. It is a colorless, odorless, tasteless, non-toxic, inert, monatomic gas that heads the noble gas group in the periodic table...
rather than flammable hydrogen
Hydrogen
Hydrogen is the chemical element with atomic number 1. It is represented by the symbol H. With an average atomic weight of , hydrogen is the lightest and most abundant chemical element, constituting roughly 75% of the Universe's chemical elemental mass. Stars in the main sequence are mainly...
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
Pierre François Verhulst
Pierre François Verhulst was a mathematician and a doctor in number theory from the University of Ghent in 1825...
. The most famous outcome of this period is the Lotka–Volterra equations.
In 1922, he joined the opposition to the Fascist regime of Benito Mussolini
Benito Mussolini
Benito Amilcare Andrea Mussolini was an Italian politician who led the National Fascist Party and is credited with being one of the key figures in the creation of Fascism....
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
Rome
Rome is the capital of Italy and the country's largest and most populated city and comune, with over 2.7 million residents in . The city is located in the central-western portion of the Italian Peninsula, on the Tiber River within the Lazio region of Italy.Rome's history spans two and a half...
just before his death.
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.
See also
- Volterra (crater)Volterra (crater)Volterra is a lunar crater that is located in the northern latitudes on the far side of the Moon. To the northeast is the crater Olivier, and to the south-southwest lies von Békésy. This is an eroded crater formation, particularly along the western side where the rim is more uneven. A small crater...
- Volterra's functionVolterra's functionIn mathematics, Volterra's function, named for Vito Volterra, is a real-valued function V defined on the real line R with the following curious combination of properties:* V is differentiable everywhere...
- Lotka–Volterra equation
- Smith–Volterra–Cantor set
- Volterra integral equationVolterra integral equationIn mathematics, the Volterra integral equations are a special type of integral equations. They are divided into two groups referred to as the first and the second kind.A linear Volterra equation of the first kind is f = \int_a^t K\,x\,ds...
- Volterra seriesVolterra SeriesThe Volterra series is a model for non-linear behavior similar to the Taylor series. It differs from the Taylor series in its ability to capture 'memory' effects. The Taylor series can be used to approximate the response of a nonlinear system to a given input if the output of this system depends...
- Product integralProduct integralProduct integrals are a counterpart of standard integrals of infinitesimal calculus. They were first developed by the mathematician Vito Volterra in 1887 to solve systems of linear differential equations...
- Volterra operatorVolterra operatorIn mathematics, in the area of functional analysis and operator theory, the Volterra operator, named after Vito Volterra, represents the operation of indefinite integration, viewed as a bounded linear operator on the space L2 of complex-valued square integrable functions on the interval...
- Volterra spaceVolterra spaceIn mathematics, in the field of topology, a topological space is said to be a Volterra space if any finite intersection of dense G-delta subsets is dense...
- Volterra SemiconductorVolterra SemiconductorVolterra Semiconductor, commonly known as "Volterra," is a fabless semiconductor company that designs and manufactures mixed-signal integrated circuits used in power management applications...
- Poincaré lemma