Charles Méray’s Geometry Tested in the Classrooms

When he published his Nouveaux Éléments de Géométrie in 1874, Charles Méray had already written the book that made him the first mathematician to propose a coherent theory of irrational numbers. Had he continued on this path, he would be more famous than Cantor today. A professor of advanced mathematics at the University of Dijon, 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 was cruel: ‘[geometry]... Finding it silent on three-dimensional space, the geometry believer willingly believes that it does not exist’. So, the Nouveaux Éléments 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 rejected by academic authorities, but new attempts at the beginning of the 20th c. would give satisfaction to many teachers who were keen to test the new methods: starting with three-dimensional geometry dealing with everyday 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 1901, first in Burgundy, then in national academic newspapers.