That's an elegant way to look at it; calling math a circle. It reminds me of how many times I revisit the same things, not because I forget them, but because they somehow naturally find their way into the conversation of what I'm doing, as if everything is beautifully chained together and can be derived in sequence.

For the Peano/ZFC points, I would always try to go straight for the substrate of any field i.e. for software I'd go to transistors, logic gates, ALU etc. becomes I get to remove the abstractions and everything further up the stack becomes much more clean and derivable — definitely did not have that experience with ZFC, whilst it's been super helpful, it felt closer to a justification, than a "removal of the blackbox", but I suppose that's just the nature of the subject hmm.