Lecture III

The mathematics existing in the age of Descartes[^2] and Copernicus can certainly be described more or less in the same terms as apply today. Take a modern mathematician, for example, who teaches geometry, and who uses his analytical formulas and geometrical concepts in order to comprehend some physical process. As a geometrician, this mathematician starts from the concepts of Euclidean geometry, the three-dimensional space (or merely dimensional space, if he thinks of non-Euclidean geometry.)[^3] In three-dimensional space he distinguishes three mutually perpendicular directions that are otherwise identical. Space, I would say, is a self-sufficient form that is simply placed before one's consciousness in the manner described above without questions being raised such as: Where does this form come from? Or, Where do we get our whole geometrical system?