It reminds me of a YouTube course on general relativity where the instructor went from most basic elements and built up towards a complete description of the full math. I was able to follow along step-by-step at the time but there were a lot of quite complicated steps which I would have no ability to reproduce myself.
I recall a few of the steps made assumptions on our ability to calculate. I think, for example, they narrowed down the set of all vector spaces to just those spaces that were differentiable. I may be mis-remembering the precise detail but it was something along those lines, and this was just one of a few instances of this kind of "throw away cases that we are unable to calculate" along the path. In some cases the narrowing was justified but in a few the instructor admitted that the entire reason we were excluding possible sets of solutions was because they would otherwise make the next steps impossible.
I recall a few of the steps made assumptions on our ability to calculate. I think, for example, they narrowed down the set of all vector spaces to just those spaces that were differentiable. I may be mis-remembering the precise detail but it was something along those lines, and this was just one of a few instances of this kind of "throw away cases that we are unable to calculate" along the path. In some cases the narrowing was justified but in a few the instructor admitted that the entire reason we were excluding possible sets of solutions was because they would otherwise make the next steps impossible.