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Recently there was a discussion on whether mathematics was invented or discovered. It is finding like these that make me lean towards discovered. The theory of relativity depends heavily on mathematics. How could it be darn accurate about phenomena like this if it was purely the product of the human brain that has no actual intuition or experience about the behavior of supermassive black holes?
Now you are confusing maths with Physics!
Physics is about describing the fundamental behaviour of reality, and so it is rather natural to think of the work as a process of discovering how to best describe it.
What maths is, is harder to say. Certainly it starts by just picking a set of rules, thus inventing a new thing with some properties.
But, much like how a developer might ”invent” a program that solves some problem, but only ”discover” the bugs they wrote, so the mathematician too must spend a lot of time working with their newly created object to ”discover” what it really does.
Math is nature’s Quine.
I'm inclined to mostly agree with you. Perhaps mathematics is discovered, but mathematical processes are invented? For eg, π was discovered (surely it wasn't invented because it's seen everywhere in nature), but calculus was invented?
I'm no mathematician though, so my understanding may not be perfect.
Edit: FWIW, Wikipedia uses the verb "developed" for calculus:
> Infinitesimal calculus was developed independently in the late 17th century by Isaac Newton and Gottfried Wilhelm Leibniz...
Hm. Now that I think about it, maybe mathematics is a language that we use to express the universe? In which case it was invented?
But surely, pi exists as a concept in nature and is something that we found, and didn't come up with? Confusing stuff.
Hannah Fry covered this pretty well for a non-maths audience: https://www.bbc.co.uk/programmes/b0bn9dth
Yes, the closer you look, the more difficult it gets.
What does it even mean to "exist as a concept in nature". Pi is a ratio derived from physical existence that humanity collectively gave a name to since its a regular property of the fact that our universe is tuned in the way it currently is.
Pi has nothing to do with our universe or the way it is tuned.
It's more fundamental than that. It would be the same value in any universe.
You don't need circles, or Euclidean space, to discover Pi. It arises in all sorts of pure mathematics that have no direct connection to physical circles.
That said I suspect you are right that we gave a name to it because it comes up so obviously in our experience.