> it's normal to not be able to derive proofs on your own without seeing them beforehand I STRONGLY disagree. Let's address this with an example: "Two planes

> it's normal to not be able to derive proofs on your own without seeing them beforehand I STRONGLY disagree. Let's address this with an example: "Two planes are either parallel or they intersect in a line" Someone who just finished high school should be able to "prove" it informally without even opening a text book. Of course high school education doesn't give you the tools to write a formal proof, but if you think about it for a while, then write an informal proof, when you finally open your book and read the formal proof it will be pretty obvious to you. Once you learn proper maths in University, you should be able to sketch a formal proof very quickly. Obvioulsy you cannot reinvent all the math from the last 5000 years all by yourself, so you need massive amounts of effort and study to learn (a part of) it. In my view, learning the basics of your problem space, then thinking informally about it, then (informally) writing your own theorems and proofs is the best way of learning. You won't come up with everything, but when you go to your book and read that all-important theorem you will think: "Aaaahhh! of course! how didn't I think of it!?"