It is very important to convince oneself to view the good work others have already done as potentially helping you, not being a burden.
It is observable that the "school-work" model of mathematics mostly presents us with obligations-to-study which are not well explained, apart from the usual threat-of-bad-grade and/or loss of funding. And, indeed, some of the traditional requirements are rather stylized, and have drifted over time, or have fallen out of sync somewhat with contemporary events, so the underlying utility can be obscured. But one should not be deceived by this picture of mathematics presented by "requirements" and such. Some things are very useful "even if they are required". :)
As some consolation, also the very model of "study" presented by school-math is itself considerably caricatured, in my opinion. The idea that one is not allowed to move forward without having done all the exercises and assimilated all the proofs of all the lemmas is needlessly and unhelpfully constrictive. Certainly not helpful in getting any larger perspective. Many of the usual exercises are merely makework, artificial, and not a good investment of time. A more mature and useful notion of "study" is to try to acquire awareness of the general pattern of events, some illuminating examples, and only return to low-level or foundational details when they become "action items", sort of thinking in terms of need-to-know.
That is, imagine there's no final exam, no quizzes, no weekly exercises to be graded, but that one should try be able to answer the "What's the point of this?" questions.
At a further point, if one wants to make genuinely useful contributions, genuinely advancing collective understanding, it is obviously necessary to have some awareness of what that collective understanding is already. Re-inventing things can be fun, and is inevitable, but one wants to do more.
In fact, I would argue that (a mature notion of) "study" is inseparable from (a mature notion of) "research". Or indistinguishable. In the endeavor of trying to improve one's understanding of some phenomena or structures, by looking at what other people have done and trying to organize it in one's mind, often one "accidentally" understands something that perhaps was not already well understood. Bingo: "research".