[vjerancrnjak]

There's also many assumptions in the initial m^2 != 2n^2 proof that many would have a hard time instantly grasping. Problem is stated in three different ways, takes quite a bit of knowledge to instantly see they are the same problem.

The proof stops at 2n-m and m-n, subtly, because that is another smaller case of can two squares fit in a big square. If you do the expansion of 2(m-n)^2 and (2n-m)^2 to see if there's a fit, you see there isn't but the proof does not need to deal with that and to me the reason is very subtle, wordy.

Graph theory proofs feel very similar.