Reviews

Osmo Pekonen, Editor

The Volterra Chronicles: The Life and Times of an Extraordinary Mathematician, 1869–1940 by Judith R. Goodstein AMERICAN MATHEMATICAL SOCIETY, LONDON MATHEMATICAL SOCIETY, 2007, xxvi  310 PP., ISBN-10: 0-8218-3969-1, ISBN-13: 978-0-8218-3969-0, US $59 REVIEWED BY GIORGIO ISRAEL

Feel like writing a review for The Mathematical Intelligencer? You are welcome to submit an unsolicited review of a book of your choice; or, if you would welcome being assigned a book to review, please write us, telling us your expertise and your predilections.

Column Editor: Osmo Pekonen, Agora Centre, 40014 University of Jyväskylä, Finland e-mail: [email protected]

T

he proclamation of the Kingdom of Italy in 1861 marked the beginning of an extraordinary effort of cultural unification and development of education and scientific research. One oft-cited example is that of three eminent Italian mathematicians—Enrico Betti, Francesco Brioschi, and Felice Casorati—who, in the years that followed, undertook a journey to study the models presented by the more advanced European countries, above all Germany and France. These were the models that would later influence the institutional and scientific development of Italian mathematics. This development was promoted with such vigour that by the end of the 19th century Italian mathematics ranked second only to the two leading countries in world mathematics. It would take too long and be too complicated to shed light on all aspects of these influences here. In a word, the German model may be said to have exerted greater influence on the organizational and institutional aspects of education. It also encouraged the establishment of a school of geometry with an interest in both “pure” algebraic geometry and differential geometry. The French model, on the other hand, stimulated interest in mathematical physics and mathematical analysis, which were

deemed to be closely linked. France also represented a point of reference at the level of “general” scientific culture. These early steps led to the creation of the renowned Italian school of algebraic geometry. After toning down the “purist” excesses of Luigi Cremona, a central figure not only in the formation of the mathematics community but also of engineers, the leaders of this school— Federigo Enriques, Guido Castelnuovo, and later Francesco Severi—placed at the focus of research such themes as that of the classification of algebraic surfaces. They made a brilliant and profound contribution, albeit in an intuitive and aristocratic approach that was unmindful of rigour and that still today is a source of inspiration for research. Vito Volterra (1860–1940) was the top representative of the school of mathematical physics, which was closer to the French view of Henri Poincaré or Emile Picard. A separate case was that of Tullio Levi-Civita, who expressed a synthesis between the French influence and that of the German mathematics: a brilliant heir to the differential geometry tradition of Luigi Bianchi, he built Gregorio Ricci-Curbastro’s research up into a rigorous foundation of tensor calculus. His solid background, both in mathematical physics and in differential geometry, allowed him to set up a rigorous mathematical foundation of general relativity. Keenly aware of the latest developments, such as applied mathematics research in the field of turbulence, Levi-Civita was perhaps the most profound and brilliant Italian mathematician of that period. And yet it was Vito Volterra who was considered abroad the main representative and ambassador of Italian mathematics in the 20th century, to the point of being nicknamed “Mr. Italian Mathematics.” The reasons underlying this special status are not dependent solely on Volterra’s scientific prestige and the fact he was older than the other main figures in Italian mathematics. There were two other decisive factors. Volterra played a very important role in the establishment of scientific institutions in

© 2008 Springer ScienceBusiness Media, Inc., Volume 30, Number 3, 2008

1

the country. He was also a man of culture in the full sense of the word. Only Enriques can be compared with him. Volterra was in any case the most effective in promoting a true cultural policy. Following Cremona’s example, Volterra realized that the country was in need of suitable institutions if it was to become a true scientific “power.” He principally took the French model as his inspiration, which proved to be a limitation, as the German model was certainly more innovative. He founded and refounded a large number of institutions, such as Società Italiana di Fisica, Consiglio delle Ricerche, and the Comitato Talassografico. He embraced the extraordinary idea that science, in order to gain prestige, needed cultural dissemination and the involvement of all sectors of society: teachers, engineers, economists, and men of general culture. The Società Italiana per il Progresso delle Scienze (SIPS), which he reestablished in 1906, played a decisive role in this direction. Until the Second World War, the SIPS congresses were a meeting place for the whole of Italian scientific culture. Voterra turned the Accademia dei Lincei, of which he was a long-time president, into one of the centres of dissemination of scientific culture. He was inspired by a moderate progressive conception. He was a democrat with enlightened views, profoundly convinced of the value of scientific and technological progress. At the scientific level, he expressed a view that may be encapsulated in the formula: to defend and extend the scope of classical reductionism based on a deterministic and differential type of mathematical approach. This led him to take an interest in and contribute actively to the application of mathematics to biology and economics, which were viewed with scepticism by many of his contemporaries. The figure of Volterra is rich, fascinating and complex, full of contrasts. The collision between his democratic and enlightened view and fascist authoritarianism was inevitable. In this clash Volterra demonstrated all his courage and nobility of character. Nevertheless, the model he proposed displayed some weaknesses. This was clearly seen when he rejected the educational reforms in a humanist direction promoted by the idealist philosopher

2

THE MATHEMATICAL INTELLIGENCER

Giovanni Gentile, who was a minister in the fascist regime. He tried to combat it with a proposal based on a partial reform of the old and inadequate Casati law. He fought against the tendency of the fascist regime to separate pure and applied research and thus materially opposed a trend that nevertheless possessed some aspects of modernity. The fascist regime with its policy of autarky (of which anti-Semitic racism represented the extreme expression) destroyed Italian science, although ideas such as that of setting up two separate institutes of Higher Mathematics (Istituto Nazionale di Alta Matematica, INDAM) and Calculus Applications (Istituto Nazionale per le Applicazioni del Calcolo, INAC) were valid. Volterra’s interest in biomathematics was a wideranging and modern intuition although his dislike of probability calculus and his view that the only serious tools for mathematics were differential equations represented a severe handicap. His proFrench and bitterly anti-German attitude—Volterra was a leader of the Latin Union—led him to boycott an Italo-German applied mathematics congress organized by Levi-Civita. In this way, he severed the relations of Italian science with the new schools of research in the field of turbulence. He was also relatively insensitive to the new developments in physics and opposed the creation of a chair of theoretical physics for Enrico Fermi. Vito Volterra had high status as a scientist, an intellectual, and a cultural organizer who played a decisive role in raising Italy to among the first scientific ranks at a world level and who was inspired by a form of enlightened rationalism that was as lofty and profound as, in certain respects, it was backward looking. It is to this figure that Judith Goodstein addresses her book. By means of a thorough and systematic use of the primary sources (including, in particular, the Volterra Archive at the Accademia Nazionale dei Lincei in Rome, and numerous other archives in Italy and the United States) and through the painstaking collection of many oral histories, the author has provided a detailed and exhaustive reconstruction of the life of Volterra, and of his scientific, institutional, and personal relations. Her achievement patently involved a great workload and the patient sifting of doc-

uments, some of them hitherto unknown, as well as a high degree of archival skills. Henceforth those interested in the figure of Volterra have at their disposal a valuable tool that provides an illustration down to the smallest details of the life of the great scientist. Among other things, the book contains a fascinating collection of photographs. Having said this, the book also has a number of flaws. The first consists in the almost complete absence of any substantial treatment of Volterra’s scientific work. The author correctly states that this was not her purpose: the title refers to the “life and times” and not the “life and works” of Volterra. The book essentially follows a time line and is mainly devoted to personal events. However, it is difficult to convey a satisfactory image of the figure of Volterra without reference to his scientific production. This omission makes it difficult to describe the significance of his cultural project, which was part and parcel of his scientific project, and to shed light on the mixture of conservatism and innovation that represents the most significant and complex characteristic of the scientist’s figure. The most significant of Volterra’s many contributions are focused on functional analysis, the theory of elasticity, integral and integro-differential equations, and biomathematics. The close links among all these topics represent both the strength and the weakness of Volterra’s programme. He has been called the founder of modern functional analysis. However, several historiographic schools have challenged this role, as the concept of “function of line” is restrictive and insufficient as far as developing a general foundation of the theory is concerned. Volterra himself sought to ward off early criticism by claiming that he had never had a purely mathematical theory in mind, and thus his research should be viewed against the background of the problems of viscoelasticity. This shows that the close links he established between mathematics and applications placed him outside the ongoing early axiomatic developments. These aspects are extremely important for a deeper understanding of the figure of Volterra. A similar situation arises in the case of biomathematics. Goodstein rightly

states that every contemporary biomathematics textbook recognizes Volterra as the founder of the discipline. However, she does not mention that most of Volterra’s program has fallen into complete oblivion. It is not only a matter of the essentially unsuccessful attempt to create a rational and analytical mechanic of biological associations [1]. It is also a matter of the difficulties of providing an empirical and experimental foundation of his mathematical theories, for which he sought support all over the world. Volterra never resigned himself to adopting an abstract mathematical modelling approach. He wanted to give biomathematics a foundation similar to that of classical mathematical physics. In this, he clashed with his sonin-law, Umberto D’Ancona. The world of scientists in which Volterra endeavoured to defend his view was doomed to disappear [2]. No mention of this is made in the book, thus omitting an aspect of fundamental importance in understanding the position occupied by Volterra at the time. Another set of observations refer to the political, institutional, and cultural aspects of his times. Also here, the description of Volterra’s activity, and in particular his courageous opposition to fascism, is oversimplified. No one can afford to have an indulgent attitude to fascism and to underestimate its disastrous effect on Italian science. However, the matter cannot simply be wrapped up by using adjectives. Mussolini was not just “a bull and a brute.” History must explain why the vast majority of Italian intellectuals, including many scientists and colleagues of Volterra (also Jews), sided with fascism [3,4]. On this point, the author should have sifted through the vast Italian bibliography on the topic which, despite the different viewpoints, shed light on the innovative aspects of fascism that account for the approval it succeeded in arousing. I mentioned the clash between Volterra and Gentile on educational reform; attentive examination and the subsequent developments show that the Gentile reform—which was supported by mathematicians such as Enriques—was more advanced and modern than the proposals made by the commission set up by Volterra at the Accademia dei Lincei. Moreover, Gentile changed his originally hostile attitude to scientific cul-

ture that he had adopted at the beginning of the century and established a close relationship with Federigo Enriques. Gentile gave Enriques the direction of the scientific section of the Treccani Enciclopedia Italiana, which during that period published articles that still today may be considered a model of scientific dissemination. In this connection it seems inappropriate to speak of a “Volterra circle” made up of mathematicians such as Enriques and Castelnuovo, as Goodstein does continually. Volterra was certainly a point of reference and a pole of Italian mathematics, but it is hard to speak of him as the centre of a “circle.” Also the figures closer to him, such as Enriques, Castelnuovo, or Levi-Civita, were scientifically, culturally, and even politically different from Volterra. In the case of persons like Severi the difference is abyssal. It must also be borne in mind that Volterra was the only Italian mathematician who did not swear allegiance to the regime and that, after 1931, his presence was considered increasingly disconcerting. He no longer attended the evening meetings with Enriques, Castelnuovo, or Levi-Civita, and Enrico Fermi, who did not fail to wear the fascist black shirt at the meetings of the Accademia d’Italia of which he was a member. It is even less appropriate to speak of a “Jewish circle of Italian mathematicians.” No such body has every existed, except in the mind of the champions of fascist anti-Semitism. This is a highly delicate point that the author would have been well advised to treat in depth, considering the vast existing bibliography available. Goodstein is quite right to call the Introduction “The Jewish Mathematician.” Among other things, this expression was already in use at the time with different meanings and intentions, sometimes with racist connotations. However, if we revive the term today we must define the meaning we intend it to have. The only meaning in which it is possible to speak of Volterra as a Jewish mathematician is on the strength of his genealogical membership of the Jewish community, which the book reconstructs in great detail. As confirmed by the numerous anecdotes in the book, it is possible to speak of the persistence of membership bonds that do not seem to extend be-

yond the tendency to mix and to arrange marriages inside the group. But as soon one attempts to discover a trace of “Jewishness” of any kind in Volterra’s life, writings, and letters, as in LeviCivita, Enriques, Castelnuovo, and many others, the disappointment is total. There is not a single reference that justifies the existence of a sense of belonging and of Jewish identity of a religious or cultural nature. One important clue is the fact that many Jewish scientists—including Volterra himself—attempted in 1938 to avail themselves of the “discrimination” procedure, which afforded them exemption from the consequences of the anti-Jewish racial laws if they were able to demonstrate their special service to the nation. The attitude held by Volterra in 1938, quite different from the vigorous one displayed in 1931 on the issue of the oath of allegiance, shows that his Jewish nature was felt more as a problem than as something to be claimed and defended. This is a complex matter, and the author ought to have treated it in greater detail as it too is of decisive importance in the construction of an appropriate image of the figure of Volterra. In-depth analysis shows that the Jewish intellectuals, and scientists in particular, were highly integrated into the surrounding culture and society, and their relationship with Jewish identity, if any, was reduced to a vague reminiscence. Volterra—like Enriques, Levi-Civita, and many others—was painfully surprised when according to the racial laws of 1938, he found himself identified as a member of a “race”: they all believed they were now Italians to all intents and purposes and were completely integrated into the social, political, and cultural reality of the country. Fascism was different from Nazism and did not have anti-Semitic racism as one of its constitutive projects. In my opinion the general tendency towards a racial and eugenic policy had set the stage for the adoption of anti-Semitic policies. Other historians consider that, on the contrary, the 1938 laws were passed merely to ingratiate Hitler. However this may be, there is no justification for attributing of a specific hostility toward fascism or toward Mussolini to a “Jewish circle of Italian mathematicians.” Enriques was a fascist until 1938. Practically no mathematicians migrated, unlike the physi-

© 2008 Springer ScienceBusiness Media, Inc., Volume 30, Number 3, 2008

3

cists. Indeed the community of physicists was projected toward an internationalist dimension of the scientific undertaking and had no difficulty in transporting its activities elsewhere. In contrast, figures such as Volterra were too closely linked to the national cultural context to be able to move elsewhere with ease. For him and a large part of the Jewish mathematicians in Italy the racial laws came as an incomprehensible and unexpected tragedy. Their Jewish identity was so unsubstantial that they were unable to lay claim to it with pride; they rather suffered their identification as belonging to the “Jewish race” almost as something shameful. This is an essential issue if we are to understand fully the figure of Volterra [4,5]. A final remark concerns the bibliography, which is somewhat incomplete. In conclusion, the book represents an important milestone in the reconstruction of Volterra’s life, but an exhaustive and comprehensive scientific and cultural biography of the scientist remains to be written. REFERENCES

[1] G. Israel, “Volterra’s ‘analytical mechanics’ of biological associations,” Archives Internationales d’Histoire des Sciences 41 (126, 127) (1991) pp. 57–104, 306–351; G. Israel, “Vito Volterra, Book on Mathematical Biology (1931),” in Landmark Writings in Western Mathematics, 1640–1940, I. Grattan-Guinness (ed.) Amsterdam, Elsevier, 2005, pp. 936–944. [2] G. Israel, A. Millán Gasca, The Biology of Numbers. The Correspondence of Vito Volterra on Mathematical Biology, Basel– Boston–Berlin, Birkhäuser Verlag, Science Networks—Historical Studies, 26 (2002) pp. x  406. [3] G. Israel, L. Nurzia, “Fundamental trends and conflicts in Italian Mathematics between the two World Wars,” Archives Internationales d’Histoire des Sciences 39 (122) (1989) 111–143. [4] G. Israel, “Italian Mathematics, Fascism and Racial Policy,” in Mathematics and Culture I. M. Emmer (ed.), Berlin–Heidelberg, Springer-Verlag, 2004, pp. 21–48. [5] G. Israel, “Science and the Jewish Question in the Twentieth Century: The case of Italy and what it shows,” Aleph, Historical Studies in Science and Judaism (2004) 191–261.

4

THE MATHEMATICAL INTELLIGENCER

Dipartimento di Matematica Università di Roma “La Sapienza” Piazzale A. Moro 5—00185 Rome, Italy e-mail: [email protected]