Proof matters. It's the name of the game. I'm a mathematician and I'm going to be a teacher and it's not wrong to get students into that mindset. Proof is justification. Proof is the confidence in knowing that you're right, because you can fully explain your point of view. Proof is covering all your bases. Possibly most importantly, proof is so very often beautiful.
I really enjoy mathematics. I hope to get some others to really enjoy mathematics with me--to bring them to a point where they can appreciate the elegance and austerity of it all. But, one might ask oneself, why should I?
Math is one of the only field of studies that is genuinely sure of the conclusions it draws. It achieves this by being aware of its context. Any student of the subject needs to know that all of mathematics is based on rules. Where those rules apply, mathematics reigns. One only needs to lay the foundations and the citadel appears whole, pristine, and without effort. It is a nearly perfect structure in which every single block rests firmly and precisely on the blocks beneath it. The mortar that holds that structure together is proof. Proof matters.
As I encounter some delightful things in mathematics, I intend to place them here that others may appreciate them. I'm starting this blog under duress. However, maybe I can make something useful and elegant in its own right.
-Mark
