The place of geometry in a mathematical education

Abstract

It is a commonplace that pictures leave a deeper impress on the human mind than abstractions and, in spite of its abstract nature, that is also true of many part? of mathematics. A proof of a theorem or the construction of a counter-example is often suggested by pictorial considerations, and that is true of algebra and analysis as well as of obviously geometrical subjects like topology. (For entertaining examples see Professor J. E. Littlewood’s book [1].) There is obviously a connection between a developed geometrical intuition of that kind and the kind of spatial experience which ought to be furnished by a school mathematics course. No one would deny its importance and the writers of textbooks on ‘modern’ mathematics are well aware of the need to stimulate geometrical intuition. What has been called in question is the relation between that kind of geometrical intuition and the formal treatment of the euclidean plane based, albeit insecurely, on Euclid’s Elements. Indeed, the traditional treatment has been abandoned with indecent haste and without serious question. In Part I of this paper we make a plea for a re-consideration of the case for some kind of formal geometry as an indispensable part of the education of the more mathematically able children.