Table Of ContentScience Networks · Historical Studies
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Volume 29
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J. 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
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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 tourorganized 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 19thand the 20thcentury. 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 époquewere 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
changesin 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 Variazioniwere 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 and their positions outside the research or educational fields. But our in-
terest goes beyond the historical facts of the period between the two World Wars and its
influences on the present problems. So the previous questions have a “modern” version
too. Can the scientific world accept – and at which conditions – a confrontation with the
political power or is it necessary to avoid these contaminations? Which are the possibili-
ties of the political sphere to orient the trends of the scientific developments? And in the
particular case of mathematics? How can a political will overcome the constraints im-
posed by the economic structure? In the light of the episode of the oath and the silence of
too many mathematicians at the sight of the racial laws, which are the ethic and political
responsibilities of a researcher?
As one can see, the questions are numerous. We just hope to give a contribution in
answering them through the analysis of Italian mathematics between the two World
Wars.
Angelo Guerraggio
Pietro Nastasi
Contents
Chapter 1 Prologue . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1. The Risorgimento generation . . . . . . . . . . . . . . . . . . . . . . . . . . 1
2. The golden age. The Italian school of algebraic geometry . . . . . . . . . . . 10
3. The golden period. The mathematical physics . . . . . . . . . . . . . . . . . 16
4. The golden age. The analysis. . . . . . . . . . . . . . . . . . . . . . . . . . 19
5. External interests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
Chapter 2 Nothing is as it was before . . . . . . . . . . . . . . . . . . . . 29
1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
2. Italian mathematicians take sides. . . . . . . . . . . . . . . . . . . . . . . . 31
3. Mathematicians at the front . . . . . . . . . . . . . . . . . . . . . . . . . . 45
Chapter 3 Volterra’s leadership . . . . . . . . . . . . . . . . . . . . . . . . 55
1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
2. Rome, 1921 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
3. The foundation of the Unione Matematica Italiana . . . . . . . . . . . . . . 67
4. The foundation of the Consiglio Nazionale delle Ricerche . . . . . . . . . . 74
5. Volterra’s scientific activity . . . . . . . . . . . . . . . . . . . . . . . . . . 76
6. Volterra and Ecology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
Chapter 4 Fascism: somebody rise, others fall . . . . . . . . . . . . . . . . 83
1. The march on Rome . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
2. Giovanni Gentile and school reform . . . . . . . . . . . . . . . . . . . . . . 85
3. The battle of the “manifestos” . . . . . . . . . . . . . . . . . . . . . . . . . 90
4. Enriques’rentrée . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
Chapter 5 One man alone in the lead . . . . . . . . . . . . . . . . . . . . . 101
1. The novelty of the Accademia d’Italia . . . . . . . . . . . . . . . . . . . . . 101
2. Severi as a mathematician, in the 1920s . . . . . . . . . . . . . . . . . . . . 104
3. Severi: politician . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108
4. The difficult presence of Algebra . . . . . . . . . . . . . . . . . . . . . . . 119
5. Enriques and his school . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
6. Castelnuovo, Probability and “social Mathematics” . . . . . . . . . . . . . . 147
Chapter 6 The CNR alternative . . . . . . . . . . . . . . . . . . . . . . . . 159
1. End of decade balance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159
2. Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162
3. Distinguished Senator, Dear Colleague . . . . . . . . . . . . . . . . . . . . 178
4. The dualism U.M.I. – C.N.R. . . . . . . . . . . . . . . . . . . . . . . . . . . 183
x Contents
5. The oath . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 194
6. Tullio Levi-Civita . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 204
Chapter 7 The 1930s move forward . . . . . . . . . . . . . . . . . . . . . 215
1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 215
2. Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 217
3. Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 222
Chapter 8 Towards disaster . . . . . . . . . . . . . . . . . . . . . . . . . . 243
1. European events . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243
2. The international Congress of 1936 . . . . . . . . . . . . . . . . . . . . . . 247
3. The anti-Semitic laws of 1938 . . . . . . . . . . . . . . . . . . . . . . . . . 251
4. Crisis signals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 268
Chapter 9 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 283
Chapter 1
Prologue
1. The Risorgimento generation
The history of modern Italy starts in 1860. In that year the various nation-states into
which the Italian peninsula had been politically and administratively divided were uni-
fied in a process called the Risorgimento. Under the leadership of Piedmont (the north-
western region of Italy on the French border, whose capital is Turin) and its hegemony, a
remarkable idealistic and democratic impulse with significant popular support led to the
unification of the country. Yet, a number of uprisings, two wars of independence against
Austria (1848–9 and 1859, the latter of which was fought with crucial help by France),
and intense diplomatic activity, were still necessary to achieve this goal.
Some of the mathematicians whom we shall shortly present, who will figure
prominently in this prologue, participated in the military mobilisation for these wars of
independence, particularly in the years 1848 to 18591. Enrico Betti was a volunteer in a
student battalion from the University of Pisa. In 1848, Luigi Cremona participated in the
defence of Venice, which had rebelled against Austrian rule and was given the rank of
corporal and later that of sergeant. Francesco Brioschi participated in 1848 in the insur-
rection of Milan against the Austrians and in 1870 in the storming of Rome.
In 1860 the peninsula had not yet been completely unified. The Veneto region (in the
north-east of Italy) was still under the sway of Austria. It would only be annexed to the new
Italian state after the third war of independence (1866). In particular, Rome was still ruled
by the papacy. In this case, public, political and diplomatic issues were of much greater
complexity. It would only be in 1870 that the Italian government could overcome the tem-
poral power of the papacy. On this occasion it exploited the opportunities offered by the
difficulties faced by the Vatican’s erstwhile ally, France, in the aftermath of the Franco-
Prussian war, the fall of Napoleon III and the end of the Second Empire. The annexation of
Rome by the Italian state would usher in a long period of difficulties in its relationship with
1 As for the commitment of Italian mathematicians during the Risorgimento, see: Universitari Italiani
nel Risorgimento(ed. by L. Pepe), Bologna, CLUEB, 2002.
