100+ reactions to 100+ solutions

People still play chess and go and StarCraft. People do what people want to do. It's not clear whether this will reduce the number of working mathematicians or increase it. There will a lot to learn from the machine proofs that will open up new frontiers as well.

So, it's like the story, "We'll see."

There has been a shocking but not altogether surprising development, and all reactions are valid.

It’s always frustrating to listen to people on HN and X, the everything app, talk about this with that characteristic smugness. “It’s totally understandable that they feel this way” “oh people still play chess!” As if what mathematicians are upset at “losing” an arbitrary strategy game. It’s a very childish way to interact with it but you can’t expect much I guess.

I like this website though because it collects a lot of the important frustrations from the mathematical community, these open problems were curated in order to organize a field around, most to all of them only have/had value in so far as they promoted study of the subject. The claim that AI proofs will open new frontiers for mathematics research could probably be true but misses the point that the manner OpenAI has gone about their “contribution” does more to cauterize the field than promote anything productive. OpenAI is functionally reducing the communities ability to ask real questions. Math is ultimately a very different field from the rest of the natural sciences, and I suspect a lot of the more simple discussion on this subject misses the objections because of those differences. All this to say, I don’t know that OpenAI is doing these haphazard releases cynically, with the assurance that all that matters is the headline, but it really does feel that way right now.

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.