Also, although I know this is not the point of your post, could you please share why you like that page/that blog.
i.e.: why is it trustworthy?
I mean to read the citations (and probably their citations) but maybe you already have convincing evidence that this guy(gal?) is methotical enough to be trusted
The link about research and life partners moved
One true thing that might be applicable: Usually math textbooks have 'neat' proofs. That is, proofs that, after being discovered (often quite some time ago) where cleaned up repeatedly, removing the previous (intuitive) abstractions and adding abstractions that allow for simpler proofs (sometimes easier to understand, sometimes just shorter)
Rather than trying to prove a theorem straight, a good intermediary step is to try to find some particular case that makes sense. Say, instead of proving the formula for the infinite sum of geometric progressions, try the infinite sum of the progression 1, 1/2, 1/4. Instead of proving a theorem for all integers, it it easier for powers of two ?
Also, you can try the "dual problem". Try to violate the theorem. What is holding you back ?
I am truly confused. This post does not endorse either side.
I just would like to note something about my cognitive process here: in the "step by step" argument, what I seem to be thinking is "rigorously the same torture" and "for more people". The argument may be sound, but it does not seem to be hitting my brain in a sound way
(just an example of such a disconnect, not a general defence of disconects)