Why are mathematical proofs so hard?
I feel like i am memorizing the proofs rather than learn how to prove

You can't learn &quot;how to prove&quot;. &quot;Proving&quot; is not a mechanical process, but rather a creative one where you have to invent a new technique to solve a given problem. A professional mathematician could spend their entire life attempting to prove a given statement and never succeed.

I can easily deal with any type of proofs that i saw before ( eg. once i saw the proof of a recurrence question i became pretty good at prooving them). My problems start when i face an unusual question.

That is normal. Any mathematics &quot;proofs&quot; course isn't designed to teach you how to take an arbitrary problem you've never seen before and be able to solve it (since nobody, not even the best mathematics professors can do that). Rather, your learning goals are

Learn how to &quot;read&quot; proofs and judge their correctness

Learn how to &quot;write&quot; down a proof in the right mathematical language

Learn about known proof &quot;techniques&quot; and how to apply them


If you are working on a new, unknown problem, it is normal that you might not be able to solve it. However, knowing and having memorized other proof techniques may help you. Often proofs involve combining a new idea with existing known proof techniques. The more, and the more varied the proofs you already know are, the better your chance of being able to solve the given problem.
You are on the right track. You should simply keep studying proof techniques. The exercises you are doing are good. Don't worry if you get stuck. As you get more experienced and your &quot;toolbox&quot; of techniques grows, you will be able to solve exercises that are less &quot;alike&quot; the previous ones you have seen.