I'm learning how to write mathematical proofs now, and just today I wrote in my notes: "talk things through out loud". It really is amazing the clarifying eff

I'm learning how to write mathematical proofs now, and just today I wrote in my notes: "talk things through out loud". It really is amazing the clarifying effect it can have. We think we have a good idea of what some concept entails, but once we speak it (or write it down), it finally starts to take a more defined "shape".