ABSTRACT
When he published his New Elements of Geometry in 1874, Charles Méray had already written the paper which made him the first mathematician to propose a coherent theory of irrational numbers. Should he have continued on this path, he would be more famous than Cantor today.
But France lost the war in 1870. Méray’s residence in Dijon was occupied by Prussian officers and he swore he would never deal with Germans again.
A professor of advanced mathematics at the University of Burgundy, he turned to elementary mathematics and focused on teaching geometry to beginners. According to him, plane geometry “does not belong to the reality of things, as nature only offers space figures”. His view on old fashioned geometry is cruel: “like those maniacs whose houses are cluttered with patched-up old wares, shown to all comers, preserved and handled like priceless jewels, [geometry] still thinks it adorns itself by loading itself with childish objects that twenty centuries have faded... By dint of finding it silent on three-dimensional space, the follower willingly believes that it does not exist”.
So, the New Elements show another way of introducing and thinking about geometry, which can be linked to the fusion movement in Europe, including the use of algebra, especially for locus problems and conic sections. In 1874, classroom experiments had been refused by academic authorities, but new attempts at the beginning of the 20th century would give satisfaction to many teachers who were keen to test the new methods: starting with three-dimensional geometry dealing with everyday life objects, use of visual intuition instead of abstract axioms, use of movement and geometric transformations, etc. Enthusiastic reports with many mentions of success were published in Burgundy in 1901.
We had the opportunity to discover Méray’s personal papers in the cellar of his former house in the vineyards, including a special folder devoted to everything about the 1903 and 1906 editions of the New Elements. From the list of recipients of copies of the book to the correspondence between Méray and his disciples, all of them give us an opportunity to take a look at the backyard of French pedagogical institutions, printers, teachers and amateurs, not to mention an undisputed master of educational thinking on the foundations of geometry for beginners, who appeared very interested in the success of his methods.
SELECTED BIBLIOGRAPHY (texts will be translated into English)
Méray, C. (1874). Nouveaux Éléments de géométrie. Paris: Gauthier-Villars. (2nd ed.,1903, 3rd ed. 1906). Dijon: Jobard.
Méray, C. (1892). Considérations sur l’enseignement des mathématiques, Revue bourguignonne de l’enseignement supérieur. Dijon, pp. 105–129 and 269–295.
Sources: correspondence between Meray and a variety of academics, mathematicians and teachers about his New Elements of Geometry and testing the new method in the classroom.