Drama at the Tree House

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’.)

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