1937 - 1954

6-9 September 1938 - New York, The American Mathematical Society celebrates the fiftieth anniversary of its foundation.

For the occasion the Society's very rich library (housed at Columbia University) is opened to the public. The library was developed thanks to the decisive impulse given by the direction of D.E. Smith.

L'Enseignement Mathématique publishes the list of Italian full professors of mathematics and astronomy dismissed from office following the racial laws of 1938; among these are high-profile mathematicians such as Tullio Levi Civita, Federigo Enriques and Guido Fubini (EM, 37, 1938, p. 218).

1939 - On 1 September

Germany invades Poland. France and Great Britain declare war on Germany, World War II begins (1939-1945)

The International Congress of Mathematicians which was to have taken place in Cambridge (USA) is "postponed until a more favourable moment" ("renvoyé à une époque plus favourable")

(EM, 38, 1939-1940, p. 165).

H. Lebesgue becomes a member of the Comité Directeur of L'Enseignement Mathématique with H. Fehr and A. Buhl, but dies shortly after, on 26 October 1941.

L'Enseignement Mathématique publishes only two volumes, number 38 for the year 1939-1940 and number 39 for the years 1942-1950. On 24 March 1949, A. Buhl, director of the journal along with Fehr, dies, so that new collaborators are brought in, among whom J. Piaget.

1945 - UNESCO (United Nations Educational Scientific and Cultural Organisation) is founded with the aim of promoting international collaboration in the areas of education.

1948 - The OEEC (Organisation for European Economic Co-operation), an international organisation for economic cooperation and development, is created.

In 1961 it will be substituted by the OECD (Organisation for Economic Co-operation and Development).

30 August - 6 September 1950 - The XI International Congress of Mathematicians takes place in Cambridge (USA) under the presidency of Oswald Veblen.

(EM, 39, 1942-1950, 149-155)

There are 2302 participants from 41 countries. Section VII, dedicated to History and Education includes a 30-minute invited lecture by G. Pólya entitled On plausible reasoning and 11 communications concerning education. In his talk, Pólya declares:

Mathematics has two faces. Presented in a finished form, mathematics appears as a purely demonstrative science, but mathematics in the making is a sort of experimental science. A correctly written mathematical paper is supposed to contain strict demonstrations only, but the creative work of the mathematician resembles the creative work of the naturalist: observation, analogy, and conjectural generalizations, or mere guesses, if you prefer to say so, play an essential rôle in both. A mathematical theorem must be guessed before it is proved. The idea of a demonstration must be guessed before the details are carried through. ( Proceedings of the International Congress of Mathematicians Cambridge, Massachussetts, USA, August 30 September 6, 1950, Providence RI, American Mathematical Society, 1952, 739).

Therefore the teacher must teach his students both demonstrative reasoning, as well as plausible reasoning, that is "the kind of reasoning on which his creative work will mainly depend" ( Proceedings, op. cit., 476).
Noteworthy among the communications is that of W. Betz, Mathematics for the million, or for the few? , in which he expresses the hope for the recommencement of the work begun in 1908 by the International Commission on the Teaching of Mathematics.
In the closing session, M.H. Stone presents a report on the meeting held at Columbia University in New York (27-29 August 1950) to prepare for the reconstitution of the IMU.

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6-8 March 1952 - The First General Assembly of the reconstituted International Mathematical Union (IMU) takes place in the richly decorated Renaissance Villa Farnesina in Rome.

Rome, Villa Farnesina, Salone delle Prospettive

During the Assembly the IMU Executive Committee is elected, with President M. Stone (USA), First Vice-President E. Borel (France), Second Vice-President E. Kamke (Germany), Secretary E. Bompiani (Italy); Other Members are W.V.D. Hodge (Great Britain), S. Iyanaga (Japan), and B. Jessen (Denmark).
22 countries are members of the IMU:
Argentina, Australia, Austria, Canada, Cuba, Belgium, Denmark, Spain, Finland, France, Greece, Italy, Japan, Norway, Pakistan, Peru, Germany, the Netherlands, Switzerland, U.K., USA, Yugoslavia (EM, 39, 1942-1950, 156-158 , cf. also LEHTO 1998, 92-100).

During the Assembly, the International Commission on the Teaching of Mathematics is transformed into a permanent subcommission of the IMU, while maintaining its original aims. The official languages remain English, French, German, and Italian, and the official organ L'Enseignement Mathématique. The name "International Commission of/on/for Mathematical Instruction" was introduced, even if for some time the old names were used as well (see M. STONE, La prima assemblea generale della Unione Matematica Internazionale (Roma, 6-8 marzo 1952), La Ricerca scientifica, 10, Ottobre 1952, 1973-1975), and E. BOMPIANI, Annual Report of the Executive Committee to the National Adhering Organizations, concerning the period: March 9, 1952 -February 14, 1953,
Internationale Mathematische Nachrichten, 27-28, 1953, 4-10).
In his report, IMU president M. Stone stresses the importance of carrying on the activities of the ICMI:

The problem of determining the place of mathematics cannot be divorced from technical considerations concerning teaching methods. If we judge by the results, we must find it difficult to escape from the conclusion that our attempts to teach mathematics as part of a program of mass education have so far been, to put it bluntly, a colossal failure, traceable to our ignorance and complacency in respect to the art of teaching. (M. Stone, La prima assemblea generale, op. cit., 1974, also in EM 39, 1942-1950, p. 159)

Stone invites the ICMI to collaborate with UNESCO. L'IMU designates H. Behnke, A. Châtelet, R.L. Jeffery, D. Kurepa as members of the new commission, and requests that H. Fehr remain available during the transition period (EM 39, 1942-1950, p. 162 ).

April 1952 - The CIEAEM, Commission Internationale pour l'Étude et l'Amélioration de l'Enseignement des Mathématiques is officially born at La Roquette par Melun, during a meeting entitled Structures mathématiques et structures mentales.

Its object is to improve the methods and the programs for teaching mathematics in light of the progress made in mathematical epistemology and in psychology.

La Roquette par Melun, April 1952,
F. Gonseth and wife, J. Dieudonné, G. Choquet

President of the CIEAEM is mathematician Gustave Choquet (Paris), Vice-president is the psychologist Jean Piaget (Geneva), and the secretary is the mathematician and an expert in pedagogy Caleb Gattegno (London).

Among the founding members are the mathematician and philosopher F. Gonseth (Zurich), the mathematicians E.W. Beth (Amsterdam), Jean Dieudonné (Nancy), A. Lichnerowicz (Paris), H. Freudenthal (Utrecht), W. Servais , formerly mathematics teacher and later Préfet des Etudes, (Morlanwelz) and some secondary-school teachers, including Emma Castelnuovo (Rome) e Lucienne Félix (Paris):

Elle réunit les vraies compétences et elle résulte de la prise de conscience que l'équipe la plus puissante qui se puisse constituer aujourd'hui pour aborder ces problèmes doit être formée de ceux qui ont montré dans leurs travaux une préoccupation couvrant en même temps plusieurs domaines : mathématiques et psychologie ; histoire des mathématiques comme histoire des réalisations mentales de certaines relations ; pédagogie comme activité englobant le monde des relations mathématiques mêlé à des techniques de transmission et des obstacles dans l'acte d'apprendre, etc. (Cf. L'enseignement des mathématiques , Neuchatel, Delachaux & Niestlé, 1955, Préface)

From the plan of work of CIEAEM, and later from its publications (1955, 1958), emerges not only the importance attributed to psychology and pedagogy but also the attention given to the students and the role of the secondary teachers, who are actively involved, the need of considering all the school levels (from primary to university), the key role of concrete materials, the empirical research and the relation between mental and mathematical structures.
Choquet, Dieudonné and Lichnerowicz are part of the influential group of mathematicians that worked starting in the 1930s under the pseudonym of Nicolas Bourbaki. Bourbaki's views and Piaget's ideas - which are considered at the time as mutually complementary through the links established by the notion of "structure" which arises in both mathematics and developmental psychology - give rise to a new approach to the teaching of mathematics usually know as the New Math movement.

20-21 October 1952 - The first meeting of ICMI takes place in Geneva with the object of reorganising the Commission and drawing up a plan of work.

Jean Piaget

The committee is constituted thus:
Honorary President: H. Fehr,
President: A. Châtelet,
Vice-President: D. Kurepa,
Secretary: H. Behnke
(EM 39, 1942-1950, p. 161).
The meeting concludes with a visit to the Bureau International de l'Education, directed by Jean Piaget.

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21 February 1953 and 15 January 1954, Paris - The Executive Committee of ICMI is completed with the co-optation of other members:

Honorary President: H. Fehr
President: A. Châtelet
Vice-Presidents: D. Kurepa, S. MacLane
Secretary: H. Behnke
Treasurer: G. Ascoli
Members: A.F. Andersen, E.W. Beth, R.L. Jeffery, E.A. Maxwell,
Ex-officio: M. H. Stone, President of IMU
(EM 40, 1951-1954, pp. 81-82 ).
During the meeting of 15 January 1954 it is established that the contribution of the ICMI to the upcoming International Congress of Mathematicians will consists in two inquiries and an exhibit of books and documents:

• "Inquiry on the Part of Mathematics and the Mathematician in Contemporary Life" D. Kurepa is charged with presenting a general report
• "Inquiry on Mathematical Instruction for Students between 16 and 21 years of age (programs, methods,...)" . A general report of this inquiry is not planned; the national sub-commissions will send a report via their delegates.(cf. ICMI Archives, 14A, 1952-1954, p. 81, EM 40, 1951-1954, pp. 82-84).
• " Exhibition of books and documents concerning actual mathematical instruction for students between 16 and 21 years of age" (text books, works on methodology, pedagogy, programs and themes for examinations or competitions, popular mathematical texts, etc.), accompanied by explanatory panels will be organised under the care of the Centre National de Documentation Pédagogique of the French Ministry of National Education. (EM 40, 1951-1954, pp. 85-90).

The lack of precise terms of reference for governing the activities of the Commission gives rise to a source of friction between the ICMI's president Châtelet and the Executive Committee of the IMU. Some of the causes of discontent become apparent in the correspondence:

M. Stone, IMU president, to A. Chatelet:

It is my understanding that the Commission has proposed an arrangement whereby it will seek the adherence of several nations and set up special national committees in the adhering nations to work with the Commission. I believe that activity of this kind is inappropriate for a Commission of the Union and that it would lead to intolerable confusion as to the relations between the Union, the Commission, and the nations adhering to one or the other. My own immediate suggestion as to the proposed way of handing the relations between the Commission and the national bodies interested in supporting it would be to urge all interested nations to adhere to the Union and to arrange for the appointment of suitable persons to the National Committees for Mathematics which have to be set up as part of the procedure of adhering to the Union. The Commission could then arrange for direct contacts with these National Committees by co-opting as members or as liaison agents appropriate members of the National Committee. (ICMI Archives, 1952-1954, 3.11.1952)

W. Hodge, member of the EC of IMU, to Stone:

About ICMI, I agree very strongly that something must be done to curb its activities. At a recent meeting of our national committee very grave concern was expressed at the fact that so many of the Commission's activities were carried on behind our backs and that we were being let in for responsibilities we know nothing about. They are demanding all sorts of things for individuals who have merely been asked to help in minor capacities, and their behaviour is quite unfair to these individuals and to the National Committee. I learn, too, that they are assuming quite unjustifiable rights in regard to their membership; e, g. they claim the sole right to replace any individual member who resigns. I think it will be necessary to lay down very precise terms of reference for the Commission, and to define its powers very rigidly. It will also be necessary to select a president very carefully. I agree that we should get rid of Châtelet ( IMU Archives, 31.5.1954, cfr. Lehto 1998, 111).

M. Stone to Châtelet:

In connection with the Constitution of the National Sub-Commissions, I recall our agreement that each such Sub-Commission is to be in the first place a Sub-Committee of the National Committee for Mathematics in the Country which it represents. (ICMI Archives, 1952-1954, 29.7.1954)

31 August-1 September 1954, The Hague - The Second General Assembly of IMU determines the Terms of Reference of the Commission on the Teaching of Mathematics and the name International Commission on Mathematical Instruction (ICMI) is adopted

ICMI consists of 10 members-at-large and 2 national delegates named by each National Adhering Organisation of the IMU. Precise rules concerning the officers and the Executive Committee are given. ICMI has a relatively free hand in its internal organisation, but IMU retains control on this important point: the President and the ten members-at-large of ICMI would be elected by the General Assembly of the IMU on the nomination of the Union's President. The Executive Committee of ICMI will be composed of a president, a secretary, two vice-presidents, and three additional members elected from among the members of the Commission. The President of IMU is an ex officio member of all Commissions of the Union (E. BOMPIANI, Union News. Record of the Second General Assembly held on August 31 - September 1, 1954 at the Hague, Internationale Mathematische Nachrichten, 35-36, 1954, 4-14 and EM, 40, 1951-1954, pp. 92-93). With regards to the aims of the ICMI :

The Commission shall be charged with the conduct of the activities of IMU, bearing on mathematical and scientific education, and shall take the initiative in inaugurating appropriate programs designed to further the sound development of mathematical education at all levels and to secure public appreciation of its importance. (E. BOMPIANI, Record of the Second General Assembly, op. cit., 12-13, and EM, 40, 1951-1954, p. 93)

In keeping with the decisions made in The Hague, the Executive Committee of the ICMI is to be renovated starting in January 1955. The General Assembly of the IMU nominates the ten members-at-large who will be part of ICMI ( Y. Akizuki (Japan), G. Ascoli (Italy), H. Behnke (Germany), Ram Behari (India), P. J. Dubreil (France), J.C.H. Gerretsen (Netherlands), R.L. Jeffery (Canada), D. Kurepa (Yugoslavia), E.A. Maxwell (England), M.H. Stone (USA), and designates H. Behnke as president of ICMI (EM 40, 1951-1954, p. 91).

2-9 September 1954 - The XII International Congress of Mathematicians is held in Amsterdam under the presidency of Jan-A. Schouten.

(EM, 40, 1951-1954, 100-104,EM II s., 1, 1955, pp. 93-191)

Amsterdam,
Royal Tropical Institute

1553 regular members from 55 nations participate.
Section VII, dedicated to Philosophy, History and Education includes two invited lectures, one by K. Piene on School mathematics for Universities and for life and the other by C.T. Daltry on Self-education by children in mathematics using Gestalt methods - i.e. learning-through-insight and the report by D. Kurepa on The role of mathematics and mathematician at present time (Cf. Proceedings of the International Congress of Mathematicians 1954, Groningen, Noordhoff - Amsterdam, North-Holland Publishing Co., 3 vols., 1954-1957, III, 297-324). The abstracts of 25 short lectures (12 in volume I and 13 in volume II) expressly dedicated to the teaching of mathematics are published in the Proceedings; of these some are dedicated to mathematical instruction for students between 16 and 21 years of age.

Duro Kurepa

The report by Kurepa (cf. also EM II s., 1, 1955, pp. 93-111 , with the Questionnaire given in an appendix) refers to the reports of the subcommittees of Germany (E. Kamke), Austria (O. Weinberger), France (G. Darmois), Holland (D. Dantzig), Italy (G. Ascoli) and the United States (A. M. Gleason) and concerns the following points: What is mathematics and who are mathematicians; the development of mathematics; publications; mathematics laboratories created in large commercial, industrial, and economic enterprises; mathematics institutes; the employment possibilities for mathematicians (new applications in industry); new fundamental acquisitions (sets, functions, logic); new machines for calculation; the growing importance of statistics and its applications to physics, medicine, human sciences, arts; the need for collaboration of mathematicians with scientists in other sectors of research (fécondation interscientifique, Kurepa cites as examples IBM, the Cowles Commission which relies on collaboration between mathematicians and economists, cybernetics, fruit of the collaboration between engineers and mathematicians); the growing collaboration between mathematicians and industry. Kurepa concludes his report by reaffirming the fundamental role of mathematics in human activities and underlining as well its function as a mutual means of comprehension between individuals. From this follows the importance of adjusting the teaching of mathematics to meet the new requirements of society.

Daltry calls attention to Max Wertheimer, one of the founders of the Gestalt school of psychologists, and to his book, Productive Thinking, and proposes a method of teaching mathematics that begins with problem solving, bearing in mind Wertheimer's suggestions: "first contemplation of the problem as a whole, second the following of 'hunches' or tensions, third the flash of insight... Children would then learn by doing, their education would be self-education - the most enduring" ( Proceedings of the International Congress of Mathematicians 1954, op. cit., III, 299-300).

Kay Waldemar Kielland Piene

Piene begins with the ascertainment that the school has become a school for the masses and thus he holds that "the mathematics program in schools must in our days be determined according to what is useful later on - in studies or in life" (Ibid, 320). He proposes a minimum program that should be taught in all kinds of schools and invites teachers to recall the unitary character of mathematics and to bear in mind the research work within psychology.

Maurits C. Escher, Day and Night

During the Congress are exhibited IBM electronic calculators and other computers. At the Royal Tropical Institute there is an exhibit of mathematics books and, under the auspices of ICMI, curators A. Cardot and E.W. Beth prepare an exhibit of didactical and pedagogical works in mathematics. An exhibit of works by M.C. Escher is on display in the Municipal Museum of Amsterdam.

29 October 1954, Paris

The outgoing president of the ICMI, Chatelet, convokes a meeting of the Executive Committee to discuss the formation of the new EC on the basis of the decisions taken at The Hague. The president nominated by the General Assembly of the IMU, Heinrich Behnke, presents the outlines of the circular that will be sent to the national committees directing them to nominate their national delegates. In particular, he underlines that: "il est entendu, en particulier, que la lettre-circulaire soulignera l'intérêt que présente le choix de délégués qui soient très au courant de toutes les questions concernant l'enseignement moyen, et recommandera, d'autre part, de maintenir, autant que possible, en fonctions les délégués antérieurement désignés par les sous-comités nationaux pour les représenter à la CIEM" (cf. ICMI Archives, 14A, 1952-1954, p. 22)

Henri Fehr

2 November 1954 - Henri Fehr, founder and director of L'Enseignement Mathématique , dies.

Secretary General of the ICMI since its founding and Honorary President since 1952, Fehr was an untiring organiser of the Commission.

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Livia Giacardi
March 2008

Editors: Fulvia Furinghetti (Università di Genova) and Livia Giacardi (Università di Torino)
Multimedia Author: Tiziana Armano (Università di Torino)
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