Throughout this general interest biography, Judith Goodstein skilfully interweaves descriptions Volterra’s intellectual development with accounts of his personal life and his wider political and academic achievements. Since he left behind no memoirs or diaries, Judith Goodstein has based her research upon the analysis of personal letters, professional correspondence and various interviews. She indicates how Volterra’s life exemplifies post-unification Italian mathematics, its international standing in the period 1900 to 1925, and what she refers to as its ‘precipitous decline’ under the Mussolini regime. There is, of course, only a general outline of Volterra’s mathematical output, but it certainly conveys the nature and extent of his overall academic achievements.
Volterra (1860–1940) was born around the time of the formation of Italy as a unified nation, and he died a few years after the beginning of the Second World War. A mathematical prodigy and protégé of Enrico Betti, his meteoric rise in the scientific and mathematical world continued with the award of a full professorial post at the age of 23; and he was later to occupy a position once held by Galileo, in that he became president of the Accademia dei Lincei (Italy’s precursor to Britain’s Royal Society). Over the course of his lifetime, Volterra became an influential international figure in the realm of analysis and applied mathematics, and he was in great demand as a contributor to international conferences, and transcripts of two of such speeches are included as appendices.
Included also is Appendix A, which consists of Sir Edmund Whittaker’s more mathematically detailed obituary of Volterra, published by the Royal Society in 1941. This begins with mention of Volterra’s independent rediscovery of results on hydrodynamics first revealed by George Stokes. Whittaker goes on to tell us about Volterra’s pioneering work on functional analysis, his papers on partial differential equations and integral equations; his contributions to the theory of elasticity, and other aspects of his work. Although Goodstein describes the circumstances that led Volterra to investigate predator-prey phenomenon, Whittaker provides a closer description on the actual mathematics of Lotka-Volterra theory.
Overall, the process of reading this book left me with the distinct feeling of being personally acquainted with Vito Volterra. It provides empathic insights into his family life and it indicates how he balanced such personal commitments with the demands of his career. Moreover, the image of Volterra as a heroic figure emerges not just because of his academic stature, but also because he was sacrificial in his political support for the recently formed Italian democratic state. Amazingly, on the outbreak of the First World War, he enlisted in the Italian Air Force (at the age of 55). But Volterra’s greatest act of heroism occurred in 1931, when he was one of the very few Italian academics who refused to swear an oath of allegiance to Mussolini’s facist regime. Other Jewish mathematicians took this oath or fled overseas, but Volterra’s stand led to him being stripped of all honours and academic affiliations and he spent the last ten years of his life in relative obscurity.
In the process of recreating the life of this ‘extraordinary mathematician’, Judith Goodstein has given us a very vivid account of the rich nature of applied mathematics in Italy — and its connections with the most eminent European mathematicians of the day. As well as being a work of serious scholarship, its readability and the scope of its thematically diverse narrative mean that it should appeal to a wide readership.
Peter Ruane has now escaped the bureaucratic confines of higher education, where he spent a working life training future primary and secondary mathematics teachers.