That's very true but I also think of one important aspect: the parts of the research space we choose to look in. And like a novel is not discovered in the absurdly large research space of sequences of random characters, nor even discovered in the absurdly large set of sequences of grammatically correct sentences, theorems are made were "we", concrete social creatures, look for them. But there is a distinction in that one activity lies in a formal logic world, the other is more free (neither formal and can even have small inconsistencies)
So maybe we just need yet another word? Discovented?
The universe exists as a geometry. That geometry has properties with different interactions. The geometry exists regardless, but we can give that geometry a name arbitrarily.
It’s also the difference between music and math which is equivalent to me as frequency and quantifying frequency.
Vibrations interact with each other. Mathematics is the observation and labeling of interaction(s).
Tricky because vibrations are continuous and now we’ve got a can of worms on continuous and non continuous numbers. Haha.
That's what the aliens could potentially do as well, but that would also be math.