Why Proof Presentation Matters: Brussels 2016

When we read a new proof, we hope to attain three goals: (i) to check it’s correct; (ii) to recall it later; (iii) to reuse the ideas it contains. Ideally, we would also like to achieve these goals efficiently, without expending unnecessary energy. In this talk I present a framework to further analyze these goals and argue that meeting them is crucial to the advancement of mathematical knowledge. I argue that the way a proof is presented can have a big effect on whether, and how efficiently, we achieve our goals, and illustrate these issues with a case study from geometry.