Was pi invented or discovered?

[Angrboda]

I'm unfamiliar with philosophy of mathematics, and also the current set theoretical underpinnings of mathematics, but it's not clear that we're even talking about things at the right level. If these things are analytical consequences of much simpler things, like a set, identity, non-contradiction, and so on, the same questions recur, but seem a much clearer consequence of how the mind makes sense of the world. In other words, simply having a mind that is human may mean automatically having knowledge of the concepts upon which things like pi and circles depend, without doing any real thought to "construct" them; they're a priori analytical, but not things which are obvious analytical consequences of the a priori. Indeed, it might even be impossible to think in the human way without already being possessed of conceptual truths whose consequences are these derivative concepts. While, as noted, I think some of these higher level concepts exist as nodes in our neural nets, of which we have privileged access, even if not, it's not clear we created these truths. (That's one of the reasons I think it's somewhat misleading to refer to them as "inventions." Seeing the world as three dimensional is an automatic consequence of the way our minds work, it's not a necessary consequence of the objective world that we should think in these terms, nor is it necessarily true that there are three dimensions. Yet I'd look querulously at anyone who claimed that we "invented" three-dimensionality.)

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Colours don't "exist" per se... the frequency of the light entering our eyes gets interpreted by the brain and in turn we have the experience of colour from a physical phenomena (the frequency of the light) that has a huuuge range, not just the range where colours "exist".

Another observation that sort of ties in with the above is that the colour "red" isn't an objective thing. In the colour spectrum, where does red begin and end?

And the existence of tetrachromatics blows that even further out of the water.

Many common things that seem to defy explanation seem to hide themselves in plain sight. Music consists of a series of notes played in sequence. Where is melody? Is it contained in a particular set of those notes, all of them, or none of them? Where is the melody?