At the very least, the single bit of information of whether a conjecture is true or false advances human understanding. It allows researchers to abandon paths which would not have been fruitful.

I'm pretty sure OpenAI's proofs, while difficult to understand, have a net-zero impact on human understanding of mathematics. It took the first Millenium problem years to verify its accuracy. It's only been days since OpenAI released its problems, surely it would take years to evaluate whether the solutions meaningfully advanced human understanding.

Who determines the objective of mathematics research?

All mathematics researchers in the whole world have agreed upon that objective apparently?

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