Vito Volterra

Vito Volterra books and biography

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Theory Of Permutable Functions

By Vito Volterra

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Vito Volterra

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Vito Volterra (May 3, 1860 - October 11, 1940) was an Italian mathematician and physicist, best known for his contributions to mathematical biology.

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 elected 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 Franois Verhulst. The most famous outcome of this period is the Volterra-Lotka equations.

In 1922, he joined the opposition to the Fascist regime of Benito Mussolini and in 1931 refused to take a mandatory oath of loyalty. He was compelled to resign his university post and membership of scientific academies, and, during the following years, he lived largely abroad, returning to Rome just before his death.


  • Volterra, V. (1926). Variazioni e fluttuazioni del numero d'individui in specie animali conviventi. Mem. R. Accad. Naz. dei Lincei 2, 31–113.
  • Volterra, V. (1926). Fluctuations in the abundance of a species considered mathematically. Nature 118, 558-560.

See also

  • Volterra
  • Volterra's function
  • Smith-Volterra-Cantor set
  • Lotka-Volterra equation
  • Volterra integral equation
  • Volterra series

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