1,017 karma · joined July 31, 2015
> Often these solutions are announced in a rush, leaving no time for a proper writeup, the isolation of new methods and ideas, and citing relevant previous work of others. As in all creative professions, this raises severe attribution and plagiarism questions.
Tao is not someone who is anti-AI for the sake of being anti-AI. He has been advocating for the usefulness of AI in maths for a long time, to the point that people have started calling him a shill for the commercial companies.
And everyone agrees that there are plenty of use cases to be had; helping with less interesting tasks like easing literature review, efficiently delving into existing work, doing review, whether on your own work or that of others, prototyping algorithms in areas where computation is useful, but also more in hands-on aspects of maths like validating potential proof directions by getting quick feedback on veracity of lemmas, etc., and, on very rare occasions, being able to one-shot the problem you care about.
The point he is trying to make here is much more subtle than "AI bad", and it's probably easy to miss if you have never engaged with research in maths: it's that the particular approach that large commercial companies have opted to take to produce marketing material can be a net negative. There is not doubt that -- even if you ignore the rampant plagiarism that has been reported across multiple problems now, the unethical attempts to oust authors, the outrageous attempts to scoop researchers instead of collaborating with them and building on existing projects -- it's nifty to have a machine that can help you figure out if a proposition is true or not. But just figuring out as much was never the point. When people have built problem lists, it's because some problems are more likely than others to provide new insight, and that insight is the target. And to than end, a poorly written paper with inadequate references and a pile of Lean is not valuable at all. Yes, now we know with higher certainty that Fermat's Last Theorem is true, but everyone expected that already.
One place where "just" answering the question can be a net negative is because the current incentive structure is set up in such a way that going in afterwards, trying to reclaim and extract the insights from a brute force solution, is considered less valuable work than that of coming up with a solution in the first place. That's a problem of incentives, and something Tao himself has addressed in e.g. his ICM talk, and that's something that we'll want to do something about. Until a better structure appears, though, if any given commercial provider of large language models really wants to help out with maths research and not just make more pre-IPO marketing material by competing with their customers, they could do so by using their magic machines to help build insight instead.
And with this paper, it looks like it may have come from an unpublished but publically available draft:
> Supplemental AI statement of the third author. Very unfortunately and without me being aware, the in-progress version of this work dated January 14, 2025 was shared publicly at the link https://www.ihes.fr/~gabber/BGV160.pdf on January 16, 2025. My understanding is that after 18 months it became a feed of the AI models. On July 23, a graduate student sent me the 37 pages pdf file at the link https://people.math.binghamton.edu/adrian/AI.pdf produced by AI when prompted on how the 7 pages AI paper https://www.ulam.ai/research/jacobian.pdf relates to BGV160.pdf; a typo in the statement of Theorem 30.1(2.j) was fixed based on what the file mentioned (its application to Theorem 30.1(10.c) did not require any change).
> To my best knowledge:
>(1) there has been no prior work before BGV160.pdf aiming to classify all étale endomorphisms of the affine spaces that have geometric degrees 3, see Section 26 of BGV160.pdf
> (2) there has been no prior work before BGV160.pdf that used systematically xy, 1+xy, and δ +xy in the construction of open embeddings, morphisms, and étale endomorphisms, including the morphism A2 K → P1 K defined by the rule (x : 1 + xy);
> (3) between BGV160.pdf and the 7 pages AI paper there exists overlap of notation (such as Γ for complements) and of intent (such as the variation of the geometric degrees, counting fibers, non-proper locus, families, the usage of 1 + xy, the computation of the normalization Xe which actually plays no role in terms of the counterexamples to the Jacobian Conjecture, etc.) which are also very pertinently and systematically presented in the 37 pages pdf file;
> (4) as of today the prompt history, the model version, and the workflow behind the 7 pages AI paper have not been disclosed publicly.
And why aim straight for scooping other researchers upon hearing rumours about their success? Normal, ethically acting, researchers would never do that.
And how about existence of non-sofic groups, which is actually the topic here?
While his concerns expressed here aren't new, it looks like the recent cases of scientific misconduct were enough to push for urgency:
> But in the immediate term, the most pressing issue is for the entire mathematical community to unite around our core values and objectives, and reject irresponsible and unsustainable usages of AI technology that only serve to advance nominal goals rather than the true underlying goals of the field.
Normally, when you tell a coworker that you're wrapping up a result, unless they're some kind of sociopath, their natural inclination would not be to try to steal it from you.
Your post says “While unlikely, we cannot rule out that de-identified data derived from their usage of our products helped improve our models .” We can discuss what it means to “read” things but obviously the issue here isn't whether you did it manually or automatically.
But more importantly, what on earth are you doing threatening real scientists to remove their coauthors, then making fun of them on social media? Does the entire company run on that toxic culture, or did those people run off of some kind of outrageous tangent?
And what's a better way of empowering people than robbing them.
Also note the lower post ID in the URL.
It seems clear now that mathematical results can be traded on some kind of obscure market made by the frontier AI labs.
I suppose it could go the other way too: “Dear Bubeck, how much will you pay me to not write that I did this with GLM-5.3?”
Anyway, if I read Tao's post and comment correctly, there's still a gap from the Vitushkin construction to a counterexample, but chances are that was in the training data. In general, it is just a serious problem for their practical applicability that the models are outputting proofs with absolutely terribly reference hygiene.
Edit: Now the OP is flagged/dead for some reason. You could disagree on their take (calling it a marketing stunt is maybe a bit much), but I think the argument is sound, so flagging seems counterproductive to the discussion.
And that's fair; this whole thing could be one-shot with any of the leading models.
From a quick look at your profile, the majority of your submissions have been Show HNs. HN only allows some fraction of your submissions to be Show HNs (imagine if the front page was nothing but), so eventually they will just be auto-flagged.
At the same time, in this corner of the world, acting Minister for Justice (also known for trying to push through Chat Control), and NGO Save the Children, have been working to make legal the generation of CSAM for law enforcement use. So that would certainly make the industry legitimate, and you would already have a customer.
https://www.justitsministeriet.dk/pressemeddelelse/regeringe...