Italian mathematician whose chief work was in the fields of function theory and differential equations. His chief method, hit upon as a young boy, was based on dividing a problem into a small interval of time and assuming one of the variables to be constant during each time period.
Volterra was born in Ancona and studied at Florence and Pisa. He was professor at Pisa 1883–92, Turin 1892–1900, and Rome 1900–31. During World War I he established the Italian Office of War Inventions, where he designed armaments and proposed that helium be used in place of hydrogen in airships. After the war he became increasingly involved in politics, speaking in the Senate and voicing his opposition to the fascist regime. For his views he was eventually dismissed from his academic post and banned from taking part in any Italian scientific meeting.
At the age of 13, after reading Jules Verne's novel From the Earth to the Moon, Volterra became interested in projectile problems and came up with a plausible determination for the trajectory of a spacecraft which had been fired from a gun. His solution was based on the device of breaking time down into small intervals during which it could be assumed that the force was constant. The trajectory could thus be viewed as a series of small parabolic arcs. This was the essence of the argument he developed in detail 40 years later in a series of lectures at the Sorbonne, France.
Volterra contributed especially to the foundation of the theory of functionals, the solution of integral equations with variable limits, and the integration of hyperbolic partial differential equations. His papers on partial differential equations of the early 1890s included the solution of equations for cylindrical waves.
He also brought his knowledge of mathematics to bear on biological matters, constructing a model for population change in which the prey and the predator interact in a continuous manner.
Volterra's main works are The Theory of Permutable Functions (1915) and The Theory of Functionals and of Integral and Integro-differential Equations (1930).