Was pi invented or discovered?

[Angrboda]

So you guys are arguing if a number was invented or discovered.
Was 1 invented or discovered?
Was 1024 invented or discovered?
Was 0.333333(3) invented or discovered?
Was e invented or discovered?
Was i (the imaginary unit) invented or discovered?
Was ∞ invented or discovered?

Yes. I'm going to interpret your questions as being sarcastically implied, and point out that the larger case of which this case is but a representative, the debate between Platonism and nominalism, is an important philosophical question. (Not assuming you consider philosophy important or not.)

While I'm certainly willing to steal a play or two from the playbook of mereological nihilism, I'm inclined to believe that things like pi emerge as a consequence of other truths (it is itself an analytical truth, derived from other a priori or a posteriori considerations), or is an emergent property of certain types of systems (in this case, specific neural networks) which compute idealizations of the properties of things as a useful shortcut in deriving behavioral solutions to the problem of survival. Thus we may have geometrical concepts which don't exist in the real world, but which can yield more consistently reliable consequences in terms of prediction if used in place of.... whatever we might use otherwise [and such computations based on idealizations are enormously more efficient, not even taking into account the properties of the computational infrastructure]. We have other, supposed, purely Platonic constructs; for example, our intuitive concept of folk psychology, the concept that a person has thoughts, beliefs and goals, is not something we actually encounter in our world [that of other people], but it is an eminently useful construct to use in predicting the behavior of people in our environment. (See, for example, Daniel Dennett, )

(ETA: Notice how, likewise, our folk psychological construct of mind can lead to unproductive predictive simplifications. The effect in psychology is a case in point. If we are reasonably competent and self-aware, we may innocently project that assumption onto someone who is not competent, nor aware of their incompetence, and quickly become frustrated trying to make sense of their behavior, when their behavior doesn't make sense in terms of our model of them as competent and self-aware.)