Responsible Release of AI-Generated Mathematics

> we ask them to stop testing advanced mathematical problems on proprietary models. Maybe I'm alone on this, but for some reason these sorts of requests strike me as akin to gatekeeping how someone should breathe air. It's math... the numbers and symbols are just out there in the platonic realm available for anyone to do as they like with them. It's patently absurd to request other people to stop. Ensuring credit where credit is due? That's fine. If your model incorporates the efforts of many others, then it's reasonable to request acknowledgement of everyone who contributed (even indirectly). But that's not what the request states — presumably their ask subsumes any advanced ML model, including those that weren't trained on a giant corpus of text.

Mostly pretty straight forward. The idea that proofs be desloppified, attribute existing literature properly, and published somewhere expediently where it can be commented on, with artifacts for verification, is all very uncontroversial stuff. I think the spicy take is definitely this stance that longstanding mathematical problems shouldn't be used as benchmarks for (specifically proprietary) models. Stated right at the very top. The justification is pretty clear. > The use of proprietary internal models by AI labs to do mathematical research risks creating a two-tier system where labs outrun the rest of the field, effectively alienating the mathematical community from its own discipline. It is all fun and games (for non mathematicians) when mathematicians can't compete with AI labs but I think the more dangerous direction is when this starts being true for the rest of everything. For example cybersecurity or whatnot. Hence why I think Anthropics whole stance of being completely against open anything is actually *extremely* dangerous due to the centralization of power which they completely ignore as a risk factor. The most discussable thing in this is certainly the idea that labs should fund mathematicians to do expositions. > One of our principles is that AI labs have a responsibility to provide support, including funding, for the development of human understanding of the AI mathematical output that they release. Obviously this directionally sounds like the role of mathematicians would be shifting towards interpreting AI results instead of making proofs. I'm not sure who would should really be billed for that. Plus how would you decide who gets the grant? An interesting thing is that by stating that that the lab that dropped the result provide the funding, this is *directly* proposing an example of taxing AI labs for displacing knowledge workers.

For every important match problem solved by AI, without mathematicians we wouldn't know about the existence and importance of the problem. Famous mathematical conjectures are social constructs, formed by decades of even centuries of attention given to them by members of the math community. Without it, the danger is that future math "progress" will be reduced to generating tables of Lean statements and a probable/unprovable bit generated by AI.

As an answer to AI companies, this is so bad: instead of trying to find a path to a win-win-ish solution with some trade-offs, this says: sorry, we cannot think of any, so just stop making money, will you? Math needs better crisis managers. But as an idea, this is even worse: does it mean to stop potential research to cold fusion, cancer and anything as long as it may touch some mathematician's interests, or does it mean math is so hopelessly irrelevant that this cannot be the case... Again, as a crisis manager, this is not how you pose it. Makes me wonder, were they hired by Sam to sabotage?

Either mathematical progress helps advance society, in which case progress is a good thing. Or mathematics is more like a hobby, and while ai may spoil their fun, they need to move on like chess and go players.