Quick clarification on authorship
Hoping to put this issue to rest for the moment

My most recent post makes the case that the Leiden Declaration’s position that “affirm[s] the humanity of authorship” is a political statement, and not a strict logical deduction from a hypothetic abstract universal concept of the author. This was meant to be a response to comments by several mathematicians who explained that they had not signed the Declaration because they believed that, under certain circumstances, authorship should be attributed to an AI system that has generated a valid proof. After I had finished the post, I learned that, on the very same day, OpenAI had issued a statement addressing this very point, in presenting its “Ten advances in mathematics and theoretical computer science”:
The emergence of systems capable of contributing to mathematical research raises questions that cannot be answered by a technology company alone. There are many views as to the role of AI in mathematics, and we have deep respect and understanding for those concerned with its impact, including the signers of the Leiden declaration on AI and Mathematics. We believe attribution should honestly reflect how a result was produced: claiming human authorship for a proof generated entirely by an AI system would misrepresent both the system’s contribution and the nature of genuine human intellectual work. We helped prepare the manuscripts and formalize the proofs in Lean, and we take responsibility for their correctness, while the mathematical arguments themselves were generated by our system. We hope the mathematical community will engage deeply with these results, place them in context, and bring the ideas behind them to life through new research and discovery.
I submitted the text to pangram.com to test for AI generation; the conclusion is that the red text was produced by AI, the rest by humans. Note how the AI-generated sentence1 directly contradicts the position on human authorship asserted unequivocally in the Leiden Declaration, which had been cited in the sentence immediately prior, which pangram identifies as human. Does this blatant contradiction reflect a conflict between OpenAI’s human managers and its LLM, that could someday spin out of control, with unpredictable consequences? Or is the “deep respect and understanding” claimed in the “human-generated” sentence just one more instance of OpenAI’s trademark insincerity, exemplified by founder Sam Altman, as memorably documented in Karen Hao’s Empire of AI and the New Yorker essay by Ronan Farrow and Andrew Marantz, in which Ilya Sutskever, apparently alluding to Altman, refers to the type of C.E.O. who “just tells people what they want to hear?”
OpenAI is apparently keen to have the material in this document attributed to its “next major model” Astra. In a private message, one of the Leiden Declaration’s authors observed
I find it sad but not at all surprising that OpenAI is trying to turn the issue of authorship on its head. It is very clever and extremely political of the OpenAI human team to say we take all responsibility and no credit…
Nevertheless, some mathematicians seem inclined to go along, as evidenced by some of the comments following my most recent post. I would like to suggest that such mathematicians give the Leiden Declaration authors a break, while we debate how best to respond to this controversy. Those of you who feel the question is too urgent are instead encouraged to write to the Association for Computing Machinery, whose website includes a clear statement of
Criteria for Authorship
ACM has established detailed criteria for determining if an individual’s contribution to a Work rises to the level of authorship or if they should be acknowledged for their contribution in the acknowledgements section of a work.
Anyone listed as an author on an ACM submission must meet all the following criteria:
They are an identifiable human being. Anonymous authorship is not permitted, although pseudonyms and/or pen names are permitted provided accurate contact information is given to ACM to fulfill this policy’s requirement that all named authors are accountable for the contents of their Work. ACM does not currently permit collective authorship.
They have made substantial and demonstrable intellectual contributions to some components of the original Work described in the manuscript, such as contributing to the conception, design, and analysis of the study reported on in the Work and participating in the drafting and/or revision of the manuscript.
They take full responsibility for all content in the published Works.
Note: All individuals who meet the above criteria should be listed as authors on the Work. The practices of gift authorship, guest authorship, ghost authorship (see the FAQ for detailed definitions of these and related terms and for discussion of related, acceptable practices), and purchased authorship are clear violations of ACM Publications Policy and when proven may have severe consequences for those found to have participated in such practices. For more information about these practices, please see the FAQ document.
Authors who meet the above authorship criteria, but who die or become incapacitated prior to publication, can be listed as co-authors with permission of their estate or next of kin.
Those who contributed to a Work, but whose contribution does not rise to the level of authorship, may be acknowledged at the end of the Work, before the Bibliography, with explicitly described roles, preferably using the roles found in the CRediT (Contributor Roles Taxonomy). In addition, those whose contribution does rise to the level of authorship, but who are unable to publish with ACM as a result of active publication bans may be acknowledged in the acknowledgment section of the Work.
OpenAI’s proposal not only contradicts the Leiden Declaration, which is a statement of principles; as you see, it also directly contradicts the stated official policy of the ACM. This matters, since OpenAI is claiming advances in theoretical computer science as well as mathematics.
I find that, as a rule, theoretical computer scientists have fewer illusions about AI, and the AI industry, than do mathematicians. The statement on criteria for authorship is presumably a reflection of this. The ACM has a long section, that I encourage you to read, on the use of AI. Although the ACM “embraces any new technologies that have the potential to improve the efficiency and productivity of the research enterprise and assist with the authorship process,” they flatly prohibit AI authorship. This means that OpenAI will have to identify human authors if they want to publish any of the articles in their “Ten Advances” in one of the ACM’s prestigious journals.
If you have a problem with that, address your objections to them, not to me.
Assuming you give full credence to pangram’s analyses; as I explain in a few of the comments, I have no opinion regarding the reliability of pangram and I don’t recommend using it to reject a student’s essay.

Decisions we make about authorship are political, in the sense that they reflect the ways we want to organise ourselves as a society -- and that the authorship question is one facet of the question "How do we ensure accountability for AI output, if at all?" My position would be that yes, we do want accountbility, and that accountability ultimately rests with primarily with human beings and secondarily with those structures we build to support people, such as companies, universities, charities, governments, ... . Accountability can only be meaningful if it can make a difference. In the authorship question, credit for the good points of a publication should go to the same entity that will take the blame for its bad points. This seems to have been widely accepted in the scholarly publications world until now. It's nonsensical, at present, to hold an AI system -- a piece of software running on a server somewhere -- accountable for the good or bad consequences of its outputs, since there is no meaningful difference that accountability can make to it. So if an AI company wants to take the credit for the positive effects of the outputs of the software it has developed, it should equally accept liability for the bad effects. Is that a position those companies are willing to cede, I wonder?
Yes, the responsibility part is the one that bites. That's why an AI alone cannot be an author of a paper. But it should be allowed to put an AI as a co-author, because you as the human are supposed to take responsibility for its contribution to the paper anyway, as the ACM guidelines say that every author needs to take responsibility for all of the content. I think that in this case, the ACM guidelines should be changed so that the AI can be listed as co-author, without itself taking on any responsibility.
As for the "contradiction" that OpenAI embraces AI authorship after "deeply respecting" the Leiden declaration: You can deeply respect somebody or something, but "genuinely" disagree with them. As I do with much of this blog.