Designing Motivated Proofs: Nancy 2016

When writing a proof, we have to make decisions about what content we include, the notation that we use, and how we structure our argument. These decisions can have serious consequences for proof readers. In particular, the proof content, how it is presented, and the background of the intended audience, affect not only whether a reader can recognize each step is correct, but also whether she can grasp the role that the steps play in the argument and what prompted the proof author to introduce them. Proofs that successfully convey this information, which I’ll call motivated proofs, help readers to attain a deeper understanding and to more effectively adapt and reuse mathematical ideas than unmotivated ones. In this talk, I will use case studies to illustrate how decisions made by the proof author can affect the degree to which a proof is motivated, before suggesting some general techniques to help us write more motivated proofs.