See the longstanding debate on whether new math is "invented" or "discovered". Most mathematicians I knew thought it's discovered.
Any design already exists as a possibility, so it could be said to be both invented and discovered, depending on how you look at it.
One can argue that mathematical facts are discovered, but the tools that allow us to find, express them and prove them, are mostly invented. This goes up to the axioms, that we can deliberately choose and craft.
Math is an abstraction of reality, it had to be invented, so more inventions or discoveries could be made within it.
...long standing indeed. It can be traced back to Plato's works.
Regardless of which, both Newton and Leibniz imprint in their findings a 'voice' and understanding different from each other and that of an LLM (for now?)
This is like saying a sculpture always existed, the sculptor just had to remove the superfluous material.
Or like a musical octave has only 12 semitones, so all music is just a selection from a finite set that already existed.
Sure the insane computation we're throwing at this changes our perspective, but still there is an important distinction.