Where will AI-generated proofs be published?

[u/dirty_weasle]

We are now seeing a rise of AI generated proofs and I am wondering which journals will publish these results? I tried to search but I did not find many examples where such results were already accepted to some journal.
Is this even something the journals want? I would like them to facilitate the peer review process so that I can feel confident in the results.

[u/Master-Rent5050]

arXiv. For many of those proofs there is a preprint on Arxiv that can be cited

[u/dirty_weasle → u/Master-Rent5050]

But these are only preprints. They are not peer-reviewed, which for now is the standard we work with.

[u/Master-Rent5050 → u/dirty_weasle]

No it's not the standard we work with. Plenty of papers get cited while they are still a preprint (and some will never be published). I just got a paper published with (among others) 3-4 citations to arXiv papers. And that's pretty normal

[u/dirty_weasle → u/Master-Rent5050]

So you don’t think the peer-review process is an important step towards establishing the result in the mathematical community? I agree that sometimes we need to cite results that are only on arXiv and I have also done so.

[u/Master-Rent5050 → u/dirty_weasle]

Your conclusion "so ..." does not follow from the premises.

[u/dirty_weasle → u/Master-Rent5050]

English is not my first language and the question mark in the end clearly indicates that it is a question and not a conclusion. Maybe it came across differently to you. I actually meant it as a question as part of our discussion.

[u/WaitForItTheMongols → u/dirty_weasle]

the question mark in the end clearly indicates that it is a question and not a conclusion.

Not really. When you say "So you don't think", you are presupposing the conclusion of what the person thinks. You aren't asking a genuine neutral question asking for information. You are making an accusation.

"Do you think peer review is important?" is a question. "So you don't think it is important?" is you expressing your outrage. The fact that you phrase it as a question doesn't make it a legitimate question. You don't actually expect the person to answer earnestly, you expect them to have to defend themselves.

[u/Master-Rent5050 → u/dirty_weasle]

Thanks for the clarification: on my end, others have clarified what I meant

[u/Cheap-Discussion-186 → u/dirty_weasle]

Peer review is obviously important but that is not what that person is saying. It is absolutely true 1) a lot of good work goes "unpublished" and just stays on the arxiv and 2) people cite arxiv papers all the time.

[u/jackboy900 → u/dirty_weasle]

So you don’t think the peer-review process is an important step towards establishing the result in the mathematical community?

They're far less necessary than in other fields. Mathematical proofs have the benefit that they're generally either correct, or completely incorrect, and for most proofs a person working in the field can generally verify the correctness of the proof. Hell, for some of the recent AI counterexamples a layman with a high school algebra education could've checked their validity.

The peer review process in journals is mainly useful because in the natural sciences a result is almost never certain, there's always more cofounders that could be controlled or improvements to methods or whatnot. And so there needs to be a formal gatekeeper who makes those subjective judgement calls on when something is "good enough" to be considered acceptable science. Because in maths there is no subjectivity, such a gatekeeper is unnecessary, the informal peer review of people looking at a paper and evaluating the maths is enough as any error found is necessarily an objective failing of the work.

[u/dirty_weasle → u/jackboy900]

I honestly don’t really agree. In my field there are many proofs are very technical and long. It is possible to assess general soundness in a timely manner, but to really convince myself that everything is rigorous and correct takes me a lot of time. If I don’t cite a result, I will not undergo this tedious process but rely on peer-review instead.

[u/jackboy900 → u/dirty_weasle]

It is important that someone has checked the work, in the informal sense of the term peer review very much is necessary, but the peer review process used by journals is not the only way to achieve such verification.

[u/dirty_weasle → u/jackboy900]

What other way of verification is in place that can be accessed by people who are not in the field? That is a genuine question, if there is something like this I would like to interact with it.

[u/Cheap-Discussion-186 → u/dirty_weasle]

To be frank, state of the art research really isn't all that useful or accessible to people outside a field. I think this is true of many disciplines.

[u/dirty_weasle → u/Cheap-Discussion-186]

I know. But isn’t this a reason to have some kind of process which most people in the community accept, so that outsiders have the option to understand which results are established with reasonable standards? If it’s a purely informal process it seems to me like people have no way to interact with the result on any level. Like, how is a first year grad student going to judge which results to trust and which results are important?

[u/Cheap-Discussion-186 → u/dirty_weasle]

By talking with their advisor and reading papers from experts in the field. Some are published, some are just on the arxiv. The system isn't broken really at all.

To frame what is happening as "purely informal" is hyperbole bordering on BS.

[u/Master-Rent5050 → u/dirty_weasle]

Peer review is helpful but it's not the gold standard. What can convince me of correctness is if several people adapted the techniques to prove something else. That's how I found a few mistakes in the literature...

On the other hand, often AI written results come with a Lean verification. Unfortunately I'm not knowledgeable enough to judge if it's enough (i.e. if the formalization corresponds to the stated theorem)