Science Networks. Historical Studies 29. Basel: Birkhäuser (ISBN 3-7643-6555-2/hbk). x, 299 p. EUR 88.00/net; sFr. 148.00 (2005).

This book is both fascinating and deeply frustrating. It opens up a whole new dimension of history, namely of Italian mathematics since the Risorgimento, which hitherto has by and large remained hidden to non-Italians due to the language barrier. One learns about the philosophical clash between the mathematicians (particularly F. Enriques) and the philosophers (B. Croce, G. Gentile) around 1911, about the impact of the First World War on the subsequent development of numerical analysis in M. Picone’s institute (first Naples, later Rome), about the sudden conversion (1929), apparently due to a mixture of vanity and fear, of the leading algebraic geometer F. Severi from anti-fascism to wearing the black shirt (which reminds one very much of the German L. Bieberbach, although Severi rejected the latter`s racist theories). There is a description of how the Italian methods in algebraic geometry became gradually obsolete compared to the modern algebra cultivated in Göttingen, from where F. Conforto reports in very interesting letters. One sees the upswing of probability (G. Castelnuovo, F. P. Cantelli), mathematical statistics (C. Gini), and mathematical economics (L. Amoroso) from the 1920s, with the latter two at least supported by the political atmosphere of Mussolini’s Fascism. One learns how V. Volterra and T. Levi-Civita tried to stem the tide and were finally put aside by the regime. One is informed with mathematical detail on the work of the two Italian schools of analysis under L.Tonelli (Pisa) and M. Picone (Rome). The clash between the somewhat more conservative Italian Mathematical Society U.M.I. and the regime-and-applications-oriented National Research Council is discussed in detail, and also the promulgation of the racist laws in 1938 with devastating consequences for Italian mathematicians like Levi-Civita and B. Segre. The lack of self-criticism by F. Severi, E. Bompiani and others after the war is mentioned. Most assertions are documented with archival material. Nevertheless the book does not fully meet scholarly standards. This is partly due to its narrative, colloquial style (`Do you remember the 1921 episode …?’, p. 231). But the main problem is that the book does not really overcome the language barrier. The English is at times incomprehensible. The constant confusion between `would’ and `will,’ and between `physicist’ and `physician’ is a problem although a more minor one. The report on the soldiers `killed and blessed in France’ (p. 57), obviously formed from a French verb, makes, sadly though, for a good laugh. But the reports on the `Italian Western (!) Africa Empire’ (p. 247, meaning occupied Ethiopia) in 1936 and on the `Congress of Monaco’ (p. 259, from the Italian word for Munich) in 1938, which sealed the destiny for Czechoslovakia, are a real nuisance. Sentences like `Thus only five Italians ennobled (!) for the Congress: among them an old Vito Volterra, worn-out by the last events and to whom the Congress of Oslo sent a warm greeting telegram.’ (p. 248) are puzzling. The above leaving it unclear whether in the end any Italians took part in the Oslo International Congress of Mathematicians of 1936 (Volterra apparently did not). The problem even occurs in a chapter title `Chapter 4 Fascism: somebody rise, others fall’. As a result, the reader is happy to have very long Italian quotations (some running over several pages) in order to check the dubious English translations (given as footnotes) - something, which was probably not intended. The publisher, who wants 88 Euros for a copy, has to take the main responsibility for this disaster. The carelessness is also evident in other respects. One photograph of Severi is reproduced no fewer than five times in different enlargements. The page headings reveal only the first of the two authors (Guerraggio), the picture on the cover, which shows the Italians Levi-Civita, Enriques, and Volterra (?), is mysteriously described as `Brouwer … on the occasion of his inaugural lecture’ (p. iv). A bibliography is also lacking. The reviewer is happy to have such an interesting book for free, even if it cost him twice the usual time to read it.