Vito Volterra

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Lore & Background

Volterra showed early promise in mathematics before attending the University of Pisa, where he fell under the influence of Enrico Betti, and 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. He was named by the king Victor Emmanuel III as a senator of the Kingdom of Italy in 1905. 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).

Reader's Guide

Volterra's significance lies in his foundational work in functional analysis and his pioneering application of mathematics to biology, most notably the Lotka–Volterra equations describing predator-prey dynamics. His research on dislocations in crystals later proved important for understanding ductile materials. He was the only person to be a plenary speaker at the International Congress of Mathematicians four times (1900, 1908, 1920, 1928). Politically, he was a lifelong royalist and nationalist who opposed the Fascist regime; in 1931 he was one of only 12 out of 1,250 professors who refused to take a mandatory oath of loyalty, leading to his resignation from his university post and scientific academies. He lived largely abroad afterward, returning to Rome just before his death. His legacy includes both his mathematical innovations and his principled stand against authoritarianism.

Did You Know?

• Volterra was the only person to be a plenary speaker at the International Congress of Mathematicians four times: 1900, 1908, 1920, and 1928.
• During World War I, he originated the idea of using inert helium rather than flammable hydrogen for airships.
• In 1931, he was one of only 12 out of 1,250 professors who refused to take a mandatory oath of loyalty to the Fascist regime.
• He was appointed a member of the Pontifical Academy of Sciences in 1936 on the initiative of founder Agostino Gemelli.
• His son Edoardo Volterra (1904–1984) was a famous historian of Roman law.