The discovery of non-Euclidean geometry in the 19th century radically undermined traditional conceptions of the relation between mathematics and the world. Instead of assuming that physical space was the subject matter of geometry, mathematicians elaborated numerous alternative geometries abstractly and formally, distancing themselves from reality and intuition. Transcript The mathematician has only one nightmare: to … Continue reading “Repugnant to the nature of a straight line”: Non-Euclidean geometry