Table Of Content4VG H e r i t a g e o f E u r o p e a n M a t h e m a t i c s
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ISBN 978-3-03719-199-6
www.ems-ph.org
Jaëck et al. | Heritage | RB 31 mm
Heritage of European Mathematics
Advisory Board
Ciro Ciliberto, Roma
Ildar A. Ibragimov, St. Petersburg
Władysław Narkiewicz, Wroclaw
Peter M. Neumann, Oxford
Samuel J. Patterson, Göttingen
Previously published
Andrzej Schinzel, Selecta,
Volume I: Diophantine Problems and Polynomials;
Volume II: Elementary, Analytic and Geometric Number Theory,
Henryk Iwaniec, Władysław Narkiewicz, and Jerzy Urbanowicz (Eds.)
Thomas Harriot’s Doctrine of Triangular Numbers: the ‘Magisteria Magna’,
Janet Beery and Jacqueline Stedall (Eds.)
Hans Freudenthal, Selecta, Tony A. Springer and Dirk van Dalen (Eds.)
Nikolai I. Lobachevsky, Pangeometry, Athanase Papadopoulos (Transl. and Ed.)
Jacqueline Stedall, From Cardano’s great art to Lagrange’s reflections: filling
a gap in the history of algebra
Peter M. Neumann, The mathematical writings of Évariste Galois
Peter Roquette, Contributions to the History of Number Theory in the 20th
Century
Jacques Tits, Œuvres – Collected Works, Volumes I–IV, Francis Buekenhout,
Bernhard Mühlherr, Jean-Pierre Tignol and Hendrik Van Maldeghem (Eds.)
Della Dumbaugh and Joachim Schwermer, Emil Artin and Beyond – Class
Field Theory and L-Functions
Martina Becˇváˇrová and Ivan Netuka, Karl Löwner and His Student Lipman
Bers – Pre-war Prague Mathematicians
Henri-Paul de Saint-Gervais, Uniformization of Riemann Surfaces.
Revisiting a hundred-year-old theorem
Gösta Mittag-Leffler and
Vito Volterra
40 Years of Correspondence
Edited by
Frédéric Jaëck
Laurent Mazliak
Emma Sallent Del Colombo
Rossana Tazzioli
Editors:
Frédéric Jaëck Laurent Mazliak
Département de Mathématiques et Applications Sorbonne Université LPSM
École Normale Supérieure Case courrier 188, 4 place Jussieu
45 Rue d’Ulm 75252 Paris CEDEX 05
75230 Paris CEDEX 05 France
France
[email protected]
[email protected]
Rossana Tazzioli
Emma Sallent Del Colombo Département de Mathématiques
Independent researcher Université de Lille
Carrer de València 69 Cité Scientifique, Avenue Gauss
08015 Barcelona 59655 Villeneuve-d’Ascq CEDEX
Spain France
[email protected] [email protected]
2010 Mathematics Subject Classification (primary; secondary): 01-XX
Key words: Mittag-Leffler, Volterra, correspondence, mathematics, history of mathematics
ISBN 978-3-03719-199-6
The Swiss National Library lists this publication in The Swiss Book, the Swiss national bibliography,
and the detailed bibliographic data are available on the Internet at http://www.helveticat.ch.
This work is subject to copyright. All rights are reserved, whether the whole or part of the material
is concerned, specifically the rights of translation, reprinting, re-use of illustrations, recitation, broad-
casting, reproduction on microfilms or in other ways, and storage in data banks. For any kind of use
permission of the copyright owner must be obtained.
© 2019 European Mathematical Society
Contact address:
European Mathematical Society Publishing House
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Germany
Homepage: www.ems-ph.org
Typeset using the editors’ TEX files: Nicole Bloye, Cardiff, UK
Printing and binding: Beltz Bad Langensalza GmbH, Bad Langensalza, Germany
∞ Printed on acid free paper
9 8 7 6 5 4 3 2 1
Preface
It is a great pleasure to see the current volume on the correspondence between Gösta
Mittag-Leffler and Vito Volterra published by the European Mathematical Society. The
exchangeofideasbetweenthetwoandtheircommonpassionformathematicscertainly
helpedMittag-Lefflerformhisvisionoftheresearchinstitutethathefoundedbydonating
his magnificent villa with its library to the Royal Swedish Academy of Sciences, to
transform it into a center dedicated to mathematical research. The villa is located in
beautifulDjursholmincloseproximitytoStockholmwheretheinstitute,whichisinfact
theoldestmathematicsresearchcenterintheworld,stilloperatestoday.
FollowingtheideasandwishesofGöstaMittag-Leffler,theinstituteisaninternational
meetingplaceforresearchandpostdoctoraltraininginthemathematicalsciences. Itfound
itscurrentformin1969underthevisionaryleadershipofLennartCarleson. Itisrununder
theauspicesoftheRoyalSwedishAcademyofSciencesandisgovernedbyaboardwith
representativesfromallNordiccountries. Itwelcomesvisitorsallyearforshortorlonger
stays.
Thepremisesoftheinstituteencompassseveralbuildings: themainbuildingincluding
alibrary,officeanddiscussionspacesforresearchersandstaff,aseminarroombuilding,
and five other buildings with housing facilities for visiting researchers. The mission of
InstitutMittag-Leffleristosupportinternationaltop-levelresearchinmathematics,with
special attention to the development in the Nordic countries. The institute is a hub for
theinternationalmathematicalresearchcommunityandformathematiciansintheNordic
countries.
Themainactivitiesincluderesearchprograms,conferences,workshops,seminarsand
summer schools, which all aim to conduct and develop current mathematical research.
The institute also publishes two mathematical journals, Acta Mathematica (founded by
Mittag-Leffler in 1882) and Arkiv för matematik (founded in 1903), all volumes of both
journalsbeingfreelyavailableonline. Inthiswaytheinstituteoperatestothisdayinthe
spiritofitsfounder. Itdevelopsmathematicsthroughinteractionsandmeetingsbetween
mathematicians from all over the world and offers a research environment where new
mathematicalideasareborn,discussed,andtestedbyworldleadingresearchers.
ItisremarkabletonotethatmanysubjectsoftheexchangebetweenMittag-Lefflerand
hisItaliancolleague—forexamplemathematicalphysicsandpartialdifferentialequations
as well as various aspects of Analysis — are connected to important research areas still
well represented at the institute, for example with recent programs in Fractal Geometry
andDynamics(2016)andSpectralMethodsinMathematicalPhysics(2019).
vi
The present book gives unique and direct access to the line of thought of two
mathematiciansthatinmanyways, acenturyago, helpedshapethemathematicalworld
of today. A particularly useful aspect is the exposition of ‘mathematics in the raw’. In
the letters, and the accompanying contextual introduction that analyzes their contents,
we meet profound ideas and problems studied directly, without formal definitions and
established methods (that were eventually formulated only later). Altogether, this set of
lettersdeepensourunderstandingbothofmathematicsasasubjectandoftheintellectual
environmentoutofwhichInstitutMittag-Lefflerwasborn.
TobiasEkholm
DirectorInstitutMittag-Leffler
Acknowledgments
Many people contributed to the realization of this work in different contexts and ways,
and we would like to express our gratitude to them. We are grateful to first mention
the two main institutions, which allowed us to publish the present correspondence —
the Accademia dei Lincei in Rome and the Mittag-Leffler Institute in Djursholm near
Stockholm. Moreover,theInstitutewelcomedusfortwoperiodsofstudyintheSummers
2017 and 2018 in order to complete the book, and we were thus able to take advantage
of the exceptional working conditions it provides to its visitors. We want especially to
warmlythankMikaelRågstedt,thelibrarianoftheInstitute,whohasfacilitatedourstay
attheInstituteinallpossibleways. WeexpressourthankstotheNobelFoundation,the
KungligaBibliothekofStockholm, andtheArchiviodellaScuolaNormaleSuperiorein
Pisaforprovidinguswithdocumentsandletters,andtotheVolterrafamilyforpermission
to publish some photographs of their property. We thank our colleagues Ciro Ciliberto
andManfredKarbefortheirlongstandinginterestintheproject. Ofcourse, thesupport
of the European Mathematical Society and its proposal to welcome the book among
its publications were essential to encourage us to lead the project to the end. Thomas
Hintermann, who oversees the policy of the European Mathematical Society Publishing
House, has been always efficient and responsive, and it is a great pleasure for us to
mention his role in this story. It also our pleasure to thank Nicole Bloye for her huge
work in editing the English language. We want also to mention the help provided by
HansEllegren,AlessandraFiocca,ÅseFrid,andJesperLützeninvariousways. Lastbut
notleast,wemustexpressourmostheartfeltgratitudetoourcolleagueandfriendPietro
Nastasiwhohadbeenyearsagotheinitiatorofthisenterprise,towhichhedevolvedgreat
enthusiasm and energy. His original drafts gave us a good starting impulse and we are
gladtoassociatehimwiththepresentbook.
Barcelona–Lille–Paris,April2019
FrédéricJaëck,LaurentMazliak,EmmaSallentDelColombo,RossanaTazzioli
Contents
Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . v
Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii
I Introductiontothecorrespondence . . . . . . . . . . . . . . . . . . . . . . . 1
A Presentationofthecorrespondence . . . . . . . . . . . . . . . . . . . . . 3
B GöstaMittag-LefflerbeforehisfirstmeetingwithVolterra . . . . . . . . 4
C ThefirstmeetingbetweenMittag-LefflerandVolterra . . . . . . . . . . . 8
D VolterrainDini’sfootsteps . . . . . . . . . . . . . . . . . . . . . . . . . 9
E FoundationofthejournalActaMathematica . . . . . . . . . . . . . . . . 13
F FromDinitoBetti,1882–1887 . . . . . . . . . . . . . . . . . . . . . . . 16
G Functionalanalysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
H Thesecondmeeting. Guccia’sroleandVolterra’sinternationaldébuts . . 20
I 1888–1902: Abel’smanuscripts . . . . . . . . . . . . . . . . . . . . . . 26
J 1891: SonyaKovalevskaya’serror . . . . . . . . . . . . . . . . . . . . . 28
K 1896: Inversionofintegrals . . . . . . . . . . . . . . . . . . . . . . . . . 31
L 1898: Mittag-Leffler’sstaranditsprehistory . . . . . . . . . . . . . . . . 36
M Mittag-Leffler’sengagementfortheNobelPrizeinPhysics . . . . . . . . 40
N 1906: Volterra’slecturesinStockholm . . . . . . . . . . . . . . . . . . . 44
O 1910: Integro-differentialequations . . . . . . . . . . . . . . . . . . . . 46
P WorldWarIanditsconsequences,1914–1920 . . . . . . . . . . . . . . . 55
II Letters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 401
Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 423
