One thing that definitely feels like “magic” is Monstrous Moonshine (en.wikipedia.org/wiki/Monstrous_moonshine) and stuff related to the j-invariant e.g. the fact that exp(pi*sqrt(163)) is so close to an integer (en.wikipedia.org/wiki/Heegner_number#Almost_integ…). I hardly understand it at all but it seems mind-blowing to me, almost in a suspicious way.