I think human mathematicians would be more enthusiastic if these frontier labs were putting out new interesting open problems. As some of them are pointing out in the responses, the purpose of having big open questions is often more about the tools and techniques used in solving them. If some can be gleaned from the AI proofs then great but, if not, the only real outcome for some (not all) of these results is that humans won't be able to develop those techniques.

If OpenAI were coming up with interesting problems that everyone could explore as they foreclosed all these existing ones, I don't think the response would be as critical. Obviously, that's much more difficult and doesn't tie into the only telos of these companies (having a huge IPO to make all their investors and equity holding employees rich).

As usual (at least, as of recently), Terry Tao's assessment is measured but trenchant. Mathematical research has been a human process of improving understanding, to an extent that if you go far back enough in time, it was not distinguished from "philosophy". Part of that involves (involved?) ac academic engagement with the pursuit of knowledge, which means that results are discussed, presented, picked apart, etc., in a community of other people in pursuit of knowledge. The end result being the sum knowledge that humanity possesses grows. The way these results were dumped unceremoniously bypasses all of that. And, because we have all seen what regard the tech leadership class have shown for humanity, even in much more concrete and significant ethical questions than "is it ok to destroy the academic community", such as "is it ok to lower the friction to surveilling and/or enacting violence on society to the extent that it's all encompassing", I think it's pretty reasonable that their complicity in the latter will extend to the former.

I should point out that this is not a categorical treatment of AI results. I think about outcomes. Would I be angry if OpenAI dropped full contents of all the Vesuvius Challenge scrolls? Obviously not.