AI disclosures done right

Posted on September 27, 2026 by Persiflage

Another shiny new AI proof, this time a proof by Constantin Kogler of the Odlyzko–Poonen conjecture which says that a polynomial with coefficients chosen randomly from \(\{0,1\}\) is irreducible. What I want to emphasize on this occasion is the exemplary AI disclosure statement. To quote just the first line, “The proofs are due to GPT-6 Astra”. I feel that in the next few months we are going to have an avalanche of new papers attributing “assistance” from AI of varying levels of honesty; I’ve already noted it will be hard for mathematicians to admit even to themselves what they actually contributed. Thus I think it is important to normalize the contributions of papers such as these which give full credit to AI. What goes unmentioned is the fact that the author clearly put in some genuine effort to craft a very nicely written paper. (The author also got Astra to formalize the proof in Lean.) I can’t speak for everyone, but I can say personally that when I see a paper such as this, it gives me great delight, and gives me no AI-related angst at all. I want to commend Constantin for his efforts! The next question is: how would a journal respond to this paper as a submission? I have some thoughts…

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9 Responses to AI disclosures done right

  1. Thomas says:
    September 28, 2026 at 6:18 pm

    I think all journals should adopt policies like the following, which place the evidentiary burden on the author rather than requiring the journal to conclusively prove the extent of AI use:

    If several referees independently suspect that a paper was written with significant, undisclosed AI assistance, the paper should be rejected. For example, this could apply when an established researcher suddenly begins producing top-level results in a completely new field and the paper contains strong indications of AI use.

    If a researcher claims authorship of a paper, even while acknowledging the use of AI assistance, but the paper itself demonstrates a lack of sufficient understanding of the material or of the core ideas behind the proof, the researcher should be permanently prohibited from submitting to that journal.

    Reply
    • Constantin Kogler says:
      October 1, 2026 at 3:31 pm

      That sounds like a reasonable policy for the current moment and I think journals should have such a policy in place as soon as possible, maybe with a temporary ban if someone submits low-quality papers rather than a permanent ban. In the long term, it might be hard to tell if the AI assistance is undisclosed.

      Do you think I should submit the paper to a journal? I want to discuss this question broadly and hear as many opinions as possible :).

      And very cool to feature on this blog and thanks to Frank for commenting on the paper posted!

      Reply
      • Marco says:
        October 6, 2026 at 1:41 pm

        I think you should submit. It is one of the best examples of how one might combine human and AI intelligence with a honest disclosure. I don’t think you would regret this in 10 years from now, which is a reasonable criterion for deciding I think.

        Reply
  2. Kevin Ventullo says:
    September 28, 2026 at 10:22 pm

    Or perhaps “how ought a journal respond?”

    Separately, would you feel more trepidation if AI was also able to craft a nicely written paper? (I realize this is very much not the case at the moment)

    Reply
  3. concerned citizen says:
    September 29, 2026 at 8:47 pm

    This is certainly more scrupulous than others (and Constantin should be praised for it!), but begs a question that’s probably more important for the future: why should he list himself as an author at all if the mathematics is not due to him? In essence, is it purely an expository effort? And what happens when AI exposition gets to strong human level?

    Reply
    • Persiflage says:
      October 1, 2026 at 2:50 pm

      For the first question, I would say that the extent to which we want mathematics to be a conversation, it is good to have people included as part of it.

      Reply
    • Constantin Kogler says:
      October 1, 2026 at 3:14 pm

      Happy to join this discussion and I’m very open to hearing criticism about my research practice.

      I think we need to redefine authorship. Authorship should just mean that the authors understand the content, are happy to give talks on the paper and answer any questions. In undergraduate theses we already apply a similar concept of authorship and also in previous expository papers authorship is not questioned. I fully agree that a nearly identical concept of authorship applies to the paper that I wrote.

      A critical question is how we should differentiate authors who (at least claim to) have contributed ideas themselves in comparison to this case. I naively think that in the long term we can’t, at least for publications, assess papers differently than for anything else that is written (or other content that is provided such as a recording of a talk) and the author is willing to identify with.

      Reply
      • Thomas says:
        October 2, 2026 at 7:52 pm

        I don’t think most mathematicians would have any criticism. You worked in the area of your expertise, you followed a chain or reasoning in collaboration with AI even if it discovered all the proofs, and you noticed the connections. You took care of writing up the results very well. You did everything right.

        Although I am not sure how, say, a top four journals would respond, given that the proofs are due to AI, I believe the top journals in the field would be happy if you submitted there.

        Reply

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