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Gray, Milton Keynes Angelo Guerraggio Pietro Nastasi Italian Mathematics Between the Two World Wars Birkhäuser Verlag Basel · Boston · Berlin Authors’ addresses: Angelo Guerraggio Pietro Nastasi Centro PRISTEM-Eleusi Dipartimento di Matematica Università Bocconi Università di Palermo Viale Isonzo, 25 Via Archirafi , 34 20135 Milano 90123 Palermo Italy Italy email: [email protected] email: [email protected] 2000 Mathematics Subject Classifi cation: 01A60, 01A72 A CIP catalogue record for this book is available from the Library of Congress, Washington D.C., USA. Bibliographic information published by Die Deutsche Bibliothek Die Deutsche Bibliothek lists this publication in the Deutsche Nationalbiografi e; detailed bibliographic data is available in the internet at http://dnb.ddb.de. ISBN 3-7643-6555-2 Birkhäuser Verlag, Basel – Boston – Berlin This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifi cally the rights of translation, reprin- ting, re-use of illustrations, broadcasting, reproduction on microfi lms or in other ways, and storage in data banks. For any kind of use whatsoever, permis- sion of the copyright owner must be obtained. © 2006 Birkhäuser Verlag, P.O.Box 133, CH-4010 Basel, Switzerland Part of Springer Science+Business Media Cover design: Micha Lotrovsky, Therwil, Switzerland Printed on acid-free paper produced from chlorine-free pulp. TCF ∞ Printed in Germany ISBN-10: 3-7643-6555-2 e-ISBN: 3-7643-7512-4 ISBN-13: 978-3-7643-6555-4 9 8 7 6 5 4 3 2 1 Preface During the first decades of the last century Italian mathematics was considered to be the third national school due to its importance and the high level of its numerous re- searchers. The decision to organize the 1908 International Congress of Mathematicians in Rome (after those in Paris and Heidelberg) confirmed this position. Qualified Italian universities were permanently included in the tour organized for young mathematicians’ improvement. Even in the years after the First World War, Rome (together with Paris and Göttingen) remained an important mathematical center according to the American math- ematician G. D. Birkhoff. Now, after almost a century, we can state that the golden age of Italian mathemat- ics reduces to the decades between the 19th and the 20th century. In the centre of interest stood the algebraic geometry school with Guido Calstelnuovo, Federico Enriques and Francesco Severi acting as key figures. Their work led to an almost complete systemati- zation of the theory of curves to the complete classification of the surfaces and to the bases of a general theory of algebraic varieties. Other important contributions came from the Italian school of analysis. Its main representative was Vito Volterra – an outstanding analyst with a strong interest in mathematical physics – who produced important results in real analysis and the theory of integral equations and contributed to the initiation of functional analysis. Guiseppe Vitali, Guido Fubini and Leonida Tonelli were well known in the inte- gration theory and the calculus of variations. At the beginning of the century Tulli Levi- Civita’s scientific adventure started: He became one of the most recognized and esteemed Italian mathematicians abroad. There also was a strong connection between the authority in the scientific disciplines and the role they could play for the future and the modernization of Italy. In chapter 1 we describe this thrilling season of Italian mathe- matics. The golden age however, is only the prologue of our history. We will focus our attention to the years between the two World Wars. The turning point during those years was marked by the Great War – it was an epochal change. Nothing remained as it was be- fore. The ingenuous hope that the war could simply be a gap of time and afterwards one could come back to the belle époque were illusions. In chapter 2 we analyze the changes in Italian mathematics. From a strict mathematical point of view the twenties and the thirties were less stimulating for Italy than the previous ones, but from the context of the whole century they were attractive on other sides: The social and political situation suddenly changed with the raise of the fascist regime (chapter 4). Also structural scientific aspects changed with the creation of new institutions which should play an important role in the develop- ment of Italian science and mathematics for the rest of the century. In chapter 3 we de- scribe the birth of UMI (Italian Mathematical Union) and of CNR (National Research Council); in the chapters 6 and 8 we deal with the consecutive presence of INAC and of Severi’s INDAM. vi Preface Naturally the next step is to consider whether there was any link between the changes in the political and scientific spheres and if these influenced the organization of the mathematical research, its contents and its quality level. We can describe the main problems dealt with by our analysis in a more detailed manner. In the period between the two World Wars the leading actors of Italian mathe- matics were rather the same as before. Perhaps the most relevant difference was the arrival of Mauro Picone on the scene. His presence was particularly noticeable in a nu- merical and applied perspective and also in the ideas that guided the creation and the development of INAC – an absolute novelty in the international mathematical panorama. Even if the names were rather the same, their role had changed. Volterra’s brilliant career was stopped by fascism, and so the old liberal generation was marginalized by the new government. Severi became piece by piece the head of the mathematical group. We ded- icate the chapter 3 and 5 to this leadership change. Like Volterra, Severi was an out- standing mathematician and a broad-minded man, and his personality was charismatic, even if different in the coherence of his behaviour patterns. His leadership should remain till the Second World War. There should be some tensions – see chapter 6: the alternative of the CNR – but in the thirties Italian mathe- matics grew with a sufficient continuity (chapter 7). It needed another external event, the tragical experience of the Second World War to induce a new discontinuity in the Italian mathematical life (chapter 8). The mathematical research itself was always at a good level. The influence of Ital- ian researchers on algebraic geometry was a strong one. Enriques contributed some im- portant historical studies to his research in this field. The “old lion”, Volterra, wrote a last relevant chapter in his scientific career by analyzing population dynamics. Tonelli’s Fondamenti di Calcolo delle Variazioni were published and his esteem – about all for the use of direct methods – was high in the mathematical world. Picone’s influence has already been described. Some other young brilliant scholars joined the already acknowl- edged researchers: Renato Caccioppoli, Lamberti Cesari, Francesco Tricomi and others. Another young man, Bruno de Finetti, increased the suspense of the probabilistic studies and anchored a research directed towards economic and social applications. Not to for- get the undoubted authority of Levi-Civita and the role he played by corresponding with Einstein and many younger colleagues. Nevertheless this survey makes a clear statement: for Italian mathematics the golden age was on the retreat. Its potential did never return after the First World War. Not quite a crisis but rather the difficulty to maintain the previously excellent level and to continue in playing a role in originality and creativity. On the contrary the orthodox respect towards a still young tradition and the acceptance of a level just achieved seemed to prevail. The new abstract and algebraic languages did not speak Italian any more. They were born in situations where the weight of tradition was lower and we could speak of a decline of Italian mathematics with respect to its level 30-40 years before compared to the new languages that were developing in the other countries between the wars. This is the point where the two histories – the Italian and the mathematical one – met. The conditions and the progress of Italian mathematics are analyzed by focusing on both the inner and the external influences. Is there any link between the establishment of Preface vii a dictatorial regime and the decline of Italian mathematics? Can we find this possible link in the most repressive fascism facts – the 1931 oath and the 1938 racial laws – or rather in its politics towards science and particularly in its attitude in favour of the applied sciences? In the following pages we will try to give an answer to these questions by analyz- ing the most important works of the Italian mathematicians living in the period, the life of the Italian mathematical community, some correspondence of the most representative members of it