26
$\begingroup$

The recent MO post, A number theoretic conjecture by Chat GPT, posed a conjecture that was generated by ChatGPT. In my opinion, it was not a particularly interesting conjecture. For me at least, the novelty factor of LLMs has worn off, so the mere fact that ChatGPT has managed to generate a conjecture that's not totally absurd isn't by itself enough justification for posting to MO.

Should MO have a policy toward ChatGPT-generated conjectures? I don't mind conjectures arising from computer experiments, or even from programs that are expressly designed to generate interesting conjectures, such as Graffiti or the Ramanujan Machine. But current LLMs aren't designed to generate mathematically interesting conjectures. Should we emphasize that a GPT-generated conjecture should be posted to MO only if the person posting it would find it worthy of posting to MO even if it hadn't been generated by GPT?

In a comment, Yemon Choi wrote, "I would be much happier if all mention of GPT were removed from the original question." I certainly don't want to see MO flooded with banal GPT-generated questions. On the other hand, if such a question does rise to an MO-worthy level, then maybe disclosing its origin is the scholarly thing to do?

$\endgroup$
16
  • 8
    $\begingroup$ One could propose the conjecture with zero mention of GPT, and it wouldn't change the mathematics. At best, one might mention it in passing in a comment, not put it in the title. Or even just say "I was playing around with some software and the statement of this conjecture was generated". Unless the question is about the mathematics (and the research-level mathematics) of LLMs, I'm not sure how that piece of information helps rather than creates unnecessary noise (and attracts chatbots-are-a-novelty-only upvotes from passers by). $\endgroup$
    – David Roberts Mod
    Commented May 23, 2023 at 9:10
  • 4
    $\begingroup$ I think the circumstance that a question has been created by particular means neither contributes to making it on-topic nor to making it off-topic. What matters is solely the question as such itself. $\endgroup$
    – Stefan Kohl Mod
    Commented May 23, 2023 at 14:30
  • 3
    $\begingroup$ I must admit that in the comments I have lapsed into arguing about GPT. I should probably have exercised greater self control, but I feel quite strongly against some of the GPT hype. As a practical matter, comments can't be downvoted, so there is always a ratchet effect where comments that attract casual passers-by get signal-boosted $\endgroup$
    – Yemon Choi
    Commented May 23, 2023 at 15:40
  • 5
    $\begingroup$ There have been periods in the pre-GPT era where certain users liked to "spam" MathOverflow with number theory questions that had elementary statements. I wasn't keen on those either, quite independently of whether they were generated by human enquiry or a set of dice or a chatbot. $\endgroup$
    – Yemon Choi
    Commented May 23, 2023 at 15:41
  • 8
    $\begingroup$ The question has been asked by a known MO user. If the same question were asked by a new user who is not well-known by the mathematics community, then I believe that the question would have been closed. $\endgroup$
    – Joseph Van Name
    Commented May 23, 2023 at 15:53
  • 3
    $\begingroup$ "LLM"? Life-Like Machine? Large Loss of Money? Low-Level Meltdown? Lake Louise Magpies? Master of Law (at Sydney University, unsw.edu.au/study/postgraduate/master-of-laws)? $\endgroup$
    – Gerry Myerson
    Commented May 23, 2023 at 22:58
  • 9
    $\begingroup$ @GerryMyerson Large Language Model. $\endgroup$
    – Timothy Chow
    Commented May 24, 2023 at 0:15
  • 4
    $\begingroup$ @YemonChoi I share your feelings about GPT hype, but attributing a conjecture to GPT doesn't necessarily attribute sentience to GPT, any more than attributing a conjecture to Graffiti or a proof to Shalosh B. Ekhad attributes sentience to a machine. It's just an issue of documenting one's methods. $\endgroup$
    – Timothy Chow
    Commented May 24, 2023 at 2:17
  • 2
    $\begingroup$ Probably it will be useful to go back to this post in case we get multiple such posts. For the moment, this post is a first one and was a bit popular because this made a curiosity. However, this post exhibits a conjecture which takes a standard conjecture (variant of Goldbach) and artificially specifies it to even squares (instead of arbitrary even numbers). After several such posts there will be no more curiosity and I guess they will be quickly closed. $\endgroup$
    – YCor
    Commented May 24, 2023 at 7:42
  • 1
    $\begingroup$ It seems to me that chatGPT is a text generator. With the beginning of a text, it generates a sequel which is the most probable sequence of words. When the beginning of the text is a question, the most probable sequence of words is a sequence of words which looks like an answer for us. Hence all hallucinations that this so-called "artificial intelligence" has. However, sometimes, it may give (by chance, and I guess rarely) something interesting. In this case, why not post it ? $\endgroup$
    – Philippe Gaucher
    Commented May 24, 2023 at 7:48
  • 1
    $\begingroup$ We should not have a policy toward posts related to GPT now. Let it be now. We can wait for one year to see ...... $\endgroup$
    – math_for_fun
    Commented May 31, 2023 at 4:44
  • 1
    $\begingroup$ I appreciate this conversatioon highlighting that the content of the question is what's being evaluated, not the origin. I think that coming from a generative language model can not, in principle, add to or detract from mathematical interest. $\endgroup$
    – Neal
    Commented Jun 2, 2023 at 11:58
  • 1
    $\begingroup$ I asked ChatGPT to prove $\pi$ is irrational, and it gave an argument saying that if $a^2 = \pi^2 b^2$ (with $a,b\in\mathbb Z$), then $a^2$ is divisible by $\pi,$ and then going on to cite Lindemann's theorem that $\pi$ is transcendental, and using that to show $0=\pi^2 b^2$ so that $b=0,$ etc. ChatGPT's answers are often total nonsense. ChatGPT also told me that Moses Robinson had represented Vermont in the U.S. House of Representatives in 1789 through 1791. This overlooks the fact that Vermont had not yet been admitted to the Union at that time and Robinson never served in the House. $\endgroup$
    – Michael Hardy
    Commented Jun 2, 2023 at 17:06
  • 2
    $\begingroup$ Technically speaking, at least according to the title of a MetaSO post, ChatGPT is banned, and, according to the first sentence of that post, "Use of ChatGPT generated text for content on Stack Overflow is temporarily banned." This seems to indicate that we don't need any such policy, because it is (at least temporarily) already covered. (In practice, it seems that the ban is only intended to be enforced on AI-generated content that is not explicitly identified as such.) $\endgroup$
    – LSpice
    Commented Jun 3, 2023 at 10:45
  • 2
    $\begingroup$ @LSpice watch this space re (moderating) AI content. $\endgroup$
    – David Roberts Mod
    Commented Jun 5, 2023 at 8:24

2 Answers 2

Reset to default
29
$\begingroup$

I don't think it is worth having a policy for one post, or even a few. We already have a small, regular stream of elementary number theory questions to which one can provide good heuristics using standard analytic number theory conjectures, but which we are unlikely to ever resolve. I like seeing how number theorists think about these sort of questions, and I don't think that this one was worse than the human generated ones.

I'd feel differently if we had a flood of such questions. The first thing I thought of when I saw that question was Gauss's opinion of Fermat's Last Theorem:

a multitude of such [conjectures] can easily be set up, which one could neither prove nor disprove

and I fear that LLM's may soon demonstrate this. But I'm fine with waiting until the multitude arrives before we make a policy.

$\endgroup$
4
  • 1
    $\begingroup$ Where is that quote of Gauss from? $\endgroup$
    – Kimball
    Commented May 29, 2023 at 14:51
  • 4
    $\begingroup$ It's from a letter to Olbers. I googled to get the phrasing and used the wording from goodreads.com/quotes/… . I haven't been able to find a copy of the original, although several sources give March 21, 1816 as the date of the letter, and I have found some different translations online. @Kimball $\endgroup$
    – David E Speyer
    Commented May 29, 2023 at 15:53
  • 1
    $\begingroup$ I like the attitude of "waiting until the multitude arrives before we make a policy." Not crossing bridges before coming to them is wise. $\endgroup$
    – Neal
    Commented Jun 2, 2023 at 11:52
  • 2
    $\begingroup$ @David A transcription of the original letter can be found here: gauss.adw-goe.de/handle/gauss/816 $\endgroup$
    – Fabian Wirth
    Commented Jun 2, 2023 at 12:48
2
$\begingroup$

Half a year on, the problem seems to have mostly solved itself. FunSearch has demonstrated that LLMs can be used in conjunction with other tools to generate significant new mathematics. This work has raised the bar, so it is less likely that someone will post low-quality, gee-whiz LLM chaff to MO. Should they do so, we can presumably deal with it just like any other question that doesn't involve LLMs.

$\endgroup$
0

You must log in to answer this question.

Not the answer you're looking for? Browse other questions tagged .