Table Of ContentMathematicians in Bologna 1861–1960
The old “Aula Magna” of the University of Bologna and the reading room of the University
Library.PhotographcourtesyoftheHistoricalArchiveoftheUniversityofBologna,AlmaMater
Studiorum.
Salvatore Coen
Editor
Mathematicians in Bologna
1861–1960
Editor
SalvatoreCoen
DipartimentodiMatematica
UniversitàdiBologna
Bologna
Italy
ISBN978-3-0348-0226-0 e-ISBN978-3-0348-0227-7
DOI10.1007/978-3-0348-0227-7
SpringerBaselDordrechtHeidelbergLondonNewYork
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(cid:2)c SpringerBaselAG2012
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A Short Overview on Mathematicians in
Bologna in the First Century after the
Establishment of Italy
SalvatoreCoen
The present volume considers the lives and achievementsof mathematicians who
studied and worked in various roles at the Bologna University in the century
following Italian unification. Most contributions to this volume are historical in
character;thefewwhichmorecloselyfocusonmathematicalresearchdosostrictly
inrelationtoadiscussionofthemathematiciansconcerned.
Without claiming to be exhaustive, the volume deals with many of the most
representative mathematicians who worked in Bologna in the period 1860-1960,
namely with Luigi Cremona (b. 1830), Eugenio Beltrami (b. 1836), Salvatore
Pincherle (b. 1853), Pietro Burgatti (1868), Federigo Enriques (b. 1871), Ugo
Amaldi(b.1875),BeppoLevi(b.1875),GiuseppeVitali(b.1875),EnricoBompiani
(b.1889),BeniaminoSegre(b.1903),TullioViola(b.1904),DarioGraffi(b.1905),
Gianfranco Cimmino (b. 1908) Bruno Pini (b. 1918) and Lamberto Cattabriga (b.
1930). Sometimes the same mathematician is presented from different points of
view by different authors. The work of a number of other mathematicians also
comes in for perusal, most notably the contributions made by Giulio Vivanti (b.
1859),EttoreBortolotti(b.1866)andFilippoSibirani(b.1880).
The University of Bologna is one of the oldest universities in the world
(indeed, it is traditionally said to have been founded in 1088) and many well-
knownmathematicianshavestudiedandtaughtthere.We mayrecallLucaPacioli,
DomenicoMariaNovara,ScipionedelFerro,GirolamoCardano,LudovicoFerrari,
Rafael Bombelli, Bonaventura Cavalieri, Pietro Mengoli, Giandomenico Cassini,
DomenicoGuglielminiandGabrieleManfredi,tomentionjustafew.Itis,however,
hardtocomeupwithacorrespondinglistforthefirsthalfofthenineteenthcentury,a
darkanddifficultperiodformathematicsinBologna,althoughstudiesofastronomy
andhydraulicscontinueddevelopingalongtraditionallines.
InordertoovercomethelocalweaknessofmathematicalresearchatBologna,in
1860,soonafterBolognabecamepartoftheKingdomofSardinia(bytheplebiscite
ofMarch 1860),the Ministerof EducationappointedLuigiCremonaas Professor
of Higher Geometry and Matteo Fiorini (b. 1827) as Professor of Geodesy. The
presence of Luigi Cremona and Eugenio Beltrami (starting from 1862) brought
v
vi SalvatoreCoen
about a dramatic improvementin the state of mathematical studies and education
attheuniversity.Unfortunately,theybothlefttheuniversityafewyearsaftertheir
nominationsothatmathematicalstudiesatBolognawentthroughanewperiodof
difficultyasfaraspuremathematicswasconcerned.Startingfrom1880,however,
a new generation of mathematicians revitalized the study of mathematics at the
university; they attracted colleagues of high quality and the number of students
in pure mathematics grew year after year. About forty years later, the founding
of the Unione Matematica Italiana (UMI), which has since continued to maintain
itsheadquartersattheUniversityofBologna,thelaunchingofthe Bollettinodell’
Unione Matematica Italiana by Salvatore Pincherle and his election as President
of the IMU in 1924 were a sign of the new improved standing of mathematics
in Bologna, while the holding of the International Congress of Mathematicians
in Bologna in 1928 testified to the international recognition that the school had
acquired.
Startingfromthetwenties,however,theeffectofthecentralgovernmentpolicy
on the university was already becoming evident. The so-called Gentile reform of
educationembodiedachangedconceptionoftheuniversity’sdutiesandobjectives.
Universitiesbecamemoreandmoreauthoritarian;Jewishuniversityprofessorswere
sacked as a result of the Race Laws of 1938. At Bologna two professors in the
College of Engineering(Facoltà di Ingegneria),Giulio Supino and Emanuele Foà
losttheirposts.Atthattime,in1938,therewerefourprofessorsofmathematicsin
theSchoolofScience(FacoltàdiScienzeMM.FF.NN)atBolognaUniversity:Pietro
Burgatti, Luigi Fantappiè, Beppo Levi, Beniamino Segre. Pietro Burgatti died in
May;SegreandLeviweredismissedandFantappièwasworkingabroad.Forafew
monthstheSchoolofSciencehadnoactiveprofessorofMathematicsinBologna.
So,onceagain,mathematicsinBolognahadtofacedifficulttimeswhichprofoundly
affectedthedirectionandnatureoftheresearchthatwascarriedout.
Thisbookisabouttheprotagonistsofthisarduousandeventfulstorywithallits
highsandlows.
What follows are some selected sources for general information about mathe-
maticalstudiesatBologna(ofcourse,manyotherinterestingpaperswerewrittenon
particularmathematicians).Reference[1]isabeautifulbookletbyEttoreBortolotti,
distributedtotheparticipantsatthe1928InternationalCongressofMathematicians
held in Bologna; [2] is a revised and 1947 updated version of [1]. For a short
introductiontothehistoryofMathematicsinBologna,see[3].
The proceedings of the international conference held on the occasion of the
IX centennial of the University of Bologna are published in [4]: the volume
containsmorethanthirtycontributionsinspiredbyresearchcarriedoutinBologna.
Reference[5]dealswithteachingofmathematicsatBolognafrom1860to1940.
Foramorein-depthstudyoftheperiod1860-1960,lateronwelistvolumesof
collectedworksbymathematicianswhoworkedinBolognaduringthoseyears.
AShortOverviewonMathematiciansinBologna vii
LIST OF VOLUMES OF SELECTED WORKS OF MATHEMATICIANSWHO
HAVE WORKED IN BOLOGNA IN THE FIRST CENTURY AFTER THE
ESTABLISHMENTOFTHEKINGDOMITALY.
Arzelà,C.1992.Opere,editedbyUnioneMatematicaItaliana,I,XXXIX+348;II,
VII+357.Bologna:Cremonese
Beltrami,E.1902-1920.OperematematichediEugenioBeltrami,editedbyUniver-
sityofRomeScienceFaculty,Tomoprimo(1902),VII+437;Tomosecondo(1904)
465;Tomoterzo(1911),488;Tomoquarto(1920),554.Milano:UlricoHoepli
Bompiani, E. 1978. Opere scelte, edited by Unione Matematica Italiana and
published with the support of the Consiglio Nazionale delle Ricerche, I, 404; II,
468;III,436.Bologna:UnioneMatematicaItaliana
Burgatti, M. 1951. Opere scelte (published under the auspices of the universities
of Bologna and Ferrara, the Accademia delle Scienze di Bologna and the Unione
MatematicaItaliana),VI+354.Bologna:Zanichelli
Cimmino,G.2002.OpereScelte(publishedbyAccademiadelleScienzeFisichee
MatematichedellaSocietàNazionalediScienzeLettereeArtiinNapoli),Giannini,
Napoli,XV+668.
Cremona, L. 1914–1917. Opere matematiche di Luigi Cremona, published under
the auspices of the R. Accademia dei Lincei, Tomo primo (1914), con note dei
revisori, VII+492, Tomo secondo (1915), con note dei revisori, 459, Tomo terzo
(1917),connotedeirevisori,connotiziedellaopereedellavitadell’autoreecon
indiceanaliticopermaterie,520.Milano:UlricoHoepli
Donati, L. 1925. Memorie e note scientifiche: elasticità, vettori, elettrologia,
correntialternative,argomentivari,XIII+350.Bologna:Zanichelli
Enriques, F. 1956-1966. Memorie scelte di Geometria, edited by the Accademia
NazionaledeiLincei,VolumeI(1956),1893-1898,XXII+541;VolumeII,(1959)
1899-1910,527;VolumeIII,(1966),1911-1940,VII+456.Bologna:Zanichelli
Fantappiè, L. 1973. Opere scelte, edited and published by Unione Matematica
ItalianawiththesupportoftheConsiglioNazionaledelleRicerche,I,646;II,420.
Bologna:UnioneMatematicaItaliana
Graffi, D. 1999. Opere scelte, edited and published by Consiglio Scientifico del
G.N.F.M.,XXXI+458.Roma:GruppoNazionaleperlaFisicaMatematica
Levi, B. 1999. Opere 1897–1926, edited by Unione Matematica Italiana and
published with the support of the Consiglio Nazionale delle Ricerche, I, il primo
decennio,1897/1906,CXXII+498;II,ilventennio,1907/1926,VIII+434.Roma:
Cremonese
Pincherle,S.1954.Operescelte,editedbyUnioneMatematicaItaliana,I,VI+396;
II,494.Roma:EdizioniCremonese
Segre, B. 1987-2000. Opere scelte, edited by Unione Matematica Italiana and
published with the support of the Consiglio Nazionale delle Ricerche, I (1987),
periodo 1923-1937, LI+420; II (1987) periodo 1937-1970 ,VIII+ 44; III (2000),
460.Bologna:Cremonese
Tonelli, L. 1960-1963. Opere scelte, edited by Unione Matematica Italiana and
published with the support of the Consiglio Nazionale delle Ricerche, Volume I
viii SalvatoreCoen
(1960), Funzioni di variabile reale, VI + 604; Volume II (1961), Calcolo delle
Variazioni1911–1924,VI+534;VolumeIII(1962),CalcolodelleVariazioni1926–
1950,508;VolumeIV(1963),Argomentivari,VI+330.Roma:Cremonese
Vitali,G.1984.Operesull’analisirealeecomplessa.Carteggio,editedbyUnione
MatematicaItalianaandpublishedwiththesupportoftheConsiglioNazionaledelle
Ricerche,XII+524.Roma:Cremonese
Acknowledgments
The presentvolume has been prepared on occasion of the nineteenth Congressof
theUnioneMatematicaItaliana(UMI),heldattheUniversityofBolognafromthe
12th to the 17th of September, 2011. We thank the University of Bologna and
the Carisbo Foundation for their support and the Organizing Committee of the
Congress.AppreciationalsogoestoCristinaChersoniandChiaraCocchiarchivists
ofthehistoricalarchivalsoftheUniversityofBologna,fortheirskillandpatiencein
myregard.Finally,specialrecognitiongoestoClaudiaBenedettiforhercompetence
anddedicationinthepreparationofthiswork.
References
1.Bortolotti, Ettore. 1928. L’ école mathématique de Bologne. Aperçu historique. Congrès
internationaldesMathématiciens,Bologna,75:N.Zanichelli
2.Bortolotti,Ettore.1947.LastoriadellamatematicanellauniversitàdiBologna,Bologna,226:
NicolaZanichelli
3.Coen, Salvatore. 1991. Preface. In Geometry and Complex Variables: Proceedings of an
internationalMeetingontheOccasionoftheIXCentennialoftheUniversityofBologna.Lecture
NotesinPureandAppliedMathematics,132,iii–vii.Dekker
4.Coen,Salvatore.(ed.).1991.GeometryandComplexVariables:Proceedingsofaninternational
MeetingontheOccasionoftheIXCentennialoftheUniversityofBologna.LectureNotesin
PureandAppliedMathematics,132,494.Dekker
5.Francesconi, Stefano. 1991. L’insegnamento dellaMatematicanell’Università diBolognadal
1860al1940.InGeometryandComplexVariables: Proceedings ofaninternationalMeeting
ontheOccasionoftheIXCentennialoftheUniversityofBologna.LectureNotesinPureand
AppliedMathematics,132,415–474.Dekker
DipartimentodiMatematica SalvatoreCoen
UniversitàdiBologna
AlmaMaterStudiorum
[email protected]
Contents
AShortOverviewonMathematiciansinBolognaintheFirst
CenturyaftertheEstablishmentofItaly...................................... v
SalvatoreCoen
Beltrami’sModelsofNon-EuclideanGeometry.............................. 1
NicolaArcozzi
GiuseppeVitali:RealandComplexAnalysis
andDifferentialGeometry...................................................... 31
MariaTeresaBorgato
Pincherle’sEarlyContributionstoComplexAnalysis....................... 57
UmbertoBottazzini
LuigiCremona’sYearsinBologna:FromResearchtoSocial
Commitment...................................................................... 73
AldoBrigagliaandSimonettaDiSieno
FederigoEnriques:TheFirstYearsinBologna .............................. 105
CiroCilibertoandPaolaGario
EnricoBompiani:TheYearsinBologna ...................................... 143
CiroCilibertoandEmmaSallentDelColombo
DarioGraffiinaComplexHistoricalPeriod.................................. 179
MauroFabrizio
PietroBurgattiandHisStudiesonMechanics................................ 197
PaoloFregugliaandSandroGraffi
Federigo Enriques (1871–1946) and the Training of
MathematicsTeachersinItaly.................................................. 209
LiviaGiacardi
BeppoLeviandQuantumMechanics.......................................... 277
SandroGraffi
ix
