I'm currently self-studying functional analysis. My general approach is to read each chapter, making sure I understand all the definitions and carefully follow every proof. I usually manage this part fairly well but sometimes I need to consult other sources to know why parts of certain proofs work.

I also want to improve my my proof writing and problem solving skills so I try to solve every exercise at the end of the chapter. I'm on chapter 3 of the book now and I've started to really struggle. I often don't even know how to begin the exercise. After spending time trying to work it out and failing, I usually resort to looking up a solution and they often turn out to be simpler than I expected. I can follow the reasoning but I never feel like I would have come up with it on my own.

The first two chapters went better and I at least had some initial ideas and sometimes just needed a hint to finish a proof. But now even after reviewing a solution I find that if I revisit the same problem days later I struggle to reproduce it correctly.

It’s starting to feel like I’m not making much progress if I regularly need to rely on hints or solutions. Is this a sign that there is something specific I should work on? What should I do when I have no idea how to even start an exercise?

I'm currently self-studying functional analysis. My general approach is to read each chapter, make sure I understand all the definitions, and carefully follow every proof. I usually manage this part fairly well but sometimes I need to consult other sources to know why parts of certain proofs work.

I also want to improve my proof writing and problem solving skills, so I try to solve every exercise at the end of the chapter. I'm on chapter 3 of the book now and I've started to really struggle. I often don't even know how to begin the exercise. After spending time trying to work it out and failing, I usually resort to looking up a solution and they often turn out to be simpler than I expected. I can follow the reasoning but I never feel like I would have come up with it on my own.

The first two chapters went better and I at least had some initial ideas and sometimes just needed a hint to finish a proof. But now even after reviewing a solution I find that if I revisit the same problem days later I struggle to reproduce it correctly.

It’s starting to feel like I’m not making much progress if I regularly need to rely on hints or solutions. Is this a sign that there is something specific I should work on? What should I do when I have no idea how to even start an exercise?