Valhuon 1883-Paris 1960


Brief scientific biography

Albert Châtelet was born on October 24, 1883, in Valhuon, a village of 600 inhabitants in the north of France. His father, François Châtelet, was the local elementary school teacher; a man also interested in farming, he received prizes for farming courses and for his reports to local societies for the improvement of agriculture. From the Valhuon school, Albert Châtelet went to the Saint-Pol secondary school, and then to the Douai lycée , where, thanks to a public grant, he prepared for, and finally in 1904 succeeded in passing, the highly selective competitive examination for the école Normale Supérieure, (ENS) in Paris. Between 1905 and 1908, after a year of military service, he therefore took the usual curriculum of the ENS, which culminated with a second place at the Agrégation de mathématiques , just behind Georges Valiron. Scholarships from the Commercy Foundation then allowed Châtelet to prepare a thesis (initially supervised by Jules Tannery, the scientific director of the ENS), Sur certains ensembles de tableaux et leur application à la théorie des nombres, which he defended on April 27, 1911 (after Tannery's death), after the publication of several Notes on the subject in the Comptes rendus de l'Académie des sciences. Châtelet also chose the same themes for the Foundation Peccot-funded lectures he gave at the Collège de France between April and June 1912 and published in 1913 under the title Leçons sur la théorie des nombres. In these first mathematical works, Châtelet studied continued fractions and algebraic numbers in the arithmetical tradition created by Charles Hermite, but he systematized the number-theoretical use of matrices (then called tableaux), and moreover, included recent German developments of number theory, for example the theory of ideals and Hermann Minkowski's geometry of numbers-a rare case in the French mathematics of the time-obtaining in particular new explicit results for cubic fields.
Just before and after his thesis, Châtelet was employed as a teacher in classes préparatoires (special classes preparing the competitive examinations for the ENS or the école polytechnique) in Paris and then in Tours. After these first experiences, he was charged with the lectures in rational and applied mechanics at the Faculty of Sciences and at the Electrotechnical Institute of Toulouse, in the south of France. He had just been given a position back in his home region, at the University of Lille, in 1914, when the First World War broke out. Mobilised on August 2, 1914, in the health services of the army, he finally joined the Commission d'expériences d'artillerie navale de Gâvre (Commission for Experiments in Naval Artillery, near Lorient in Britanny) in April 1916. He worked there (like other mathematicians such as Jules Haag or Arnaud Denjoy) on a variety of ballistic questions, including "the loading, priming and efficiency of projectiles, [...] personally directing with great competency the preparation and execution of firings and experiments of all kinds," as said in the post-War testimony of satisfaction from the War Ministery, which also praised Châtelet for "his practical sense, a great clarity of judgment and a remarkable spirit of implementation." Châtelet finally took up his position in Lille in February 1919 (although he continued to act for years as advisor for the Artillery Commission). From this moment, although he still published a few research articles on number theory and algebraic structures, his career took a new direction; he took on increasing administrative responsibilities, first as Doyen de la faculté des sciences de Lille (Dean of the Faculty of Sciences of Lille) from 1921 to June 1924 and then as Recteur de l'Académie de Lille (State Superintendant of Education for the Lille region) until January 1937. The whole region, and in particular the University, had been severely affected by the War, and Châtelet was at the origin of many projects for its reconstruction during this period. Among these, we can mention an institute of fluid mechanics, a laboratory of astronomy, an observatory, an institute of social sciences, the construction of a new medical faculty, housing and a restaurant for students.
In 1937 Châtelet was appointed Director of Secondary Education at the Ministry of Education-meaning that he was in charge of the organization of teaching in France from elementary school to high school-and launched, with the support of the Minister, Jean Zay, a modernization and democratization of the school system, unifying in particular the programs of the various tracks. In 1940, he was fired by the Vichy Government and found himself for a time without a position but the Faculty of Sciences of Paris decided to create a chair for higher arithmetic and proposed Châtelet as its candidate. Although this proposal was rejected by the Government and Châtelet was officially posted to another university, he nevertheless lectured (on higher arithmetic) in Paris. In 1945 this position became permanent when Châtelet was hired as Associate Professor in April, and then full Professor in October, in the newly-created Chair of Arithmetic and Number Theory of the Faculty of Sciences of Paris; he would become Doyen (Dean) of the Faculty in 1949 until his retirement in 1954. He worked actively for the renovation of the University and its buildings. It was also during this period, from 1947 on, that Châtelet organized with Paul Dubreuil a regular seminar on algebra and number theory which would continue under various organizers until the present day. He also participated in the edition of Georges Halphen's and Henri Poincaré's complete works.
Châtelet was very active at a high administrative and political level. From July 1945 to August 1946, he was director of the Youth Movements and Popular Education (Mouvements de jeunesse et de l'éducation populaire) at the Ministery of National Education . He wrote various reports for the Government about education, research and universities, and became vice-president of the Commission de la recherche scientifique et technique, in charge of planning a modernization and equipment program for theoretical and applied research. He was also engaged in the development of cultural relations with other countries: for example in December 1949 he was sent to establish cultural agreements with Vietnam, and later promoted scientific and cultural links with the Soviet Union, Germany, China, as a means to further international peace. He also belonged to several commissions of UNESCO, and chaired the International Commission for the Teaching of Mathematics from 1951 to 1954 (he was the first President of the renovated ICMI). From 1955 on, he was also president of the Union Rationaliste, an association created by Paul Langevin in the 1930s to promote rationality and science in public debate. The high point of Châtelet's political engagement was probably his participation in the Union des Forces Démocratiques (UFD, Union of Democratic Forces), a political party created in 1958 around personalities such as Alfred Kastler, Pierre Mendès-France, François Mitterrand and Laurent Schwartz; it was a left-wing, non-communist party, opposed to Charles De Gaulle's policy, in particular with respect to colonization. Châtelet, a militant against the Algerian War, accepted the candidacy of the UFD against De Gaulle (and the Communist Party candidate, Georges Marrane) in the French presidential election of 1958, obtaining 8.4% of the votes of the electoral college. Albert Châtelet died in Paris on June 30, 1960.

Commitment to education

Châtelet expressed his interest in mathematical education as early as 1909 (the same year as his first number-theory papers), when he published a study of the principles of geometry and their impact on elementary teaching in a pedagogical journal. From then to his death, he maintained his interest; due to his various responsibilities, both at a local and a national level, Châtelet was able to renovate the French educational system, extensively planning new sites, facilities and buildings. He also organized or participated in several conferences about education. As for the ICMI, Châtelet's correspondence allows us a glimpse of the difficulties faced by its first officials: to decide the conditions for admission and representation of new countries (when mathematical life in the 1950s could vary considerably from one country to another), to solve delicate issues of independence with respect to the different national mathematical societies and to the International Mathematical Union (particularly explicit on the occasion of the 1954 International Congress of Mathematicians in Amsterdam and the subsequent administrative meeting of the IMU in The Hague), or simply to obtain recognition for pedagogical work. In August 1954, Heinrich Behnke, then secretary of the ICMI, wrote to Châtelet:
"It is a very difficult matter to have mathematicians, well-known for their research work, engage with problems of education. Most of our colleagues refuse to be active in our commission because they regard this kind of work as of little value, and then even neglect to forward circulars. Twice I have sent out a letter asking to set up sub-commissions and to designate delegates, to all member national organizations, using a list with addressees which I had received from Prof. Bompiani. There were only a few answers. ... It was not so easy to convince the organization committee in Amsterdam of the value of our efforts." (Fonds Albert Châtelet, 81J doc. 21, Archives départementales du Pas de Calais, Arras, France).
The journal L'Enseignement mathématique, which had become the official journal of the ICMI, also suffered various problems (in particular financial) and Châtelet accepted its directorship after Behnke replaced him as president of the ICMI.
Châtelet was also active at a pedagogical level. Besides developing new university courses (for instance on vector calculus and algebra), he launched a collection of scientific textbooks for secondary teaching with the publisher Baillière (including his own Géométrie et algèbre, written in 1935 with Roger Ferrieu, or an Arithmétique of 1943). He also directed a series of books for the teaching of arithmetic at a more elementary level (nursery and primary schools), written together with schoolteachers, which enjoyed numerous editions. Like Jean Zay, as well as the psychologist Jean Piaget with whom he collaborated, Châtelet favored an active and inductive pedagogy, developing the critical and reflexive minds of the pupils. One of his arithmetic books for 10-year-olds has the title: I Learn to Reason. "The various textbooks should be linked by their very content", Châtelet wrote, and for this "it suffices to accept the need for a humanist learning. e.g., in physics, not to be satisfied with technical study, but to also present the problems with their philosophical, historical, etc., aspects."
Methods should be based on concrete manipulation of material objects, or personal observation, and teachers should encourage collaboration among pupils, as well as among themselves. Châtelet's books for elementary classes thus promote the use like dominos, sticks, and marbles, and his correspondence with his publisher shows him discussing details of color illustrations of hens and farmers, as well as whether or not one can legitimately write a product as "100 m x 100 m" in the chapter on areas. Châtelet however insists on a non-dogmatic approach. In an address to the Congress of Childhood in 1931 on number learning, he concluded: "the good method, the true method, the unique method, is the one [the schoolteacher] knows how to handle and to apply. The best way of teaching is that which each teacher practices in her class, provided that she does so confidently and joyfully."

Primary bibliography

A. CHÂTELET 1911, Sur certains ensembles de tableaux et leur application à la théorie des nombres, Annales scientifiques de l'école normale supérieure 28, 105-202.
A. CHÂTELET 1913, Leçons sur la théorie des nombres, Paris: Gauthier-Villars.
A. CHÂTELET, J. KAMPé de FERIET 1924, Calcul vectoriel. Théorie, applications géométriques et cinématiques destinés aux élèves des classes de mathématiques spéciales et aux étudiants en sciences mathématiques et physiques, Paris: Gauthier-Villars.
A. CHÂTELET 1928-9, La théorie des nombres positifs et négatifs dans l'enseignement du second degré, L'Enseignement scientifique, nov. 1928, 40-48; décembre 1928, 70-76, janvier 1929, 107-115, février 1929, 136-140, mars 1929, 169-174. Repr. as La théorie des nombres positifs et négatifs dans le second degré, Paris: Eyrolles, 1929.
A. CHÂTELET 1929, Les modifications essentielles de l'enseignement mathématique dans les principaux pays depuis 1910: La France, L'Enseignement mathématique, 6-12.
A. CHÂTELET (dir.), L. BLANQUET, E. CRéPIN 1947, Pour apprendre les nombres, à l'usage des maîtres de l'école maternelle et des cours préparatoires des écoles primaires, suivi de J'apprends les nombres, Paris: Bourrelier (one of several textbooks with various collaborators at the same publisher).
A. CHÂTELET and R. FERRIEU 1935, Géométrie et algèbre, classe de 3e, Paris: Baillière et fils.
A. CHÂTELET 1954-1966, Arithmétique et algèbre modernes, 3 vols., Paris: PUF.
A. CHÂTELET 1953, Notice sur les titres et travaux scientifiques de Albert CHâTELET. Archives de l'Académie des sciences, Dossier Châtelet, Paris.

Secondary bibliography

Collectif, Hommage à Albert Châtelet, plaquette éditée à l'occasion de l'inauguration du centre universitaire Albert Châtelet le 6 juin 1963, sous la présidence du ministre de l'Education nationale.
CÉLINE SENAME 2001, Répertoire numérique détaillé du Fonds Albert Châtelet, 81 J 1-128, Arras-Dainville: Archives départementales de Pas de Calais
JEAN-FRANçOIS CONDETTE 2007, Albert Châtelet, in C. Pennetier (ed.), Dictionnaire biographique du mouvement ouvrier et du mouvement social. Période 1940 à 1968, Paris : L'Atelier, vol. 3: CA-COR, 254-257.
JEAN-FRANçOIS CONDETTE 2009, Albert Châtelet. La République par l'école (1883-1960) , Arras: Artois Presses Université.
SÉBASTIEN GAUTHIER, Albert Châtelet: de la théorie des nombres à la politique universitaire, in C. Goldstein and D. Aubin, La Grande Guerre des mathématiciens français, to appear.


Le Courrier rationaliste, 24 juillet 1960, 154-156.
L'Enseignement mathématique 2e s. 6, 1960, 1-2.
JOSEPH PÉRÈS 1960, NÉcrologie: Albert Châtelet, Annales de l'université de Paris, 4 (octobre-décembre), 578-582.
HENRI PARISELLE 1961, Notice Albert Châtelet, Bulletin de l'association amicale de secours des anciens élèves de l'école normale supérieure, 31-32.

Sébastien Gauthier
Université Claude Bernard Lyon 1, Institut Camille Jordan

Catherine Goldstein
CNRS, Institut de mathématiques de Jussieu