Vito Volterra Biography

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World of Mathematics on Vito Volterra

Vito Volterra had a major impact on the development of calculus, and he originated the concept of a theory of functions. Perhaps his most famous work was on integral equations.

Volterra was born to a poor cloth salesman on May 3, 1860 in Rome, Italy. The Volterras became virtually destitute when Mr. Volterra died when Vito was about two, so the boy and his mother moved in with her brother. Volterra grew up mainly in Florence, attending the Istituto Tecnico Galileo Galilei and the Scuola Tecnica Dante Aligheri. An extremely precocious child, Volterra became interested in the geometry of Adrien-Marie Legendre at age 11, and was soon devising original problems that he would then try to solve.

With his obvious interest in science and mathematics, Volterra rebelled against his family's insistence that he become a bank clerk or similar professional. However, an uncle intervened and persuaded Volterra's relatives to let the gifted boy continue his studies, even helping him to get a job as an assistant in the physics laboratory at the University of Florence. Meanwhile, Volterra was still in high school, from which he graduated in 1878. Later that year, he enrolled at the University of Florence's Department of Natural Sciences.

In 1880 Volterra won a contest to become a resident student at the prestigious Scuola Normale Superiore in Pisa, Italy. There he took classes in mathematics and physics, gradually narrowing his interest to mechanics and mathematical physics. He graduated from Pisa with a doctorate in physics in 1882, having written his thesis on hydrodynamics. Soon afterward, one of his professors, Enrico Betti, hired Volterra as an assistant. A year later, Volterra, still only 23, won a competition to become the mechanics professor at the university. When Betti died, Volterra assumed the chair of mathematical physics.

In about 1883, Volterra thought of the idea of a theory of functions that depend on a continuous set of values. This work would lead to the development of such fields of analysis as the solution of integral and integro-differential equations. In addition, he contributed the seeds of what would become the key concept of harmonic integrals. The following year, Volterra began studying integral equations and by 1892 he was publishing influential papers on partial differential equations. These concentrated particularly on the equation of cylindrical waves.

Volterra accepted a new post--as professor of mechanics at the University of Turin--in 1892. Four years later, he published a series of papers on what mathematicians would later call "integral equations of a Volterra type." In 1900 he became chair of mathematical physics at the University of Rome. When World War I began, however, Volterra interrupted his academic career briefly to enroll in the Italian Army Corps of Engineers. Although he was 55 at this point, the army gratefully accepted technical assistance from such an illustrious scholar, inducting him as an officer in the air branch. In this position, Volterra was the first to suggest using helium instead of hydrogen in dirigibles, thus helping perfect this new type of airship.

After the war, Volterra returned to his post at the University of Rome. His interests began turning to mathematical biology at this point, and he produced works on such pertinent topics as predator-prey equations and mathematical models of other biological associations. In 1922, his attention was again diverted by political matters as fascism began spreading across Italy. As a member of the Senate (appointed in 1905), he fought against what he and a few others quickly realized would be death to Italian democracy. Eventually, Volterra was forced to leave the University of Rome when he refused to take an oath of loyalty to the fascist government of Benito Mussolini in 1931. In 1932, he had to surrender his membership in numerous Italian scientific academies.

After being banished from Italian academia, Volterra lived mainly in Paris and Spain. He wrote one of his most influential books, The Theory of Functionals and of Integral and Integro-Differential Equations, in 1930. Starting in 1931, he accepted numerous invitations to lecture all around Europe, spending only short periods of time at his Italian country home in the Alban Hills near Rome. Afflicted with phlebitis beginning in 1938, Volterra nevertheless continued his pursuit of scientific knowledge.

Volterra, who did not dedicate himself exclusively to research but also enjoyed associating with many of the prominent artists, politicians, and writers of his time, died on October 11, 1940 in Rome. He and his wife had married in 1940.