1913 - 1921

1913 November - preparatory studies for the Paris Congress
(Cf. Publications du Comité central rédigées par H. Fehr, Conférence internationale de l'enseignement mathématique. Travaux préparatoires; EM 15, 5, 1913, pp. 394-412).
At the Heidelberg meeting (21-23 July 1913) the Central Committee decides to increase its membership from 4 to 7:

President F. Klein,
Vice-Presidents G. Greenhill and D. E. Smith,
Secretary General Fehr,
Members G. Castelnuovo (Rome), E. Czuber (Vienna) and J. Hadamard (Paris)

The Commission decides to concentrate its attention on the two following questions:
A. The results obtained by the introduction of differential and integral calculus into the upper years of middle school
B. The place and role of mathematics in higher technical instruction

To this end, two questionnaires are drawn up in the 4 official languages: French, German, English, Italian, EM 15, 5, 1913, pp. 396-412

1-4 April 1914 - Paris Congress
(Cf. Publications du Comité central rédigées par H. Fehr, Compte rendu de the Conférence internationale de l'enseignement mathématique tenue a Paris du 1er au 4 Avril 1914; EM 16, 3, 1914, pp. 165-226; EM 16, 4-5, 1914, pp. 245-356).

The sessions take place at the Sorbonne. The general opening session is presided over by Gaston Darboux, Secrétaire perpétuel of the Académie des Sciences. More than 160 people from 17 different countries are in attendance.
After Fehr's report on the activities and publications of the Commission and the official welcome of P. Appell, in the name of the French delegation, Castelnuovo makes the opening speech in place of Klein, who is unable to attend the meeting (EM 16, 3, 1914, pp. 188-191). Castelnuovo, among other things, reports on a broadening of the field of investigation of the Commission, which is no longer to be limited to secondary schools, but which now covers schools of every type and level. In addition, he outlines the Commission's aims:
On a exprimé parfois des doutes sur nos intentions. On pensait, qu'en abusant de nos pouvoirs, nous tâcherions de faire triompher une tendance déterminée dans les méthodes d'enseignement des mathématiques. Je tiens à déclarer que rien n'est plus loin de nos propos… chaque Etat doit régler, comme il croit mieux, ses écoles, en harmonisant le respect de la tradition avec les exigences de la vie moderne. Mais il faut bien constater que les relations plus fréquentes entre les peuples, et l'analogie des conditions économiques ont créé chez les différentes nations des besoins pareils auxquels l'instruction doit pourvoir. Il devient donc toujours plus nécessaire de connaître, même en matière d'instruction, ce que font nos voisins et de profiter de leur expérience. La connaissance d'ailleurs n'impose pas l'action, mais l'action serai aveugle sans la connaissance. (p. 189)
Gaston Darboux
Castelnuovo's speech is followed by that of G. Darboux who describes the situation in France and illustrates the changes introduced into secondary school teaching by the 1902 reform highlighting in particular :
1° l'introduction dans l'enseignement élémentaire du Calcul des dérivées et même de notions de Calcul intégral :
2° l'emploi systématique dans la géométrie des méthodes de transformation qui simplifient l'étude et apportent un principe de classification ;
3° le développement donné aux applications qui sont posées par la pratique, à l'exclusion de ces problèmes qui ont aucune racine dans la réalité;
4° le développement aussi complet que possible de l'initiative personnelle chez tous les élèves qui prennent part à l'enseignement et une préoccupation incessante d'une bonne formation de l'esprit.
(p. 197)
Émile Borel
The general session closes with the lectures of E. Borel and M. d'Ocagne. In his contribution on L'adaptation de l'enseignement secondaire aux progrès de la science (pp. 198-210) Borel emphasises the importance of the early introduction of differential and integral calculus, "à la fois les plus utiles et plus éducatives que tout autre branche des mathématiques" (p. 210), into secondary school teaching. D'Ocagne, in his lecture on Le rôle des mathématiques dans les sciences de l'ingénieur (pp. 211-222), highlights, with numerous examples, the great services that mathematics has rendered technology and hence the importance of providing future engineers with a vigorous mathematical training.
E. Beke presents his paper on Les résultats obtenus dans l'introduction du calcul différentiel et intégral dans les classes supérieures des établissements secondaires (EM 16, 4-5, 1914, pp. 245-282 ). Beke's report shows that elements of infinitesimal calculus figure in the official syllabuses or in the curricula drawn up by schools themselves in the following states: in some German states (Bavaria, Wurtemberg, Baden, Hamburg), in Austria, Denmark, France, British Isles, Italy, Romania, Russia, Sweden, and Switzerland. Beke then deals with the following points: the scope of the teaching of infinitesimal calculus, its applications (geometric, physical, …) and the question of rigour, the interactions between calculus and other subjects and, finally, the reactions from secondary and university teachers. On this last point in particular, Beke points out that while secondary school teachers were enthusiastic, university professors expressed a certain coolness, if not hostility. The reason for this behaviour is to be attributed, according to Klein, to the lack of rigour of the textbooks of infinitesimal calculus, and to the gulf which exists between teachers and academics. Beke concludes his paper by emphasising the great training value of mathematics (humanités scientifiques) and inviting university professors to support the reform movement by collaborating with secondary-school teachers and writing textbooks.

Beke's contribution is followed by Ch. Bioche's paper on the teaching of infinitesimal calculus in the French lycées, by some additional observations from the delegates, by extracts from the national reports of Germany, Austria, and the British Isles and by a lively debate (pp. 285-306). In particular, the importance of avoiding both falling into automatic patterns of thinking (J Hadamard) and infinitesimal pseudo-intuition (A. Padoa), of establishing the true extent of the programmes of infinitesimal calculus and of making its teaching gradual (G. Castelnuovo, G. Darboux, A. Thaer,…). J. and P. Tannery's textbook, Notions de Mathématiques (1902) is quoted by way of example.
P. Staeckel presents his paper on La préparation mathématique des ingénieurs dans les différents pays (EM 16, 4-5, 1914, pp. 307-328 ). At the outset Staeckel explains that there are two different systems for training engineers: in most countries there are Technical Universities, while in the rest, it is traditional universities which manage the preparation of engineers, often supported by special schools. The speaker goes on to deal with a number of questions: what kind of teaching it should be, which subjects, methods, books, and who should teach mathematics, whether mathematicians or engineers themselves.
The debate which follows is rather lively, above all, on the questions of method and on the rigour of the teaching (pp. 328-356). Nonetheless, the speakers generally agree in affirming that an engineer should receive a solid mathematical training, which, however, should forgo questions which are too specialised and of purely theoretical interest.

The Commission decides to reconvene in Munich in August 1915. As the principal subject for debate it proposes Theoretical and practical training of mathematics teachers at the different levels teaching considering these three broad categories :
A. Secondary school teaching (gymnasiums, lycées, modern schools )
B. Vocational teaching (technical middle schools, …)
C. Primary school teaching.
G. Loria (Genova) is charged with presenting a general report on point A.
map of europe

1914-1918 - World War I

1914 November - December
Fehr, without consulting the Central Committee, announces that the work of the Commission would be interrupted during the war (EM 16, 1914, 477-478) . In October 1914 Klein, like many other intellectuals, had signed, without having ever read the text, the scandalous document "Aufruf an die Kulturwelt", which denied any war crimes by the German army. Fehr invites him to resign his post and cede the presidency of the Commission to Smith, but Klein is supported by the most part of the Central Committee, and especially by Smith and Castelnuovo. (cf. G. Schubring 2008)

1915 January
The Questionnaire for the Inquiry into the training of teachers of mathematics in secondary schools in different countries is published (in the 4 official languages) in L'Enseignement Mathématique (EM 17, 1,1915, pp. 60-65, 129-145 )

1916 - The International Congress of Mathematicians scheduled for this year in Stockholm does not take place because of the World War I

The Commission does not meet, and brief reports of the work of some national sub-commissions and several papers on the technical and practical training of mathematics teachers in secondary schools are published in L'Enseignement Mathématique (Belgium, EM 18, 1916, pp. 335-352; Germany, ibidem pp. 353-361 ; United States, ibidem pp. 427-439 ; Argentina, EM 21 1920, pp. 281-304 , Bolivia, EM 22, 1921-1922, pp. 286-290). In 1919 L'Enseignement Mathématique does not publish its annual volume and puts out a single volume for the years 1921 and 1922.
July 1919
The International Research Council (IRC) meets in Brussels to discuss the creation of the International Mathematical Union, but "les mathématiciens présents à Bruxelles ne s'estimèrent ni assez nombreux ni suffisamment accrédités pour réaliser sa constitution définitive" (Comptes Rendus du Congrès International des Mathématiciens (Strasbourg, 22-30 Septembre 1920) publiés par Henri Villa t, Toulouse, Imp. Édouard Privat, 1921, p. XXXIV). For this reason, a provisional Bureau is appointed.

Fehr accepts the exclusion of the former Central Powers (EM 20, 1918, pp. 294-297, 21, 1920-1921, pp. 59-60) from international cooperation and urges liquidation of the Commission (EM 21, 1920-1921, pp. 137-138).

C. de La Vallée-Poussin
Charles Jean de La Vallée-Poussin

20 September 1920 - The International Mathematical Union is established in Strasbourg
The definitive Bureau is established with Honorary Presidents: C. Jordan, H. Lamb, E. Picard, V. Volterra; President: C. de La Vallée-Poussin; Vice-Presidents: P. Appell, L. Bianchi, L.E. Dickson, J. Larmor, W. H. Young; and Secretary General: G. Koenigs.
There are 11 member countries: Belgium, Czechoslovakia, France, Greece, Italy, Japan, Poland, Portugal, Serbia, United Kingdom, United States. The former Central Powers, Germany, Bulgaria, Austria and Hungary, are excluded for political reasons.

22-30 September 1920 - The International Congress of Mathematicians is held in Strasbourg under the chairmanship of Emile Picard
200 mathematicians from 27 countries participate, the former Central Powers are excluded. In the closing session Picard says:
The  Astronomical Clock of Strasbourg  Cathedral
The Astronomical Clock
of Strasbourg Cathedral
Le monde de 1920 est bien différent de celui du débout de 1914, et il est peu d'hommes de science qui soient aujourd'hui disposés à s'isoler dans une tour d'ivoire… Quant à certaines relations, qui ont été rompues par la tragédie de ces dernières années, nos successeurs verront si un temps suffisamment long et un repentir sincère pourront permettre de les reprendre un jour, et si ceux qui se sont exclus du concert des nations civilisées sont dignes d'y rentrer. Pour nous, trop proches des événements, nous faisons encore nôtre la belle parole prononcée pendant la guerre par le cardinal Mercier, que, pardonner à certains crimes, c'est s'en faire le complice. (Comptes Rendus du Congrès International des Mathématiciens 1921 cit. pp. XXXII-XXXIII)
Concerning the Section IV, dedicated to philosophical, historical and pedagogical questions, in the proceedings appears only a brief summary by Koenigs of the paper on the problems of teaching of M. Dubecq, Sur l'enseignement en République Argentine. The plenary lecture of Vito Volterra was devoted to teaching issues: Sur l'enseignement de la Physique Mathématique et de quelques points d'Analyse. (pp. 81-97)
The mandate of the International Commission on the Teaching of Mathematics is not renewed.

1921 April - Declaration of the dissolution of the International Commission on the Teaching of Mathematics
(EM, 21, 1920-1921, pp. 317-318 ) The new conditions imposed on official international scientific relations oblige the international Commissions or Associations created before the war to proceed to their dissolution or to their reorganisation. With the approval of the delegates, the members of the Central Committee decide to dissolve the International Commission on the Teaching of Mathematics. National sub-commissions may, however, continue with their work and may still send them to L'Enseignement Mathématique for publication. Fehr presents an outline report on the activities of the Commission from 1908 to 1920 complete with a list of the publications of the Central Committee and of the national sub-commissions of Germany, Argentine Republic, Australia, Austria, Belgium, Denmark, Spain, United States, France, Holland, Hungary, British Isles, Italy, Japan, Romania, Russia, Sweden, Switzerland (EM 21, 1920-1921, pp. 305-337 ).

Livia Giacardi
March 2008