@cirnog @Comatoast @Kazak

If a person presented 4-sided triangles as a definition, I would be more curious if it behaved like a 4-simplex, or a square, or something else.

Personally, I can try to get what was meant from its implications, because most communication is fairly vague.

Math research papers are also vague. There is an established common overall process. So it can be pieced together most of the time. Formal computable math also relies on conventions on what things mean for the machines to process it, but it is purposely more stable and automatable. The description itself can be considered objective, if you assume intelligence is possession of a universal grammar, and some qualia was not described.

The ontology is not split on what is being described by the math, as far as I believe. But proofs do not count as metaphysical objects for everyone. So the proof statement being objective can be either true or false.