Opinions: was Mathematics invented or discovered?

Does it matter?

We were just having a discussion on another thread so we thought it'd be fun to take it to a new thread for everyone to share ideas

I'm not criticising the discussion - just trying to raise an interesting point, what consequences arise if maths was discovered v/s consequences if maths was invented.

I think it's discovered as it all seems to work so beautifully, however the notation of it was invented as a tool to understand maths

I see..

I think if it was invented, that would imply there are infinitely more things to find out (aka invent ourselves) about the subject. Whereas if it was discovered, that could imply there is a finite number of things left for us to discover!

Why could we not discover something that was infinite? You could say we 'discovered' space and the vastness of the universe, which is infinite. So why could we not discover mathematics and have it be infinite?

Also, we can't just invent things at random, it needs to maintain itself as a non-contradictory system.

Hm fair point. But the universe is ever expanding, right? So whatever quantity you are to 'measure' the universe with (perhaps distance) at THIS point in time, in 1 hour it will have grown bigger than it was now. So we could say that it's countably 'infinite', right?

Unfortunately, concepts like countably infinite don't apply to physical systems like the universe.

Do they not? When you take a ball in your hand, can't you assign any integer value to any point on the surface?

Something working beautifully doesn't mean it was discovered - this is only further obscured by the fact that beauty is a subjective concept.

That is, I could say that the workings of a computer are beautiful (and they indeed are), but it doesn't imply that it's discovered. So your implication doesn't quite hold true.