TITLE: How do you resist thinking about you may not be able to go further in mathematics?
QUESTION [11 upvotes]: I believe that every mathematical "apprentice" more or less once found that some stuff that had been unclear somehow became clear; for example, some books might be unaccessible to you two years ago but totally accessible now. Even having these experiences, from time to time I would still be tempted to think that I may not be able to go further in mathematics when facing those now-unaccessible stuff. Now my question is how you develop a good mindset to turn away from the time-wasting behavior of doubting your own ability?
This question is possibly opinion-based, in all conscience; but it depends on people's flavor.

REPLY [3 votes]: Personally, I think back to times I previously thought this, and subsequently learnt the material anyway. It's especially noticeable in my current project of working through Awodey's Category Theory. Every so often I flick through the future chapters of the book and ask myself, "Can I understand the words on this page yet?" The answer is always no. Yet after I've read through a chapter and done the exercises, and thought around it a bit, I understand its content.
Similarly, I used not to know what a linear map was. I would look at any mathematical Wikipedia page and reel back from it in horror. Now, there's a reasonable chance that I will at least be able to parse a given Wikipedia mathematics page.
Remember the number of times in the past you've thought you couldn't do it, and the number of times in the past you became able to do it after working hard.