Unfortunately we need to postpone the next session (on the theme of Continuity and planned for 31st March). Victoria has decided to cancel or postpone current evening events at the Tree House due to the Government programme aimed at delaying the spread of corvid-19. Clearly this is a sensible move in light of the rapid escalation of developments in recent days. It’s a pity – I was just getting into the main story-line for our session – and Leon was practising using Desmos to show us nice examples of the various ways a function can be discontinuous. It’s only a postponement but, in light of current predictions, it is likely we shall not be able to resume until September or so.
We had some (modest) drama in the last session (Episode 4: Proofs and Fallacies) when some audience members took the part of students in a Lakatos seminar, and Leon and I had a dialogue highlighting the change in perspective on visual proofs in geometry that has occurred over the last 50 years. (You can see this dialogue if you missed it on the webpage for episode 4. )
Discussion following the talk focussed on ways that proofs, and how they are judged, change – both over time and across cultures. The case of the intermediate value theorem was mentioned and so was the issue of computer assisted proofs. I think I should have emphasised more the role of logic in mathematical proofs compared with science and medicine where empirical evidence plays a more dominant role. We showed an example (‘proving’ that all triangles are isosceles) where it was not the logic at fault but the diagram – although only slightly inaccurately drawn – was completely misleading. (The example may be found in E.A. Maxwell, ‘Fallacies in Mathematics’.)