Vito Volterra (3 May 1860–11 October 1940) was a public figure of tremendous prestige and influence. He was a Senator of the Kingdom, Dean of the Faculty of Sciences at the Universities of Pisa and Rome, co-founder of the Italian Physical Society, founder and the first president of the Italian Society for the Advancement of Science, the first president of the National Council for Research, President of the Accademia dei Lincei.

Volterra was a physicist and a mathematician whose stature in the mathematical world was compared to that of David Hilbert. His work on integral and integro-differential equations and “functions of functions” led to the development of functional analysis. He worked in geophysics, hereditary mechanics, biomathematics, and population dynamics. He is credited (along with Alfred J. Lotka) with the development of the first predator-prey model. Volterra gave keynote lectures at four International Congresses of Mathematicians (1900, 1908, 1920, 1928). He was a member of practically all important world science academies. Later in his life he became known as “Mr. Italian Science”.

A biography of a person of such caliber needs to be a biography of the epoch he lived in. Angelo Guerraggio and Giovanni Paoloni deliver an impressively comprehensive picture of the Italian society in the period straddling the 19th and the 20th centuries. The book could be called a “public” or “academic”, and also a “scientific”, biography, but there are of course some personal details.

Vito Volterra was born in 1860 in the ghetto of the city of Ancona to a poor Jewish family. Around this time the Jews of Ancona were granted full civil rights. He died in 1940 following the issue by the fascist government of Mussolini of the 1938 “Declaration of Race” which stripped the Jews of Italian citizenship.

His birthday was recorded on the flyleaf of a Hebrew/Italian edition of the “Psalms of David”, apparently by Volterra’s mother. This was followed by a note recording the death (when Volterra was just two years old) of his father, Abramo Volterra. Volterra’s mother was focused on his pre-school education, and Vito is said to have responded well to his mother’s proddings. However, as an adult, he is described as a non-practicing, assimilated Jew.

At age 9, Vito discovered on his own “that the oscillations produced by a twisted string are isochronic, like those of a pendulum.” At 11 he read Joseph Bertrand’s *Arithmétique* and Legendre’s *Géométrie*. At 13 — after reading Jules Verne — he calculated the trajectory of a rocket traveling to the Moon. At age 15 (according to my calculations) Vito entered Instituto Technico Galileo Galilei, where Cesare Arzelà was one of his professors. Later, in 1905, Arzelà wrote to by then his friend Volterra:

I can truly say that you are not only the most beautiful mind but also the most beautiful soul of all among our mathematicians.

While a student at the Scuola Normale in Pisa, Volterra published papers on the foundations of Riemann integration and real analysis. He modified the definition of Cantor’s set to obtain a nowhere dense set of positive measure. He gave an example of a function with bounded derivative that did not satisfy the Fundamental Theorem of Calculus. He also proved that that two non-intersecting dense sets could not both serve as the sets of continuity of two different functions, with the corollary that there is no function continuous on the set of rational numbers and discontinuous on the set of irrational numbers.

The book outlines these and other major Volterra’s contributions to science and mathematics so that the reader gets a very good idea of the important role he played in the development of those subjects.

As an Italian patriot, Volterra volunteered for the Army at the beginning of the World War I. At that time, he calculated the firing tables for the mountain guns mounted on dirigibles and proposed filling the dirigibles with helium instead of more flammable hydrogen. He was promoted to the rank of captain and awarded the *Croce di guerra* for military valor.

In 1931, as a firm opponent of the fascist regime, he refused to take the oath of allegiance, with the result that he was dismissed from his professorship at the University of Rome, and subsequently, expelled from all Italian academies. Volterra was one of only 12 professors who refused to take the oath. In 1938, as a Jew, he lost his last position at the Insitituto Lombardo di Scienze e Lettere.

The book supplies many more details on life and activities of Vito Volterra — I do not see how I can mention more than a small part of what he accomplished in his lifetime. Volterra was a giant of science, with a strong belief in the importance of science to societal progress. The book underscores his role in the promotion of science nationally and internationally and describes a crashing reversal that ideology brought on progress of science and education in Italy in the last years of his life.

I found the book edifying and absorbing reading.

Alex Bogomolny is a former associate professor of mathematics at University of Iowa. He lives in New Jersey, maintains a popular site Interactive Mathematics Miscellany and Puzzles, with a server somewhere in Michigan, and blogs at CTK Insights. In an extreme need you can tweet him at @CutTheKnotMath.