1 Introduction

L’Enseignement mathématique (EM hereafter) was founded in 1899 by two mathematicians, the Frenchman Charles-Ange Laisant (1841–1920), then sixty years old, a “répétiteur” (trainer) and “examinateur d’admission” (member of the admissions committee) at the École polytechnique, and a young Swiss privat-docent from Geneva University, Henri Fehr (1870–1954). Both had the very ambitious goal of establishing an Internationale of mathematical educators, making their journal an instrument of universal scientific progress and of collaborative solidarity among men dedicated to mathematical education.

This ambition took shape within the context of the new dynamics of mathematical internationalism at the very end of the nineteenth century and at the first International Congress of Mathematicians (ICM) held in Zurich in 1897, which Laisant helped establish. This international editorial project, which was the third such project launched in the field of mathematics at the end of the nineteenth century, following that of Mittag-Leffler and his journal Acta Mathematica (1882), and Guccia and his Rendiconti del Circolo matematico di Palermo (1888), had some unique features. These features were specific to the journal’s purpose: Laisant and Fehr felt that there was an urgent need at the time to improve mathematical education in every country, and that such improvements could not happen without confronting national situations and debates at an international scale. The journal was also intended to reach a specific readership: the two mathematicians decided to create their journal in order to provide all mathematics teachers in the world with a place to learn, publish, and disseminate information about what was happening in the various places where they lived. Laisant (Fig. 1) and Fehr (Fig. 2) thought that this would help this specific sector of the field of mathematics join the new era of internationalization that mathematicians themselves had already entered. Finally, the project was unique unique in its physical organization as it was co-directed and co-edited from both Paris and Geneva.

Fig. 1
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Charles-Ange Laisant (1880s). Public domain

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Fig. 2
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Henri Fehr (1920s). Public domain

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All of the journal’s sections, as presented in Laisant and Fehr (1899), reflected this internationalist ambition. The “articles généraux” and the “études pédagogiques” were intended to present the structure of mathematical education and current ideas on pedagogy in different countries. The “Chronique” section reported on local or international events in the world of mathematics and teaching, as well as on school programs and examinations. The “Bibliography section”, which was composed of book reviews and a “Bibliography Bulletin”, included announcements or summaries of the greatest possible number of publications, periodicals or otherwise, that were of interest to mathematics educators and had been brought to the attention of the directors.Footnote 1

In 1908 EM acquired an additional identity. An International Commission for Mathematical Instruction (CIEM) was created at the ICM held in Rome: Henri Fehr was appointed General Secretary of the Commission, Felix Klein was appointed president, and EM became its official journal. This relationship was beneficial for both the journal and the Commission. Both directors of EM, who had also played key roles in earlier ICMs, particularly in sessions devoted to education, saw this step as validation of their sustained efforts to promote international cooperation in the world of mathematical education. As for the Commission, partnering with the journal gave it a regular forum for communicating with a readership of mathematical educators. Beginning in 1908, the EM regularly dedicated a portion of its Chronique section to the CIEM, in which it published official documents, records of meetings, reports on the work of the national sub-commissions, materials related to the CIEM survey, and so on.Footnote 2

In this paper we will focus on what studying the issues of EM published from before World War I to the end of the 1920s reveals about the new realities of the world of mathematics in the aftermath of the war. In the first part, we will explore the extent to which internationalist ambitions—which the journal propagated—were preserved or transformed in the face of World War I, and their reconfiguration once the war was over. In the second part, we will seek to identify, as far as possible, new individuals and organizations, as well as new geographical territories, that arose in the world of mathematics in the 1920s, by studying EM.

To achieve this, we have chosen to focus on two sections of the journal that provide specific insight into the internationalist aspects of EM and the different mathematical environments in which they developed. The first section is the Bulletin bibliographique (bibliographic bulletin), which was included in each bimonthly issue and was dedicated to announcements and brief analyses of periodicals. The directors highlighted this issue, announcing from the very start that they wished to “give special attention to this part of [their] programme so that teachers would be kept as fully informed as possible of what may be of interest to them” (Laisant and Fehr 1904).Footnote 3 The Bulletin reflected the implementation of the directors’ internationalist editorial plan based on their personal viewpoints and their efforts to create a single source of mathematical and educational news, which was often dispersed throughout local periodicals.

We will also focus on the Chronique, which was devoted to the CIEM. This section reported on initiatives developed by the CIEM, within its Central Committee or its different national sub-commissions.Footnote 4 These were therefore “institutional” pages which, in a way, because of their association with a specific institution, did not come under the personal responsibility or initiative of either of EM’s two directors. The internationalism evident in this section was therefore reflective of that present at the national level, at a quite different scale than that seen in the Bulletin bibliographique.

2 International Configuration of the Pre-war Mathematical World as Depicted in L’Enseignement Mathématique

2.1 Laisant and Fehr: Building an Internationale of Mathematical Educators

A “Patronage Committee”, listed on the covers of various EM issues published between 1899 and 1914, provides the first indication of the geographical configuration of the mathematical Internationale that Laisant and Fehr sought to build at the beginning of the twentieth century. Putting together the most international sponsoring committee possible, and one that included the most famous mathematicians of the time, was one of Laisant and Fehr’s primary concerns when creating the EM, as can be seen from their correspondence.Footnote 5 This committee was composed of twenty mathematicians from fifteen countries, including fourteen European countries and the USA (see Table 1). The “center of gravity” of the international mathematical community that sponsored EM was located in Europe—a rather wide swathe of Europe from West to East and from North to South—though the USA was also part of this community. While some of the names on the Committee list changed between the time of its creation and 1914, due to the death of several of its members, the geographical distribution of the Committee members’ countries of origin remained the same.

Table 1 Territories of the sponsoring committee of L’Enseignement mathématique
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The composition of the committee seems all the more relevant, as many of the participating mathematicians were signatories of the invitation letter to the first International Congress of Mathematicians in Zurich in 1897. It is also noteworthy that most of these mathematicians were, in fact, at the head of various mathematical journals, either as directors or influential members of editorial committees. Fehr and Laisant sought to position their new journal at the heart of the international mathematical editorial space, which was reflected by the Committee’s composition. The list of the patronage committee members—and everything it symbolized about the pre-war mathematical world—disappeared from the covers of EM in 1915.

In addition to the presence of this list on the cover page, we will examine how the internationalist ambitions and efforts of the two directors were reflected in their journal. We will try to understand the outline of the mathematical educational Internationale that they presented to their readers, through the periodicals selected for review in the columns of the Bulletin Bibliographique.

In the last third of the nineteenth century, new bibliographical tools designed to showcase mathematical articles published in periodicals were created, such as, for instance, the Jarhbuch über die Fortschritte der Mathematik or the Répertoire des sciences mathématiques (Rollet and Nabonnand 2002). Nevertheless, reviewing other periodicals was far from being a universal practice for mathematical journals. This was an editorial choice that some mathematical journals made, but that most others did not. EM belonged to the first category, and regularly devoted a specific section to reviewing other periodicals.

Correspondence between the journal’s directors showed how much this editorial practice involved interactions with other journals. Indeed, the periodic publications that were sent to EM were, a priori, those that the journal announced or analyzed. These exchanges between journals were crucial, because journal issues were costly resources that could not go to waste. Because of the high price of some journals (such as the Acta mathematica or the American Journal of MathematicsFootnote 6), this reciprocity, and therefore personal contacts between journal directors, was essential. This was particularly important for EM, as it had made an editorial choice to give an account of the largest number of periodicals possible, but was limited to those sent to the journal’s directors or editors.

In order to draw up a map of the editorial world proposed by EM’s directors before the war, we examined the bibliographic bulletins of the bimonthly issues published from 1910 to 1912.Footnote 7 Fifty-eight periodicals were reviewed more or less regularly in these issues. Among the places of publication of these periodicals, one city dominated: Paris, with 13 periodicals, followed by Leipzig (seven periodicals), Berlin (four periodicals), and Vienna (three periodicals). This mathematical editorial map ultimately featured 27 cities (see Map 1), all of which were located in Europe, apart from six American cities. In terms of countries, at the very beginning of the century the United States joined the leading trio—that is France, Germany, and Italy—in terms of the number of mathematical periodicals published.

The periodicals presented in EM were mainly supported by institutions: learned or professional societies or associations, universities, schools, or administrations.Footnote 8 Almost all of them local in scope and rooted in a specific city, such as those published by universities, schools, or certain learned societies, or a country, such as those published by national learned or professional societies. Taken together, they formed a large part of this periodical editorial landscape, whose international, “universal and confraternal”, dimension was reflected in EM, which presented an overall picture of this mosaic of local dynamics. Similar to the internationalization of mathematical teaching that Laisant and Fehr wished to promote by sharing knowledge of local teaching, the internationalization of the periodical editorial world, as demonstrated by the Bulletin bibliographique, resulted in part from sharing the content of local or national journals.

Map 1
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The 1910–1912 mathematical editorial world as presented by the EM’s ‘Bulletin bibliographique’ Footnote

I would like to thank Jules-Henri Greber, who produced the various maps presented in this chapter. For a complete list of the cities shown on this map, see page 4 of the appendix to my article for Historia Mathematica already quoted.

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2.2 The CIEM as Presented in the EM’s Chronique Section—A Geographical Representation of the Educational Mathematical World?

As mentioned above, in 1908 EM became the official voice of the newly created CIEM. However, this information did not appear on the cover of EM until 1915, seven years after this decision was made at the ICM. Unfortunately, no archival sources are available to document this surprising delay. It is possible that, despite Fehr’s role as the general secretary of the CIEM, Fehr and Laisant preferred to feature the membership of the patronage committee on the journal’s cover, at least until 1915. We will come back to this topic later.

The documents published in the Chronique section of EM from 1908 to 1914 show which countries and individuals (members of the Central Committee as well as delegates of the national sub-commissions approved by their national governments) were involved in carrying out CIEM’s initiatives. The general report from the conference held in Paris in May 1914 lists the country of origin of the more than 160 individuals (members or delegates) who registered for the conference. This report provides a picture of the world of “civilized nations” interested in scientific education.Footnote 10 This world (see Table 2) included 17 countries—15 European countries, plus Egypt and the United States—and the relative numbers of attendees from each of these countries offer some surprises.

Table 2 Territories represented at the CIEM Conference held in Paris in May 1914 (L’Enseignement mathématique, 16 (1914), p. 169)
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While France naturally had the greatest number of participants at this Conference, given that it was held in Paris, it appears that, on the eve of World War I, France, Hungary, Germany, Switzerland, and Russia were the main countries represented at the Paris conference.Footnote 11 However, the attendees at the Paris Conference represented only a subset of the countries associated with the CIEM, whose institutional membership included 28 countries.Footnote 12 Of the eleven countries that were not represented at this conference, four were European (Bulgaria, Greece, Norway, and Portugal). Taking the other member countries of the CIEM into account greatly enlarged the apparently restricted world shown in Table 2. These countries included Argentina, Australia, Brazil, Canada, Cape Colony, Japan, and Mexico. However, this world was not egalitarian, and each nation’s place in the forums and discussions varied depending on their participation in the first ICM congresses.Footnote 13 All non-European countries, except the United States, were only associated nations, and Bulgaria and Serbia shared this second-rank position. Moreover, the work regarding the realities of mathematics education that was carried out in the various member countries under the leadership of the Central CommitteeFootnote 14 paints yet another picture of the level of commitment of the national sub-commissionsFootnote 15: the most active sub-commissions was the German one, followed by the French, the British, and the United States sub-commissions.

3 Internationalist Editorial Practices in EM During and in the Immediate Aftermath of the War

Laisant and Fehr’s preface to the 1913 volume of EM concluded with the following forward-looking statement:

EM will strive to pursue its educational mission, which is a work of both agreement and harmony; for all men, in every country and at every latitude, are directly or indirectly interested in scientific progress, which cannot be separated from progress in teaching. (Laisant and Fehr 1913, 8)

The thunder of war and the immediate post-war period would significantly complicate the ambitions of EM and its two directors. It is therefore important to shed light on their editorial choices at this time, when internationalism was being swept aside. In 1916, Laisant, who was both an anarchist and a pacifist, signed the “Manifeste des seize” written by sixteen French libertarians, which took sides with the Entente against “German aggression”. Fehr, who was a citizen of a neutral nation but also the leader of an international educational association, was also required to face this split in international relations, although in a different way.

3.1 EM Covers: Not in Step with the Times?

A first consequence of the war can be seen on the covers of EM. The cover page of the 1915 volume no longer showed the list of the members of the patronage committee, in which the names of mathematicians from countries now at war appeared side by side. It is not clear if this choice was made by the directors or was the result of a request from some of the mathematicians on the committee. It is well known, for instance, that the Frenchman Émile Picard held extremely harsh nationalist and anti-German views from the very beginning of the war. But Picard was not the only one. In 1915, the Council of the French Mathematical Society decided that “because of the state of war” it would remove individuals “who belong to enemy nations” from its list of members.Footnote 16

However, beginning with the 1915 volume, another international reference replaced the list of the patronage committee members. For the first time, the cover stated (in French) that the journal was the official journal of the International Commission for Mathematical Education (Organe officiel de la Commission internationale de l’enseignement mathématique). This anonymous image of mathematical internationalism must have appeared more acceptable than explicitly listing the names of mathematicians from hostile countries.

This reference to the EM as being the official journal of the CIEM remained on EM covers until 1923, which is rather surprising when one considers that the CIEM was an ICM-related commission. Indeed, in 1918 the Inter-Allied Conference of the Scientific Academies, under Picard’s leadership, decided to form new scientific associations excluding scientists from the Central Empires and to dissolve the old associations. A new international mathematical organization, the International Mathematical Union (IMU), was created for that purpose.Footnote 17 It would have seemed logical for the CIEM to be dissolved as soon as IMU was created,Footnote 18 but we could not find any mention of a decision concerning CIEM dissolution in the records of the first IMU Congress held in Strasbourg in 1920. In fact, there was no mention of CIEM at this congress at all.

And yet, the statement indicating that the EM was the “official journal” of the CIEM would appear on its cover for another two years.

3.2 Maintaining the Journal’s Ambition and Bibliographical Bulletin During the War

We have already discussed the choices made by the French Mathematical Society, which had dramatic consequences for its editorial policy. The number of journals that the Society officially exchanged with other societies or journals decreased by ca. 20% during the war and the immediate aftermath compared with before the war. Most of the cancelations were of German or Austrian journals. However, Laisant and Adolphe Buhl (1878–1949) (Fig. 3) did not choose for EM to engage in this type of patriotic censorship. Buhl, a professor at the University of Toulouse, had been assisting the two directors for many years, and had begun to play an increasingly important role in managing the journal, particularly the bibliographic aspects. In the absence of archival sources regarding this period,Footnote 19 by reading EM we can infer that the three men—Fehr, Laisant, and Buhl—chose to preserve the internationalist ambitions of their journal amidst the turmoil of war.Footnote 20

The bibliographical bulletin continued to be published throughout the war, with a little more than 40 journals listed each year, except for the 1918 volume, in which the number of journals listed fell sharply to 26. While several journals, such as Borel’s Revue du Mois, suspended publication during the war years, this was clearly not the case for most of the mathematical or scientific journals reported on by EM. Indeed, there was no apparent nationalist ideological censorship or discrimination due to the war, as the geographical distribution apparent in this section remaining roughly the same as that observed in 1910–1912. In fact, this situation was not exceptional, as can be seen from other publications at the international level that published reviews of current literature. The German review journal mentioned above, Jarhbuch über die Fortschritte der Mathematik, continued to list publications from throughout the mathematical world during the war years, without any obvious change in its editorial policiesFootnote 21; similarly, the list of journals that the Circolo matematico di Palermo exchanged with the Rendiconti, during the first years of the warFootnote 22 was identical to that of the pre-war years.

Fig. 3
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Adolphe Buhl (bust by A.Carretier). Personal scan from Enseignement Mathématique’s obituary Footnote

The sculptor Antoine Carretier, born in 1908, was a militant of the French anarchist movement, together with the writer Maurice Laisant (1909-1991) one of Charles-Ange’s grandsons.

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The editors of EM do not seem to have experienced any major practical difficulties during the war, either in terms of receiving journals or communicating with each other between Toulouse, Geneva, and Paris, despite the conflict. Regardless of the origin of the periodicals, the issues listed in EM were most often those from the current year. Their network and the working system put into place when EM was established proved to be particularly effective: Fehr reviewed the German-language titles, Buhl reviewed the French-language titles, and both handled those in English or Italian. In the 1918 volume, the Bulletin bibliographique announced the creation of a new mathematical journal in Germany, the Mathematische Zeitschrift, published in Berlin at Springer’s initiative.Footnote 24 This can be considered one of the first steps in the reconfiguration of the editorial mathematical landscape in Germany, whose center shifted from Leipzig (Teubner) to Berlin (Springer) in the 1920s (Springer also took over the Mathematische Annalen from Teubner in 1919).

Furthermore, there is no obvious evidence of nationalist censorship in other sections of EM devoted to current activities: announcements concerning meetings of mathematical societies in France and Germany continued to be published side by side, as did obituaries, awards, nominations, work anniversaries or retirements of mathematicians from all over Europe and United States. At the same time, the war is evident from the signatures of some of the articles published in EM’s columns, in which the authors added, along with their names, the mention “Aux Armées de France” (Gérardin 1917) or “Armée belge, Sur le front belge” (Godeaux 1918: 81, 89). The war can also be perceived in the nationalist overtones in some of Buhl’s writing. In 1918, for instance, Buhl concluded an article on two recent geometry papers (Buhl 1918) dealing with treatises by Darboux and d’Ocagne by emphasizing that there “appears so clearly [in them] the genius of this geometrical science whose most beautiful developments are due to French geometers”.Footnote 25

3.3 Maintaining a Chronique Dedicated to the CIEM, or How Directing the (Possibly Virtual) Activity of an International Scientific Organization

In alignment with the international mathematical congresses, in 1908 the CIEM received a mandate lasting until 1916. In the meantime, the CIEM held the Paris Conference on April 1914, which was, as we have seen, a great moment in internationalism for speakers from all nations. The war was declared less than four months later, prevented the meeting which was originally planned for Munich in 1915 from being held. The outbreak of war also prevented any meeting of the Central Committee, which at the time comprised Klein, Smith, Fehr, Castelnuovo, and Czuber. The CIEM Central Committee did not produce any official documents during the war and post-war years,Footnote 26 and so the only texts published in the Chronique during those years were articles and statements signed “H. Fehr secrétaire général”.

Two issues dated September 1914 and November 1914 were published in the first months of the war. The first contained a routine announcement of the agenda of the Munich conference, and the announcement of the upcoming publication of a questionnaire regarding the training of mathematics teachers that the national sub-commissions were requested to complete for this conference. In the November 1914 issue, published in December, a text signed by Fehr mentioned that “works of peace such as ours necessarily take a back seat” (Fehr 1914) and concluded by stating that the Munich conference could not take place and that the Central Committee was forced to postpone its planned projects. Notably, the famous Manifesto of the 93, Die Aufruf an die KutlurWelt, signed by Klein, president of CIEM, was published between the September and November Chroniques.

The January 1915 issue provides an example of the complexity of fulfilling Fehr’s desire to promote the Commission activity. The “Notes and Documents” section contains the questionnaire about the training of secondary mathematics teachers that was decided on in Paris in 1914; it was published first in French and then, later in the year, in the three other official languages of the EM. This questionnaire was preceded by “Preliminary Observations” and followed by “Complementary Observations”. The “Preliminary Observations” seem to have come from the Central Committee, and stated that, while it had to forego convening meetings of the Commission, the Central Committee intended to continue pursuing its work as far as possible. Indeed,

Science and first and foremost mathematics should be able to remain outside and above the terrible conflicts of the present time. They form a neutral ground upon which scientists from all nations can continue to work together. (Fehr 1915) Footnote 27

But the “Complementary Observations”, dated January 1915 and signed only “H.F.”, indicate that “these notes” were written at the beginning of the war and that “since then the conflict has worsened terribly and has invaded the most diverse fields of human activity”. Thus, “the Central Committee was obliged to postpone the survey”. Fehr added that it was at the request of national sub-commissions eager to launch the survey that he published the questionnaire “for documentary purposes” (Fehr 1915).

In any case, EM published reports on the publications of several sub-commissions at different times during 1915 and 1916. A Chronique published in 1917 listed the publications of several national sub-commissions since 1 April 1914, and specified that “20 new issues have been distributed”. The layout of the issue was such that the presentation of the new reports from the German sub-commission began on the very same page on which Gérardin’s article, mentioned, above, ended with the mention “Aux Armées de France” in its signature. In April 1921 Fehr would indicateFootnote 28 that, as the Commission headquarters were located in a neutral country, he had been able to remain in contact with most of the delegates, except those from Russia, and had striven to continue the journal’s work throughout the war.

The 1918 volume, Volume 20, clearly belongs to the aftermath of the war and to the new era of international scientific cooperation that was first organized and promoted by France. The last issue dated 1918—whose drafting and publication overflowed into 1919Footnote 29—published the declarations and resolutions voted on by the Inter-Allied Conference of the Scientific Academies in a Chronique. These declarations advocated dissolving pre-war international scientific associations and replacing them with new ones that excluded Germans and scientists from the other Central Empires. While these resolutions would obviously have affected the CIEM, the EM does not comment on them at all, nor on the potential impact they could have had on the CIEM. Moreover, the same Chronique that published these conflicting resolutions went on to announce news of prizes, nominations, and awards from the German academic world.

The consequences for the CIEM were presented in the next volume, which was printed in 1921 but dated 1920. First, in a short Chronique (Fehr 1920–1921a), Fehr indicated that, similar to other international commissions created before the war, the CIEM had to consider its own dissolution. He added that “consulted individually by letter, the members of the Central Committee recognized that, under the current conditions, the dissolution of the CIEM [had] becom[e] inevitable”.Footnote 30 He concluded by stating that the Commission would cease its work, leaving it to the national sub-commissions publicize the findings from the work that had been carried out.

Second, in his long “Summary Report” on the CIEM from 1908 to 1920 (Fehr 1920–1921b), Fehr published an excerpt in French from a letter from D. E. Smith dated April 1920 (Smith 1920). Smith considered it “desirable, although perhaps impossible” to continue the Commission’s study, which had begun in 1908. However, he continued, the current conditions were not favorable, and “it seems preferable to end the Commission’s work”. In conclusion, Smith listed a number of questions to be addressed, expressing the hope that they would be addressed in the not too distant future by a Commission with a mandate from an International Congress of Mathematicians. Although Fehr stated later in this report, in a paragraph entitled “Dissolution of the Commission”, that “in their turn, the delegates approved the proposed plan for dissolution” (Fehr 1920–1921b, 317–318), nowhere does the EM state that the CIEM was actually dissolved. Neither do the reports on the first IMU international Congress in Strasbourg mention any decision concerning the dissolution of the CIEM, as we have already pointed out. Moreover, as we know, the cover of EM still declared it the “Official journal of the CIEM” for two more years!

What does the this Chronique dedicated to the CIEM say about EM’s internationalism? First it is apparent from reading the various issues of EM that it maintained a very moderate tone, without portraying any country as anathema. Second, EM still described itself as the official journal of the CIEM, despite the “unavoidable dissolution” of the latter. Third, it regularly published reports on national sub-commissions from every country, including those of the Central Powers, and was published in the four official languages of the CIEM. It is important to reiterate that EM was a noticeable exception in the landscape of French-language journals. It seems clear that the internationalism of EM and Fehr did not significantly weaken in the aftermath of the war.

However, Gert Schubring’s look behind the scenesFootnote 31 based on correspondence between Fehr and Smith tells a different story. Schubring first pointed out the question of Klein’s resignation, which was raised between December 1914 and the spring of 1915. Fehr asked Klein to resign and be replaced by Smith (who was from a neutral country), but Smith and Castelnuovo, whom Klein consulted, disagreed with Fehr. Smith’s argument was that there was no objection in Great Britain to collaborating with German scholars. The correspondence between the Central Committee members stopped in 1915 and only resumed in 1919 or 1920. Therefore, all the texts written by Fehr for the CIEM Chronique—all signed “H. Fehr, secrétaire general”—were, in a way, expressions of his personal views. A second point is the question of dissolution (1919–1920). Fehr only contacted the “allied” members of the Central Committee to ask their opinion about dissolution. He specifically did not ask Klein’s opinion; but once again, Smith disagreed with Fehr and contacted Klein. However, Klein no longer considered himself president, and asked both vice-presidents to settle the question during the Strasbourg congress; although, as we have seen, the CIEM was not represented at Strasbourg.

Thus, according to Schubring, Fehr supported the French hard-liner position in favor of excluding Germans. Given the contents of the Chroniques and the Bulletin bibliographique, however, Schubring’s conclusion about Fehr’s political desire to exclude German mathematicians seems dubious. Overall, it seems difficult to identify any real change in Fehr’s and EM’s attitude toward internationalism during the war.

4 EM’s Path in the World of the 1920s

Laisant died in May 1920, after writing a short mathematical article that would be published in EM shortly after his death; indeed, by that time his involvement with EM had become very minimal. Buhl officially became director, along with Fehr. It was not an easy task to lead EM in the 1920s. First, at a practical and financial level Buhl complained, in a letter to Élie Cartan from April 1928, that “[…] when you have published a volume of EM, you always wonder if you will be able publish the next one because the financial situation is so discouraging”.Footnote 32 The irregular publication schedule of EM in the 1920s reflects these difficulties and uncertainties. There were no volumes dated 1919, and the first truly post-war volume (volume 20), was dated 1920 but not published until 1921; the following volume, dated 1921–1922, appeared two years later in 1923, at which point the situation appears to have improved, as volume 23 was dated, printed, and released that same year. In the second half of the 1920s, even though the directors’ concerns persisted,Footnote 33 the situation finally seemed to return to normal. Second, at an editorial level, due to the new geopolitical situation in Europe and the rest of the world, several new institutions (societies, universities) were creating mathematical journals that could have been of interest to the EM. Finally, at the level of mathematical internationalism, tension and opposition concerning the hard-line exclusion policy applied by the new international organizations were increasing. Fehr, who through his journal promoted cooperation with German scientists, was nevertheless elected in 1924 to be vice-president of the new IMU, which had to decide on the still unclear fate of the CIEM.

4.1 Internationalism in the Mathematical Editorial World of the 1920s, Practical Difficulties and the New Geopolitical Situation

As Buhl observed in the abovementioned letter regarding his journal, the European press was facing an important financial crisis in the post-war years. It is well known that there was severe inflation, but there were also specific concerns affecting publishers such as a substantial rise in the cost of producing journals due to the sharp increase in the price of paper, typographer’s wages, and so on. The financial situation of several scientific and mathematical journals, in France as well as in other European countries, was so “desperate”Footnote 34 that the Rockefeller Foundation included support for European scientific publications in its agenda and launched programs to save them, through a massive subscription campaign, despite their high prices.Footnote 35 Buhl, who was also the secretary of the Annals of the Faculty of Sciences of Toulouse (AT), wrote to Cartan regarding the consequences of the situation. For instance, in a letter dated April 1927, he wrote: “But the AT (sic) are in a slump and we can only publish 180 pages per year… Times are appallingly hard. Before the war, we had 480 pages per volume. […] At the AT the committee decided to only publish 48 p. per author free of charge. The supplemental charge is 50f per page. That is frightening enough to say!”.Footnote 36 A few months later, Buhl complained about the difficulty of publishing the articles he received in the AT, given the pressure exerted on him by the editorial board: he wrote that “it is as complicated as if we wanted to elect a professor […]. People like you or Villat write letter after letter and send recommendations through all possible channels… Really this is too much”.Footnote 37 In general, Buhl observed, “the overcrowding of mathematical periodicals is insane at the moment”.Footnote 38

Despite the picture of the French and European situation that we have painted above, bibliographical enterprises had to face another difficulty that, for instance, Ludwig Bieberbach emphasized in his report on the Jahrbuch über die Forschritte der Mathematik published in 1930.Footnote 39 From the beginning of the century and even more so in the 1920s, there was a strong increase in the volume of mathematical literature being published worldwide. Bieberbach observed that reviewing this mathematical production had become too big of a undertaking, given Jahrbuch’s financial and human resources. He thus noted the irregularity of and delays in the publication of Jahrbuch volumes, which, since the war began, had no longer been published annually. For instance, the volume dedicated to literature published in 1923 was published in 1927–1928. This chaotic situation led to the establishment of a new competing bibliographic enterprise in Germany in 1931, the Zentralblatt für Mathematik und ihre Grenzgebiete.

EM, with its internationalist ambitions, therefore had to face a profoundly new context in the 1920s. Examining the Bulletin bibliographique for 1920–1923 reveals that 68 journals were reviewed in these three volumes. The selection of journals does not show any apparent discrimination based on the country in which the journal was edited, which remained a very notable policy for a French-language journal, given that the censorship applied by the French Mathematical Society remained in place until the 1930.Footnote 40 The Bulletin bibliographique continued to include the main mathematical journals from the pre-war period, regardless of their city or country of publication. The list also included a dozen journals that had not previously appeared in the bulletin. The first of these were new European journals created in the aftermath of the war (including one based in Hamburg, Germany, for instance), but some were also from non-European countries. In addition, there were also journals that had been in existence before the war from non-European countries such as Argentina, India, and Japan, that had not previously been included in the bulletin. The question of what the Bulletin bibliographique reveals about territorial dynamics is therefore a significant one. Among the 40 cities represented in the bulletin during this time, ten had not been mentioned in the bulletin before the war. There are two important points in this regard: first, the (larger) European cities, including German cities, maintained their rank, but cities in Eastern or Central Europe (such as Vienna or Warsaw) grew in relative importance as new journals were founded there (see Map 2). Second, EM began to include non-European periodicals that had existed before or were created after the war, from several cities in Japan, India, and South America.

Map 2
figure 5

The editorial world featured in the EM’s Bulletin Bibliographique in 1920–1923Footnote

For all of the cities that appear on this map, see page 5 of the annex to the abovementioned article in Historia Mathematica.

Full size image

To appreciate these results that were achieved due to the directors’ efforts to promote editorial internationalism, it is helpful to compare EM to the 1923 volume of Jahrbuch. During that year, Jahrbuch reviewed 210 journals, three times more than EM. Among them, 30 were newly reviewed (though not necessarily newly created) journals, which was approximately the same proportion as in EM, but many were Italian journals and, to a lesser extent, journals from the United States and Germany. As a whole, the editorial world as seen through the lens of the Jahrbuch reports, compared with EM, was still primarily a European one. In addition, the number of periodicals from local or national institutions reviewed in EM further increased compared to the pre-war situation.Footnote 42 The international dynamic presented by EM came to resemble more and more a patchwork of local dynamics assembled and put into perspective by its directors.

This can be clearly seen in the other sections of EM dedicated to the current events in the mathematical world at that time.Footnote 43 We will discuss one example from Volume 28 of 1929, which is all the more interesting because it appeared one year after the international congress of mathematicians in Bologna, which we will return to in the following section. The same page of the Chronique presented,Footnote 44 one after the other, two pieces of information concerning highly symbolic local congresses: the first was a meeting of Romanian mathematicians which had just been held in Cluj, a city that became Romanian in 1918 and in which Romania’s third university had just been createdFootnote 45; the other was an announcement of the first USSR mathematics congress, which was to be held in June 1930 in Khar’kov. The first of these events, organized by D. Pompeiu, G. Tzitzeica, and I. Ionescu, brought together 150 participants, including foreign delegates, among others “MM. V. Volterra, from Rome, P. Montel, from the Sorbonne and W. Sierpinski, from Warsaw”; 50 communications were presented during the congress. The announcement of the second event included a call from the organizers for foreign mathematicians to participate, and provided the address to which registrations should be sent.Footnote 46 The same volume included a long article written by F. Leja, professor of mathematics at the University of Warsaw, which was devoted to the first congress of Slavic mathematicians that took place in Warsaw in September 1929 (Leja 1929) . This congress, which had been entrusted to the Polish Mathematical Society, was “of a purely regional character [whose] aim was to facilitate scientific collaboration between mathematicians from neighboring countriesFootnote 47 and whose languages are related”. It was attended by 180 participants, and 50 papers were presented. IMU sent a delegation. Thus, EM presented and promoted a new mathematical geography of Europe of the 1920s.

4.2 EM and the CIEM: The New Position of International Institutions

Let us again consider EM’s covers. As was already mentioned, the journal retained the reference to itself as the “organe officiel de la CIEM” until 1923, though this seems to have lost any meaning. This statement then disappeared from the cover, but reappeared on the volume published in 1930, which is to say soon after the ICM in Bologna took place, at which the official status of the CIEM became clearer. The ICM held in Bologna in 1928 was an opportunity for the CIEM to make a comeback in the pages of the journal: indeed, the Commission had been absent from EM since Fehr’s 1920 review of its work and organization.

The 1928 volume of EM contained a short Chronique signed “H. Fehr” , entitled “CIEM at the Bologna Congress”. The first sentence of this article describes the new international landscape of science policy: “For the first time since the international conference held in Paris in April 1914, the International Commission on Mathematical Education was present at a congress to which scientists from all countries could once again be invited” (Fehr 1928). Unlike the previous congresses held in Strasbourg and Toronto, German mathematicians were not excluded from this congress, which was sponsored by the University of Bologna and not the IMU, whose president, the Frenchman Gabriel Kœnigs, still maintained the hard-line position he had in previous years and refused to participate in this normalization of international scientific life.Footnote 48 Fehr wrote that he “seized the opportunity” to make the Commission’s work public, and announced that, at the initiative of the American sub-commission, there would be a new series of reports published in EM on the progress made over the past ten years in its main member countries. He announced in particular a resolution stating that the Congress would decide to “extendFootnote 49 the powers of the Central Committee”. Four individuals were appointed to this Committee: Smith, who became the new president,Footnote 50 Hadamard and Castelnuovo, who were made vice-presidents, and Fehr, who remained secretary general—and the Central Committee was asked to choose a fifth member. It appointed W. Lietzmann, from Göttingen, who had been Klein’s right-hand man at the CIEM since the beginnings.

This resolution invites several comments. First of all, the status of the resolution is unclear, as the IMU authorities were not officially present in Bologna: it was adopted by the section “Elementary Mathematics, Didactic Questions, Mathematical Logic” and “approved” by the President of the congress. Moreover, the terms used are ambiguous, as the word extend (“proroger”) appears to mean that the CIEM, and its Central Committee, had not been dissolved. Finally, the new Central Committee was not comprised of new committee members.Footnote 51 Far from it: Smith, Fehr, Lietzmann, and Castelnuovo had been strategic members of the Committee since its creation, and Hadamard had belonged to the international mathematical elite since at least the beginning of the century.

In his Bolognese Chronique, Fehr indicated that CIEM had resumed its activities, which would include the Commission’s investigation into the theoretical and practical training of mathematics teachers once the Commission had been filled out “so that all the nations participating in the Congress would be represented in it, once the cooperation of their governments had been obtained”.Footnote 52 However, the EM issues published after the Bologna congress reveals that business resumed very slowly at the CIEM.Footnote 53 The year after the Bologna congress, one of the entries under the heading “Notes and documents” was explicitly devoted to the CIEM, but only contained information on the “decisions” made at the Congress, the new Central Committee, and the organization of the Commission, followed by the questionnaire on teacher training, which had been revised and corrected from the 1914 version published in 1915.Footnote 54 The first article on the Commission and its activity did not appear until the 1932 volume, and was devoted to the meeting that the Commission held within the framework of the ICM held in Zurich in 1932 (Fehr 1932).

On the other hand, from 1929 to 1931 EM published the series of national reports announced in Bologna under the generic title “Essential Changes in Mathematics Education in the Major Countries since 1910”. A preamble to the first series of reports, written and signed by Fehr, stated that these reports had been undertaken on the initiative of the “American delegation of the CIEM”, but no further mention was made of any relationship to the CIEM or its national sub-commissions (Fehr 1929). The “major countries” in question that were listed in this preamble, presenting a narrow view of the mathematical world, particularly compared to the range of countries that had that participated in the CIEM’s work before the war.Footnote 55 The only “new” country included was Czechoslovakia. This narrowness is all the more striking because, as we have seen, EM continued to reflect a much broader and more diverse mathematical world.

5 Conclusion

At this point we can draw some conclusions about the various points raised at the beginning of this chapter. First, regarding EM’s emphasis on internationalism, I think I have shown that this did not wane during the war and its aftermath. Even so, it is clear that Fehr did not succeed in restoring the activity of CIEM to its pre-war level. Second, detailed analysis of two specific sections of EM has revealed the new mathematical territories that developed in the post-war period. At the editorial level, cities in Eastern and Central Europe gained new importance as the sites of new journals that had been founded in connection with the structuring and development of new mathematical activities; outside Europe and the United States, EM also began to feature periodicals from Japan, India, and South America, some of which had existed before the war, and some of which were created after the war. Furthermore the pre-war ambition of achieving an Internationale of the world of mathematics education had shifted somewhat by this point. There were fewer pedagogical and educational journals listed in the EM’s bibliography than before the war, and more mathematical research journals. This may be related to the difficulties that Fehr encountered with the CIEM after the war.

Finally, regarding the question of whether studying EM would reveal the involvement of new participants in the world of mathematics education, whether individuals or institutions, after the war, my answer is clearly no. It is true that the Sponsorship Committee, which represented the great figures of the “old” pre-war mathematical world, had disappeared from the cover of EM. However, these men still presided over the destiny of the mathematical world as it was presented in the EM in the 1920s. In addition, the Central Committee of the CIEM symbolized the “old world”; the men of the Committee members were still present, as part of the post-war Central Committee. They followed the old model of the Commission’s structure and working style, and this was, in a way, a failure for the CIEM.

Fehr and Buhl did not, for instance, invest in the new associations and new international networks for intellectual cooperation and scientific and education exchange that had been set up after the war by the Société des Nations (SDN).Footnote 56 While a delegate from the International Institute of Intellectual Cooperation (IICI) of the SDN was present at the Bologna ICM in 1928, his reportFootnote 57 was not particularly positive. This congress of mathematicians, which had been convened in the old pre-war mode, dealt only with “strictly scientific questions”, and “there was no mention of any bibliographic organization project or anything of this sort”,Footnote 58 with one exception: “the report presented by M. Fehr in the name of the CIEM”.Footnote 59 The IICI delegate also related how little importance the Congress seemed to give to his presence:

Personally, even though I was invited as a representative of the Institute, I was not received on the same footing as government delegates, and the congress organizers were by no means informed about my presence.Footnote 60 I pointed this out discreetly on one or two occasions, but did not find it useful to make a formal complaint about it.Footnote 61

The delegate’s report also provides some information about the conditions required for international scientific cooperation in the 1920s and the difficulties that Fehr faced with the CIEM. It comments on the discussion held by the Pedagogy and Teaching section about the continuation of the CIEM’s work and mentions the emphasis placed on the need to increase the number of members of the Commission, in order to obtain better representation of the various States, especially those that did not exist before the war. The IICI delegate went on:

One of the speakers suggested that the League of Nations could be approached in order to help obtain financial support from governments. I intervened in the debate in a discreet manner, confining myself to explaining how the Institute and the Commission functioned, without giving any cause for hope, while on the other hand, I drew attention to the Institute’s activities regarding intellectual statistics which would address some of the suggestions that had just been made.Footnote 62

Finally, the delegate stated that he had had an opportunity to talk to Fehr who “promised to keep him apprised of subsequent developments on this matter”.Footnote 63 It does not appear that Fehr had any ongoing contact with IICI afterwards. There is only one entry in the Fonds Henri Fehr about this Commission, and it dates from 1922; it is a list of the Commission members.Footnote 64 Similarly, neither Fehr’s name nor Buhl’s name appears in the description of the IICI Fund. Fehr was not among the Swiss individuals proposed to serve on the International Commission for Intellectual Cooperation, nor was he a member of any of the networks closely associated with it. EM and the CIEM did not belong to this new world, which primarily developed in the 1930s. In France, Émile Borel was the main mathematician who became particularly involved in the IICI in the 1920s, and he never had any special connection to EM or the CIEM. These were two separate worlds, and this partly explains the relatively minor role of the CIEM and later, the evolution of EM towards a more classical mathematics journal.