Early last month Shinichi Mochizuki’s proof of a famous conjecture in number theory known as the abc conjecture appeared in Publications of the Research Institute for Mathematical Sciences (PRIMS). While the publication of the first proof of an important theorem is usually cause for celebration, the publication of Mochizuki’s proof has caused controversy because mathematicians … Continue reading It’s not as easy as abc: What happens now a controversial proof has been published?
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?