> How to make sense of a proof > When you finish you should know why each step follows from what came before. You may not see how anyone could have thought to

> How to make sense of a proof > When you finish you should know why each step follows from what came before. You may not see how anyone could have thought to do the proof that way, but you should be able to see that it is correct. Knowing that something is true is not the same as knowing why it is true. I don't know what the problem is with understanding, but here's three thoughts: 1. You need a deeper level understanding - you can't understand a problem at the same level you encountered it. Perhaps, understanding different but related areas, so you see the same problem from a different perspective. Perhaps understanding the formal system that is used to define terms used in the problem description. 2. You need familiarity, which creates the feeling of "intuition". If you know how it behaves in all situations, you will feel you understand it, even if you don't. So, just lots of practice/exercises. 3. You need to fully understand the components from which the problem is formed. For example, the natural numbers and addition, and build up from there.