Goodstein, Judith R. The Volterra chronicles: The life and times of an. extraordinary mathematician , History of Mathematics, 31, AMS,

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1 MR Goodstein, Judith R. The Volterra chronicles: The life and times of an extraordinary mathematician , History of Mathematics, 31, AMS, Providence, RI; LMS, London, xxvi+310 pp. ISBN: ; This biography charts the rise and fall of the mathematician Samuel Giuseppe Vito Volterra as well as that of his homeland, Italy. Born in 1860 at the height of the Risorgimento and, more importantly, the start of the liberation of Italy s Jewish ghettos, by the time of his death in 1940, Volterra had been dismissed from his teaching position after refusing to sign a loyalty oath. The outline of Volterra s life is rather well known, but the author, a Cal Tech archivist who has worked on this project for at least 35 years, has added significant material on his family, colleagues, and sojourns to the U.S., based solidly on interviews and exhaustive archival searches in several countries. The major part of the book consists of an introduction, fifteen chapters ordered chronologically, and a short epilogue. Much of the introduction and all of Chapter 1 deal with Volterra s immediate family, concentrating on his mother Angelica, her brother Alfonso, and their cousin Edoardo Almagià, Volterra s future fatherin-law. Chapters 2-5 track Volterra s education, with family correspondence providing details of his determined fight to pursue his passion for mathematics over Angelica s and Alfonso s desire for a more pragmatic career in engineering.

2 His geometry teacher at the technical high school in Florence was the mathematician C. Arzelà, but it was the physicist A. Ròiti who exerted a greater influence on the budding scientist. At age 17 Volterra moved to the University of Pisa, where he began a lifetime of moving back and forth between pure mathematics and its applications, majoring in mathematical physics but learning pure analysis from U. Dini. Moreover, the school s director, E. Betti, served as a model not only for good teaching but for an abiding interest in applications of mathematics. During this time Volterra published his first two papers, at age 20, which prompted a meeting with the visiting G. Mittag-Leffler that resulted in a lifelong friendship. Yet his doctorate, obtained two years later, was in physics and based on a dissertation on hydrodynamics. Volterra accepted a professorship at Pisa at the very young age of 23. Chapters 6-9 discuss his academic positions at Pisa and Turin , a period during which he established his reputation as a first-rate scientist. The growing reputation included a stint as an examiner to Sicily, where he survived a gunshot from a distraught student. During the 1890s he extended his scientific contacts into France and Germany; a decisive stay in Göttingen in 1891 brought him in contact with G. Mittag-Leffler and M. Bôcher. But climbing the academic ladder caused disputes with Dini and Peano. Chapter 10 interrupts the scientific chronology to describe his arranged marriage in 1900 at age 40 to a second cousin, Virginia Almagià, who supported him

3 throughout the rest of his life, beginning with his professorship in Rome, Chapter describe Volterra s meteoritic rise during , when he became the undisputed head of the Italian school of mathematics that included a formidable group of Jewish mathematicians, including F. Enriques, G. Castelnuovo, and T. Levi-Civita. Beyond his homeland, Volterra was regarded as one of the world s foremost mathematicians, and he became Italy s international ambassador for science, delivering invited lectures at four International Congresses and sets of lectures in England, Norway, Sweden, and Argentina. In 1909 he sailed across the Atlantic for a six-week trip to the U.S., visiting several leading universities in much the same way Felix Klein had done sixteen years earlier, and culminating in lectures given at the 20-year celebration of the founding of Clark University. He also renewed acquaintance with Bôcher, whose student Griffith Evans completed his dissertation on Volterra s integral equations the following year before going to Rome. Toward the end of Evans two-year post-doctoral tour, Volterra met the American Edgar Lovett in Paris and induced him to come to Rome, where he hired Evans on the spot. Evans remained at Rice until departing to build a world-class department at Berkeley in Volterra had spoken at Rice on his second trip to the U.S. in (Only one sentence is devoted to his last visit to the country in 1919, probably due to lack of sources.) Incidentally, the unknown Evans correspondent (p. 298, footnote 29) was likely the Harvard geometer Julian Coolidge.

4 Volterra influenced the American mathematical community in several other ways. His work with the Italian Army Corps of Engineers during WWI led to close cooperation with Allied personnel in Britain and America, and this paid dividends for scientific societies on both sides of the Atlantic. For instance, National Research Councils were established in both the U.S. and in Italy; arguably the founding of the CNR in Italy represents Volterra s greatest achievement as an institution builder. This development, as well as several others, is dealt with only briefly in the concluding part of Chapter 15. Of prime importance is Volterra s role in the founding of two national societies. He was also instrumental in obtaining Rockefeller funding for Enrico Fermi and two other young Italian physicists. The remainder of the chapter deals with the rise of Fascism and the decline of Volterra s scientific and personal influence, beginning with his dismissal from the University of Rome because of a refusal to sign a loyalty oath to the Fascist government in 1931 and extending to the Manifesto of Italian Racism in 1938 that put into effect infamous racial laws. Volterra died peacefully in 1940 but his family survived Fascist/Nazi death camps only due to the intervention of the family s maid and her family. There are very few sources in English on Volterra, and recent definitive studies by G. Israel, U. Bottazzini, and G. Paoloni have not been translated from Italian, so this volume in the AMS/LMS History of Mathematics series helps fill a definite gap. However, it does not mention the decisive role he played in establishing an

5 Italian research institution in 1909 devoted to studying the Mediterranean Sea, which is covered in a recent book in Italian by S. Linguerri. Little mathematics per se enters Goodstein s biography or physics, biology, or economics, fields to which Volterra also contributed, for that matter but the book contains three appendices, one of which reprints a 1941 obituary by Sir Edmund Whittaker that provides an incisive analysis of various parts of Volterra s contributions to mathematics. The book also includes a list of his publications, numbering 236 in a long and fruitful lifetime from 1881 through David E. Zitarelli June 14, 2007

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