Alternative Proof Presentations: San Diego 2018

The way a proof is presented can raise or lower the entry barrier required to understand it. As both students and researchers alike want to learn new mathematics, proof presentation is thus important both in teaching and research contexts. In this talk, I will consider different ways of presenting the same geometric proof to illustrate more precisely how presentation can make it easier or more difficult to understand. In particular, I will focus on how decisions about notation, diagrams and argument structure affect how efficiently the resulting proof presentation manages information.  Good information management can make it much easier to understand, while bad information management can make it much harder. As part of this discussion, I will also consider different senses of mathematical understanding.