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 g … | Continue reading
Euclid inspired Gothic architecture and taught Renaissance painters how to create depth and perspective. More generally, the success of mathematics went to its head, according to some, and created dogmatic individuals dismissive of other branches of learning. Some thought the unc … | Continue reading
The use of diagrams in geometry raise questions about the place of the physical, the sensory, the human in mathematical reasoning. Multiple sources of evidence speak to how these dilemmas were tackled in antiquity: the linguistics of diagram construction, the state of drawings in … | Continue reading
My general teaching philosophy can be summarised in three principles or axioms regarding learning. They concern the source, the process, and the goal of learning respectively.My first axiom is this: In a perfect world students pursue learning not because it is prescribed to them … | Continue reading