Comment by layer8

To quote an old adage, the map isn’t the territory. That we can’t fully write it down (which we can’t even for countable infinities, or even something like 10^10^10 symbols) doesn’t mean that it doesn’t exist. All of the territory still exists, even if any map that we can draw will only capture certain aspects of it.

Regarding “ideas”, to me math is primarily exploration and discovery, rather than invention. That’s one way how it corresponds to the territory analogy.