That's not really a good point. Sometimes a question can be designed to show you understand a concept. If you solve the problem without demonstrating the concept the answer is wrong, regardless if the logic is correct.
No, literally a correct proof is correct. There's nothing more or less to it.
If you can prove something you understand some aspect of the problem. Pure math (like abstract algebra) needs no "intuition".
It's not something you can really understand unless you've been through multiple proposition, theorem, proof style classes where all you do is prove things.
Sure, sure, I've never taken advanced math classes to be able to understand. But I have been through enough reactor design, unit operations, transport phenomena courses to know that if the reactor volume is the correct volume, you can still be wrong if you used X numerical method instead of Y method or if you didn't state Z assumption, or set up all the equations. But whatever floats your boat.
I'm not trying to hurt your ego, although you seem to think I am.
A proof is literally correct if it's correct. I'm just repeating myself at this point, which is exactly why I said it's not something you can understand. Because you're having trouble understanding what I'm saying. ---
"Never argue with an idiot, they drag you down to their level, then beat you with experience."