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.
replyI'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.
It may provide that one bit of information but it could still be a net negative if it destroys current institutions (such as graduate studies) and no new institutions can be developed that provide a clear signal of who is doing meaningful work. That was a byproduct of solving open problems that are now lost. These are not my ideas, these are things that Terence Tao and others have written about that were recently on the front page of HN, e.g.:
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