Thanks to this discussion I now have a new idea that popped into my head:
Is mathematics an emergent phenomenon?
Hear me out on this one. Obviously we have to distinguish between a) that which mathematics describes and b) the formalism itself. But I think that in some cases an argument could be made that this line is blurred a bit. In any case, as we go “down the food chain,” so-to-speak, the understanding of mathematics that species have most likely decreases (for example, I would be shocked if ants could figure out a square root). Presumably the phenomena described by the mathematics is still there though. Where does complex mathematics “emerge” from this (if it emerges at all – perhaps it’s simply “there”)?
I don’t know why the nature of mathematics is so on my mind lately, but there you have it.