Cultivating Mathematics in an International Space: Roles of Gösta Mittag-Leffler in the Development and Internationalization of Mathematics in Sweden and Beyond, 1880 – 1920 by Laura E. Turner B.Sc., Acadia University, 2005 M.Sc., Simon Fraser University, 2007 a thesis submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy (Ph.D.) in the Department of Science Studies c Laura E. Turner 2011 AARHUS UNIVERSITET October 2011 All rights reserved. This work may not be reproduced in whole or in part, by photocopy or other means, without permission of the author, except for scholarly or other non-commercial use for which no further copyright permission need be requested. Abstract This thesis aims to investigate several areas of mathematical activity undertaken by the Swedish mathematician Gösta Mittag-Leffler (1846–1927). These not only markedly impacted the de- velopment of mathematics in Stockholm, where they were centred, but transformed, by virtue of their roots in both nationalist and internationalist movements, the landscape of mathemat- ics across Scandinavia and Europe more broadly. These activities are Mittag-Leffler’s role in cultivating research activity from his students at Stockholms Högskola as the first professor of mathematics there (1881–1911); his establishment (1882) and development of Acta Mathematica, an “international” journal that could bring Sweden onto the scene as an arbiter of mathematical talent and establish the nation as a major locus of mathematical activity; and his attempts to establish a broader Scandinavian mathematical community through the foundation of the Scan- dinavian Congress of Mathematicians (1909) according to a belief that cultural solidarity would both enrich each country involved and afford a united group more clout than could be gained by each of the small nations alone. By analyzing Mittag-Leffler’s strategies and tactics in these connections, and by carefully considering exactly what he sought to achieve and how, this thesis aims to shed new light on the ways in which an ambitious man could seize opportunities presented by the precise infrastructural, cultural, social, and political configuration of mathematics in Sweden and Europe more broadly during the late 19th and early 20th centuries, not only to influence the development of mathematics in his own country but also to alter the image of the country from one of a peripheral player to one that was accepted among the major mathematical power as serious and important. Two central features of this investigation which frame several discussions are Mittag-Leffler’s own ideas concerning what constituted a “contribution” to the development of mathematics, and a discussion of the important attributes of what I describe as the “international space” of mathematics which emerged during this period. iii iv Acknowledgments This project has benefited greatly from the help and guidance of my supervisors, Kirsti Andersen, Henrik Kragh Sørensen, and Tom Archibald. Matthias Heymann, an additional supervisor, deserves thanks as well, as do Catherine Goldstein and Frédéric Brechenmacher for their helpful comments and suggestions. I would also like to express gratitude to my colleagues at the Centre for Science Studies at Aarhus University for creating an enjoyable and productive working environment, and to my family and friends, and in particular Kristian Hegelund, for their continuous support and encouragement. Finally, I am very grateful to SSHRC (Social Sciences and Humanities Research Council of Canada) for support in connection with this project; to June Barrow-Green, Umberto Bottazzini, and Jeremy Gray for sharing yet-unpublished works of which I have made use in this project; and the helpful staff at the Institut Mittag-Leffler in Djursholm, Sweden, and in particular Mikael Rågstedt for his assistance in navigating the archives and for his kindness in scanning certain documents which I had missed. Laura Turner, October 2011 v vi Contents Abstract . iii Acknowledgments . v Table of Contents . vii List of Tables . ix List of Figures . xi 1 Introduction . 1 1.1 Survey of Relevant Literature . 4 1.2 Research Questions and Methodology . 12 1.3 On the Notion of an “International Space” . 16 2 Mathematics in Sweden . 20 3 A Biographical Discussion . 40 4 Establishing Sweden as a “Contributor” . 59 4.1 On the Notions of “Contribution” and “Validation” . 62 4.2 Images and Identities of Mathematics . 65 4.3 Mittag-Leffler’s Images of Paris and Berlin . 67 4.4 Constructing Sweden as Mathematically Peripheral . 75 5 Mittag-Leffler at Stockholms Högskola ........................ 88 5.1 On the Notion of a “Mission” . 91 5.2 On Mittag-Leffler’s Students . 94 5.3 The Origin and Development of Mittag-Leffler’s Mission . 100 5.4 Structuring Study . 103 5.5 Mittag-Leffler’s Establishment of the Research Imperative . 111 5.6 Phragmén’s Time in England . 124 5.7 On the Question of a Mittag-Leffler “School” . 129 5.8 Connection to Mittag-Leffler’s 1904 Aims . 131 6 Roles of an International Journal . 139 6.1 Analysis of Articles by Nationality and Subject . 143 6.2 Roles of Acta Mathematica in Sweden . 146 vii 6.3 The Situation of Mathematics in Italy . 150 6.4 Italian Mathematicians as a Community of Scholars . 153 6.5 Italian Publications in Acta Mathematica: Three Examples . 155 6.6 Analysis of Italian Use of Acta Mathematica . 162 6.7 Roles of Acta Mathematica in Italy . 174 6.8 Mittag-Leffler on the Importance of International Journals . 190 6.9 Rhetorics and Contrasting Notions of “International” . 199 6.10 Findings and Potential for Generalization . 213 7 Mittag-Leffler and the SCM . 218 7.1 Bridging the Local and the “Universal” . 219 7.2 From National to Transnational Mathematics in Scandinavia . 222 7.3 Consolidation of the SCM . 228 7.4 Delineation: Establishing the Borders of the SCM . 235 7.5 International Relations . 238 7.6 Relations to National Contexts . 240 7.7 Mathematics and Mathematicians in the Public Space . 244 8 Concluding Remarks . 249 Appendices A Danish Newspaper Article of 1911 . 257 B 1894 Memorandum . 259 Bibliography . 263 viii List of Tables 6.1 Division of articles in Acta Mathematica by subject during Mittag-Leffler’s pe- riod as editor. Classifications by field are taken from the annual volumes of the Jahrbuch über die Fortschritte der Mathematik, with the leftmost column in En- glish representing my own construction, intended for organizational purposes. 146 6.2 Division of articles in Acta Mathematica in topics in analysis during Mittag- Leffler’s period as editor. Classifications are taken from the annual volumes of the Jahrbuch über die Fortschritte der Mathematik. 147 6.3 Article division for Acta Mathematica by country, based on numbers of articles and authors, 1882–1927. 148 6.4 Articles and Jahrbuch subject classifications of works published in Acta Mathe- matica by Italian mathematicians during Mittag-Leffler’s term as editor. 168 6.5 Average length of articles appearing in Acta Mathematica by Italian mathemati- cians during Mittag-Leffler’s term as editor. 169 ix x List of Figures 2.1 “The Barbarians enter the Forum” . 27 2.2 “Vision of the future” . 28 3.1 “Our famous mathematical guest” . 44 4.1 “Relative Standing of Mathematical Centers of Europe” . 81 5.1 “Autumn lectures at Stockholms Högskola in 1892” . 138 6.1 Mathematics and War in Swedish Newspapers . 195 7.1 Telegram from Danish Participants Following 1909 Scandinavian Congress of Mathematicians . 227 A.1 “A conversation with the renowned professor” . 258 B.1 1894 Memorandum . 262 xi xii Chapter 1 Introduction The Swedish mathematician Gösta Mittag-Leffler (1846–1927), who represents the first profes- sor of mathematics at Stockholms Högskola, the founder of Acta Mathematica, the first so-called “international” journal of mathematics, and the creator of the Institut Mittag-Leffler for the pro- motion of (Scandinavian) research in pure mathematics, is widely understood as an important figure in the development of mathematics in the late 19th and early 20th centuries. This is both implicit in the appearance of his name and discussions of his activities in a multitude of works on the history of analysis and the internationalization and professionalization of mathematics,1 and also explicit, for instance, in references to Mittag-Leffler as a “prominent individual” who played “decisive and influential roles in the formation of an international community of math- ematics” (see Parshall & Rice 2002b, p. 10) and grandiose depictions of Mittag-Leffler as the “father of Swedish mathematics” whose tenure at Stockholms Högskola marked a “golden age” for mathematics in Sweden (see Gårding 1994, pp. 83, 109). While we understand a great deal about certain aspects of Mittag-Leffler’s mathematical activity, however, many facets of his career remain unexplored. In particular, while (Gårding 1994), (Domar 1978) and (Elfving 1981) describe certain early works of his Swedish and Finnish students, respectively, and (Heinonen 2006) discusses his efforts to ensure academic freedom at Stockholms Högskola, little attention has been devoted to his roles in the shaping of his local research communities and in the development of his students at the University of Helsinki and then Stockholms Högskola as research mathematicians. Similarly, while (Barrow-Green 2002) discusses the foundation and early years of Mittag-Leffler’s operation of Acta Mathematica, little scholarly effort has been devoted to investigating the ways in which the existence of an international journal impacted entire schools, communities, or networks of individuals or texts, 1Among them: (Stubhaug 2010; Barrow-Green 2002, 1996, 2010; Bottazzini 1986, 2003; Bottazzini & Gray forthcoming; Brigaglia 2002, 1993; Cooke 1984; Crawford 1984; Dauben 1979, 1980; Hermite 1984, 1985; Elfving 1981; Ferreirós 1995; Goodstein 2007; Gårding 1994; Heinonen 2006; Lehto 1998; Poincaré & Mittag-Leffler 1999; Nabonnand 1999; Siegmund-Schultze 2001; Stubhaug 2000; Sørensen 2006a,c; Nastasi & Tazzioli 2005; Turner 2007). 1 2 CHAPTER 1.