This post focuses on how we can, and why we should, take the time to craft motivated proofs, i.e. proofs which do not contain any puzzling steps. Imagine that you’re a mathematician and you have just proven a new theorem. You’re excited to show your proof to colleagues around the world, not just to get … Continue reading Motivated Proofs
This post focuses on efficient mathematics, why it is valuable, and the challenges involved in producing it. “A good mathematician is a lazy mathematician,” at least according to some of my old math professors. It’s a jokey phrase, but one which contains an important element of truth: good mathematicians find ways to do mathematics quickly … Continue reading Lazy Mathematicians?