Mathematicians Tell AI Labs: Stop Testing Advanced Math on Proprietary Models
Responsible Release of AI-Generated Mathematics
A set of recommendations for AI labs that produce significant mathematical results. Drawing on over 600 responses from the mathematical community, the document argues that labs must not treat math results as marketing, should release proofs with full attribution and formalization, and must fund human understanding of AI-generated mathematics. It also warns that proprietary models risk creating a two-tier system that alienates mathematicians from their own discipline.
We do not endorse this practice, and we ask them to stop testing advanced mathematical problems on proprietary models.
- kingstnap
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 mathemati […]
- throwaway713
> 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.
- mchusma
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.
- unddoch
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.
- astaza123
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?
- LelouBil
I saw an interview (in French) of Cédric Villani, speaking on behalf of him and other Fiels medalists, who said that in order to advance mathematics we need three things:
- ideas
- students
- problems
Basically, students to bring original ideas to try and solve existing problems and this generates new ideas and possibly new problems for new students to try and solve with new ideas and so on.
And he continued to say that the issue with LLMs in mathematics, is that he's afraid they could run out of problems, and so students wouldn't bother trying, and this could hurt understanding of mathematics as a whole.
It's totally not my field so I'm not sure what to think of it but it seems important
- Animats
This paper wants AI companies to pay human mathematicians to understand AI-generated stuff.
That's an unusual ask.
- dsign
> However, it is now the case that AI can output mathematical arguments in situations without the human who prompted it being able to understand the arguments, verify them, or take responsibility for them.
I read this as "anybody can prompt, few can understand". And "we need more who can understand". If we had more mathematicians (than we have today) all of them piloting advanced models, the pie would grow. The problem is that AI capabilities drain (by disincentivizing) the education pipeline that would get us those mathematicians, and if recent rumbles about what AI is doing to education are to be believed, it does so many years before students even get to grad school.
IMHO, it is not that bad. Not having any human who understands linear algebra after the Butlerian Jihad is a win :-) .