The Volterra Chronicles: The Life and Times of an Extraordinary Mathematician 1860–1940

  • Judith R. Goodstein
American Mathematical Society/London Mathematical Society: 2007. 310 pp. $59 0821839691 | ISBN: 0-821-83969-1
Vito Volterra modelled predator–prey dynamics. Credit: CENTRO PRISTEM - ELEUSI

Vito Volterra was an extraordinary mathematician. He was also a pioneer of biological modelling — a research tool that has increased in popularity by leaps and bounds since the publication of his seminal 'predator–prey' model in 1926. Volterra lived at a time when Italy was undergoing bouts of political upheaval, as a child in the wake of the Risorgimento — the country's unification in the 1860s — and then under Benito Mussolini's fascist regime. As a senator, Volterra withheld his support for the regime and was therefore expelled from the University of Rome in 1931 and from all Italian academies in 1934. The Volterra Chronicles is a rich biography set amid this turmoil.

Author Judith Goodstein captures the human, political and social environment of the age. The story of Volterra's life stems from his very close Italian Jewish family, with their strong patriotic sentiments. He was born in Ancona in May 1860, when the town belonged to the Church, and grew up in a country still deeply affected by the ideals of the Risorgimento. He graduated in physics from the University of Pisa and became a professor there when he was only 23 years old. Later he moved to the University of Turin, then to the University of Rome, where he married his young cousin Virginia Almagià.

The Volterra Chronicles describes the early research done by the young Volterra and his deep and precocious interest in mathematics and its applications. His papers on real and complex analysis, on mathematical physics, hydrodynamics, electrostatics, elasticity, differential, integral and integro-differential equations are still classics. In addition, he is considered a father of functional analysis, one of the main branches of contemporary mathematics. But he never lost contact with the experimental sciences, and the final chapter of the book covers his ground-breaking incursions into biomathematics.

Volterra was a key participant in scientific organizations in Italy and worldwide. He was president or vice-president of important research institutes including the International Bureau of Weights and Measures (1921–40) and the International Research Council, and founder of, among other things, the Italian National Research Council and the Italian Society for the Progress of Science.

His family has generously donated several archives to the Accademia dei Lincei in Rome, which are now fully catalogued. This biographical material has been invaluable for scholars, and important contributions about Volterra have been published during the past decade or so — for example, by Giorgio Israel and Ana Millán Gasca in 2002 and Rita Levi-Montalcini in 1996.

The Volterra Chronicles is different from these other works in that it is a dedicated biography of Volterra, based on original documents, which invites us into the mathematician's intimate circle. Short passages translated from his correspondence provide insight into his intense relationships with the most prestigious mathematicians of his time, which were always grounded in mutual scientific and personal respect. The book reveals his knack for spotting talent in young scientists, including Tullio Levi-Civita, André Weil, Griffith Evans, Marcel Brelot, Enrico Fermi and Joseph Pérès, whom he helped in various ways or with whom he collaborated. The characters of his family and friends, including Carlo Somigliana and the physicist Antonio Ròiti, and of his teachers Ulisse Dini and Enrico Betti are perceptively drawn.

Volterra was resolutely in favour of military intervention by Italy during the First World War to fight alongside France, Britain and Russia. He volunteered at the age of 55 when he was a senator and a member of many illustrious academies. During the conflict, he was involved in military action and scientific research, and cooperated closely with scientists in allied countries, particularly France.

He was a fierce opponent of fascism. In 1924, still a senator, he cast a no-confidence vote in Mussolini as head of the government and in 1931, he refused to sign a loyalty oath professing allegiance and devotion to king, country and the Fascist regime. This refusal cost him his university post and academy memberships, as well as the support of most of his colleagues. He also faced persecution under racial laws issued in 1938. But the regime allowed him to keep his passport and he continued to travel until his death in October 1940, four months after Italy joined the Second World War.

One of three appendices (the others being translations of his most important speeches) to The Volterra Chronicles reproduces a touching and sensitive obituary written by the distinguished English mathematician Edmund Whittaker. It is a fitting end to a biography of an outstanding scientist, which is remarkable for its accuracy and scholarly rigour, and — unlike its predecessors — for its potential to engage a wide readership.