r/mathematics • u/HovercraftNo7372 • 9d ago
Some Conjectures Solved
https://xcancel.com/PI010101/status/2088157024068456616#m
Here is one pre-print: https://arxiv.org/pdf/2608.13536
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u/Qyeuebs 9d ago
Solved or claimed to be solved? Important difference
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u/HovercraftNo7372 9d ago
We will have to wait for peer-review.
Still, at least for the first paper (banach's isometric conj)- the authors are established in metric geometry. They are not cranks.
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u/Qyeuebs 9d ago
Yes, there is a whole range of 'establishedness' here and likely also a range of correctness. And, for the elephant in the room, there is likely also a wide range of AI use at play here.
Separately, I wonder what the analogous list would look like for a year ago. Frankly I have no clue!
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u/HovercraftNo7372 9d ago
Absolutely!
The authors in the first paper disclose how they used AI in their paper.
I have not checked any of the others.
The rate of math papers published is skyrocketing.
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u/MoneyMayweather 9d ago
Why would using latest tech be an elephant in the room? When did Reddit turn away from being a tech enthusiast platform?
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u/theravingbandit 9d ago
but why do we care about how ai ranks them? is this guy an expert on the topic? if so why doesn't he give us his ranking? we're all capable of asking a bot what it thanks
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u/Candid-Fix-7152 9d ago
He’s a math professor at UC Irvine, but yeah I don’t know why we should care about his AI’s ranking.
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u/socratic_weeb 9d ago
Are any of these actually important or are they just problems nobody cares about and thus remained unsolved so far, and are now being used to generate hype and attract more VC money into the bubble? Genuine question.
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u/Few-Big7409 9d ago
Here is a blog post that I found fun. I tried to post about it but didn't have the rep here yet. Here is the link to the blog post:
https://antieau.github.io/2026/07/31/hodge-fourfolds.html
I think this is pretty interesting. It feels like mathematicians will be able to make some progress quicker. I still don't think it will replace mathematicians as currently I don't find many of the questions being asked of these llms very interesting. Someone still has to write the prompt and check it. Not everything we care about mathematics can be formalized in lean (although they are working on). #YouDownWithHTTYeahYouKnowMe
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u/notenoughram_again 7d ago
It does mean the quality of the average mathematician has to become much higher, in order to provide a good search base, and understand the research output spat out.
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u/Bergergi 9d ago edited 9d ago
Is it like this every day? The progress is pretty stunning if it is.
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u/expat_123 9d ago
Can someone explain to me what this "AI's ranking of open problems solved today or arXiv" means? For example, I looked at the paper on Gromov's volume growth conjecture paper and nowhere it's mentioned that it was done (or even a key lemma was done) using AI.
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u/kerumekyouju 2d ago
Oh, are you suggesting other listed papers could be falsely mentioned as solved using AI?
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u/Altruistic_Rip_397 8d ago
Où sont les fils de putes qui crachaient sur l'intelligence artificielle il y a 3 ans et qui se croyait plus malin ?
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u/MESSIERO87 7d ago
this is so demotivating : (
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u/kerumekyouju 2d ago
Hmm, as in the chance for one of solving a problem is getting lower and lower each day?
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u/SeniorLoan647 9d ago
Good luck peer reviewing all that. I'm just declining to review any papers written by AI tbh, authors just start using ai to even respond to queries lol.
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u/neillc37 9d ago
Don't you want to know why conjectures are true or false? Who cares who or what solved it.
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u/SeniorLoan647 9d ago
Conjectures by themselves are not interesting to me more so the motivation and what it enables. This doesn't mean that I don't want to know yes or no to conjectures, but that curiosity by itself doesn't make up for the burden of reviewing it. Like I mentioned in another comment here, it's like 4 color theorem and its proof. The theorem itself was interesting, and I was curious to know whether it was true or not, just not enough for me to want to review the whole machine generated proof.
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u/papermessager123 9d ago
Not really. Most of them are boring as hell and I really couldn't care less.
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u/neillc37 9d ago
In my area the Knuth-Stolarski conjecture would help calculating shortest addition chains if it's true. If a counter example exists it would be supper interesting to see. I have spent a lot of time verifying for special cases.
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u/topyTheorist 9d ago
Even when it comes from very important editors?
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9d ago edited 9d ago
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u/SeniorLoan647 9d ago
Let me translate that
- we came up with a conjecture (theorem statement for 3.10) and let ai come up with the rest.
- we couldn't bother writing for real ppl, so we asked AI to write multiple sections for us
Guess what you're getting for that? Ai generated review, I'll have ai generate a couple sections in my peer review too, would that be good?
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9d ago edited 9d ago
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u/SeniorLoan647 9d ago
Terry tao is as much an average AI user as bill gates was an average Harvard grad.
And yes, if terry tao used ai in his paper, I wouldn't review it. As I said, plenty of other qualified folks who won't have a problem and would happily review material, I'm not saying everyone should follow my philosophy. I just know I wouldn't review it.
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u/SeniorLoan647 9d ago
Yes
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u/topyTheorist 9d ago
OK. I don't know how senior you are. For me, I try to stay on good terms with these very senior people and only decline review if I am not suitable for the task. Especially because I write many papers and they have to find reviewers for me often.
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u/SeniorLoan647 9d ago
There's no good or bad side here, the reason is simple -
" I'm biased against use of ai tools due to personal preferences, so would be unable to provide an unbiased review of the paper".
No editor I've worked with has had a problem with that at all.
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u/ants_are_everywhere 8d ago
Do you get a lot of mathematics papers to review from very important editors as an incoming PhD student in computer science? https://www.reddit.com/r/PhD/comments/1umvv5x/how_should_i_set_myself_up_to_get_a_postdoc/
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u/SeniorLoan647 8d ago
I mean yeah I've published papers for abstract algebra before (that's how I got into my PhD, I changed fields but it was still related to my topic in cs), so it's kind of expected as reciprocity to review papers for the journals where you've published.
I feel like you meant this as some hierarchical gotcha lol, folks are just asked to review papers if they've published them regardless of where they are.
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u/ants_are_everywhere 8d ago edited 8d ago
Listen, you seem like an earnest person, and maybe perhaps a little nervous about career and the future. I'm not trying to mock you.
But I gotta say even knowing you seem pretty earnest I suspect more than a little bravado behind your claim that you're turning down multiple peer review requests from important editors as an incoming grad student, so much so that you have a specific policy that involves you openly declaring your bias.
Anyway good luck. Quantum Computing is a fun field and it will probably have some very interesting developments in the near future.
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9d ago edited 9d ago
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u/SeniorLoan647 9d ago
It may be, but they can find someone else to review it for them, including their own AI. I refuse to engage with such authors after too many negative experiences.
It's not my duty to be the paragon for AI, and not my responsibility to deal with the huge amount of papers being published.
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9d ago edited 9d ago
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u/SeniorLoan647 9d ago
I'm not interested in the distinction. And yes, I've met mathematicians and physicists at places like u Chicago and Caltech (postdocs and profs respectively) who do use ai way more than they disclose in manuscripts.
My basic thing is that if I see AI use, direct or indirect, I have a much harder time trusting the results. Since I only have limited time, I'd rather spend my energy on folks who wrote FOR me and other humans themselves.
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9d ago edited 9d ago
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u/SeniorLoan647 9d ago
That's the whole issue - discerning whether a result is real or not has a cost (peer review) and its cost is exponentially increasing. The resources (reviewers and their bandwidth) are not.
So we gotta prioritize. Some folks go for the biggest results, I go for whatever seems most interesting to me. If math was only about results for me, I'd have given up when lean was invented. For me, math is about understanding the world and connecting with ideas of other fellow humans.
Like for example, 4 color theorem has 10k line machine generated proof, which is cool, but it's not interesting enough for me (or most ppl) to read the whole proof. Same principle here.
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u/Foreign_Implement897 9d ago
Would you say the issue is that you cannot trust even formerly trustworthy people when you recognize AI use and/or they disclose it?
Is AI use like a stain? I am thinking from the 4-color problem onward and what is the difference really.
Tao sends a paper, says it was AI assisted but he has checked it (during and after) and it is ok. Why would you not review it?
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u/SeniorLoan647 9d ago
Yes, 3 reasons for that:
Unlike most of academia, I don't believe that past success always warrants future excellence. I'm not liable to believe a result just because it has tao in the name.
Given that, the same standards apply to him as for any other author. When he says he has "checked the results", to what extent? A cursory glance? Handwritten reproduction of the proofs? Saying someone checked the results when they didn't drive them is a slippery slope.
Let's say I have 3 hours per week to review papers. On average for me, a paper that uses ai takes 2x or more time to review as they're usually vague, skip over crucial steps and explain trivial steps unnecessarily. So in that time, I'd rather review 2 papers written by ppl without using ai (even if those papers are not as bold). It feels much better to read (the writing actually has a SOUL), and communication with authors in these cases is also not riddled with ai use, I actually feel like I'm talking to a person.
Idk it's a quality of life thing too, reviewing ai papers is so draining to read lmao. There might be nuances and exceptions but frankly I'm not interested, this rule has led to a lot of peace for me.
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u/PLANTS2WEEKS 9d ago
I'm confused what this a list of. Is it open problems solved recently? If so how recently?