The Role of Education and Visual Experience in Geometric Intuition
Abstract
How do experience and education transform our geometric intuitions ? The lecture reviews several experiments carried out among children and adults from relatively isolated populations with no access to formal mathematics education. Their results demonstrate the presence of deep intuitions for all the essential concepts of geometry, whether Euclidean or even non-Euclidean (on the sphere). Thus, the major categories of geometric thought (circles, straight lines, parallels, etc.) develop relatively spontaneously in the absence of explicit instructions. Are they then derived from perception ? The lecture continues with an analysis of experiments carried out on the mathematical sense of congenitally blind people. These show that vision is not necessary for the development of universal mathematical representations and their neural networks. Thus, geometric intuition appears to be fundamental : in our species, it is probably this intuition that underpins our apprehension of the sensible world, rather than the other way round.
