Post by @tao@mathstodon.xyz

2026-08-06 05:47 UTC

When multiple researchers accomplish the same result, who is credited with priority? When I was a graduate student, the primary yardstick for priority was the date of publication in a peer-reviewed journal. Every so often, this would lead to a sordid drama in which a referee of a submitted paper was accused of using the ideas in that paper to rush out a competing paper to a faster journal. Within a decade, though, the arXiv preprint server, with its trusted submitted timestamp, supplanted the journal publication date. This largely solved the previous problem of being "scooped" by one's referees. However, it created a new problem of rushing to place a preprint on the arXiv as soon as possible. In recent months, even the arXiv has been deemed too slow for those racing to claim priority on AI-generated proofs, which are now often announced on social media without waiting for an arXiv submission (and definitely without waiting for a journal publication). This creates significant incentive to cut corners on all the later stages of proof development, such as verification, literature review, exposition, or digestion, to the point where such announcements become a net negative to the collective mathematical literature. I believe that the time has come to change the priority standard once again. To the extent that we need to compete to be "first" at all, we should no longer assign priority to the first to release a preprint, or even a formal proof certificate, as this devolves to a race to who can prompt their AI the fastest. Rather, priority should be awarded to the first author(s) who can present the results clearly in a scientific lecture (and, ideally, answer questions from the audience).

Replies (19)

@sorenhave@mastodon.nu 2026-08-06 07:17

@tao@mathstodon.xyz Like when Wiles held his series of lectures: https://www.newton.ac.uk/news/ini-news/wiles-flt-30/

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@tao@mathstodon.xyz 2026-08-06 13:47

Thanks for all the feedback! I had truncated the proposal somewhat to fit inside Mathstodon's post limits, but I realiize now I should have clarified and modified a few things. 1. "scientific lecture" should become "publicly available scientific exposition". This can include a traditional lecture, but also non-traditional formats such as expository blog posts, self-recorded video, etc.. Eventually, I hope that standard arXiv-like repositories as well as journals for expositions will appear, although the infrastructure is not there yet. (But see the new "Mathematical Discourse" journal at https://www.mathematicaldiscourse.org/ for a first step in that direction.) 2. The exposition artifact is meant to supplement the paper artifact (and the formal certificate artifact, if available), rather than replace it. So the actual "date of release" under this proposal would be max(preprint release date, exposition release date). Once autoformalization becomes routine, one can also add "formalization release date" to this max as well. More broadly, in the past we had a single artifact - the paper - that was supposed to record four separate aspects of a proof: generation, verification, exposition, and publication. In the future, we may decouple this into multiple artifacts - a generation artifact (e.g., AI chat logs), a verification artifact (e.g., Lean code), an exposition artifact (e.g., a recorded talk), and a publication artifact (the traditional paper). Priority then becomes a question of who was first to provide a complete set of artifacts. 3. "But what if AI can automatically generate good expositions also?" I would actually be happy with this outcome; cf. https://xkcd.com/810/

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@Quantensalat@scicomm.xyz 2026-08-06 05:53

@tao@mathstodon.xyz "I have proven the Riemann hypothesis using Claude Fable. Unfortunately, the margin of my Instagram is to narrow to show how I did it, and the TikTok too short. Anyway, I won."

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@tomkalei@machteburch.social 2026-08-06 06:04

@tao@mathstodon.xyz I agree but this also is a deviation from the principle that we should not judge the person, but only the quality of the research. The AMS had even introduced double blind review procedures for all their journals. This is the opposite.

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@human_in_exile@mathstodon.xyz 2026-08-06 06:20

@tao@mathstodon.xyz It will devolve to said AI race, this is a product of the socio-economic structure, and the distance of pure math results from revenue generation. Unless the entire grant system and funding system is reworked, this is inevitable IMO.

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@rainerzufall_le@mastodon.social 2026-08-06 06:36

@tao@mathstodon.xyz Back to the roots

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@11011110@mathstodon.xyz 2026-08-06 06:45

@tao@mathstodon.xyz I'm not convinced that using talks rather than preprints as a basis solves anything. Invited seminar slots go to the already-well-known or well-connected. Computer science gives priority largely through conference presentations rather than journal publication but some results can bounce around from conference to conference many times before being accepted; the same sordid reviewer issues have arisen there as well; making everyone fly to conferences around the world raises issues both of carbon footprint and financial equity; and, the CS conference system has not scaled well to broad megaconferences instead giving rise to an overabundance of specialized conferences and ingrown research communities.

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@liuyao@mathstodon.xyz 2026-08-06 07:21

@tao@mathstodon.xyz It may be a step backwards, that only the ones that are already well-connected in academia get to give a talk at all. AI is a force of democratization, that you don't need to be trained by top researchers in a specific subfield to have a chance at pushing the frontier. The ideal world is one in which Fields-medal-worthy results (machinery, more than specific theormes) are being made by people (+AI) not in top institutions in US or Europe.

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@cheng@masto.ai 2026-08-06 07:33

@tao@mathstodon.xyz I feel that we need to have a community discussion about what our expectations are for a "scientific result". My background is in machine learning, where the community decided that a conference publication is good. I also collaborate in other fields where my co-authors have trouble believing that a single fixed deadline without revisions gives good results. More recently arxiv computer science has decided that surveys and reviews need peer review before preprint acceptance.

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@johncarlosbaez@mathstodon.xyz 2026-08-06 08:37

@tao@mathstodon.xyz - this can turn into a race to get invited to give a talk. There are also other problems, mentioned by other people here. But it's interesting how this parallels the new trend toward giving students oral exams (preferably disallowing Meta's AI glasses).

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@djb@mastodon.cr.yp.to 2026-08-06 08:39

@tao@mathstodon.xyz We want proofs to be completed and published, so we should assign credit to the first to publish a complete proof. We also want comprehensible exposition (e.g., shorter proofs), so we should also assign credit for that. The weights naturally adjust depending on difficulty.

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@pbloem@mathstodon.xyz 2026-08-06 08:52

@tao@mathstodon.xyz This is in line with a view of the future of mathematics where the job of mathematicians is much more about explaining results than finding them. The machines can find the results, but people may still be needed to reach the point where a human brain can comprehend them. In that case prestige and recognition will shift from the discoverers to the explainers.

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@srinivas@mathstodon.xyz 2026-08-06 09:39

@tao@mathstodon.xyz @pbloem@mathstodon.xyz Perhaps till such "result-claim seminars" grow numerous enough and are given a sufficiently good quality function, allowing a good explanation/successful result-claim to become an artificially-trainable skill. So any such differentiation from AI seems, at best, only a near-term solution, pushing the problem from "AI assisted proof" to "AI assisted proof + claim/explanation". I suspect that the longer-term solution here involves a more fundamental look at why mathematicians do mathematics.

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@jesusmargar@mastodon.social 2026-08-06 11:21

@tao@mathstodon.xyz that has the problem that some people will get invited to speak while others won't because they are in the network of the organisers (eg former students). I think the solution you propose is more problematic than the problem it aims to solve. I don't have a good solution myself but if results can easily be provided in a matter of hours by an AI perhaps there's not much credit to be given in the first place, just like you wouldn't give credit for computing Betti numbers using MAGMA.

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@Bielefelder@mathstodon.xyz 2026-08-06 11:30

@tao@mathstodon.xyz But talks at which institutions would count as fine. To give a local example from my Alma Mater: Would Math colloquium at Friedrich Schiller University Jena be fine? Would math colloquium at Ernst-Abbe-Hochschule Jena ("Fachhochschule", not allowed to give PhD.) be equally fine?

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@Bielefelder@mathstodon.xyz 2026-08-06 11:53

@tao@mathstodon.xyz In times of more than enough proofs: is it still important (at least for theorems and proofs on "normal level") who has priority? In particular if the proofs were generated with AI help. - Probably good new models and good open questions will become more important, also priority questions concerning them.

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@torgeirlysen@mathstodon.xyz 2026-08-06 12:48

@tao@mathstodon.xyz Could it make sense to have something like a pre-preprint server for AI generated results? Basically a repository to post all these AI results, then a mathematician can clean it up and post it to arXiv which will be reserved for human written papers. I find that it’s somewhat demoralising to read something if I don’t know if a human has spent any time writing it.

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@ibrahimtencer@mathstodon.xyz 2026-08-06 23:33

@tao@mathstodon.xyz who is going to award this priority? What is the incentive to slow down the process, rather than speeding it up as arXiv did? Currently I don't see really any academic incentives for expository work in math. You can think for example of Perelman's sketch of the proof of the Poincare conjecture, which he did not present publicly or explain in detail. And when Cao and Zhu wrote an expository article on it, they got accused of trying to take credit for it. And certainly they didn't get the Millennium prize for it - would the prize go to the explainer? This seems to fly in the face of mathematical practice.

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@gotanegra@mathstodon.xyz 2026-08-10 10:41

@tao@mathstodon.xyz I agree that priority based on rushed, unverified AI-generated announcements is becoming problematic, but replacing timestamps with the ability to give a scientific lecture risks creating a different and perhaps older problem: access. Established researchers can obtain seminar invitations, audiences, and institutional attention almost immediately, while unknown or independent researchers may struggle even to be heard. A public, immutable timestamp for a sufficiently complete and verifiable proof is at least neutral with respect to reputation. Lectures and Q&A are excellent tools for validation and demonstrating understanding, but I would hesitate to make access to them the criterion for priority itself.

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