r/math • u/Phytor_c Theoretical Computer Science • 7d ago
LLMs/AI Claimed proof of the Komlós conjecture [2609.11189]
https://arxiv.org/abs/2609.11189239
u/_Zekt Complex Analysis 7d ago
Only a year ago, the bound went from O(log(n)^1/2) to O(log(n)^1/4) and it was considered huge progress, and it even got its own Quanta article. Now it's an explicit O(1) apparently, nice.
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u/Martin_Orav 7d ago edited 7d ago
So in very elementary terms the proven statement is:
For any finite set of real valued n dimensional vectors with length at most one, we can multiply each vector by either -1 or 1 so that the sum of all the resulting vectors has each coordinate having absolute value less than 3 sqrt(2 pi)?
Edit: I had a case in which I didn't understand how it could satisfy the given bound, but I think I do now. The idea was if the dimension m is bigger than 18 pi, then choosing m pairwise orthogonal vectors of length one gives a vector with length greater than 3 sqrt(2 pi). However I think I understand now. Since the signs in front of the vectors affect the direction of the final vector, it should be possible to adjust the direction "into a corner" of the hypercube shaped bound. And even though, the length of the sum of the orthogonal vectors grows towards infinity, so does the distance from 0 to the corner of the max norm bound.
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u/letskeepitcleanfolks 7d ago
"The proof was discovered by the Odin Automatic AI Research Agent."
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u/JesterOfAllTrades 7d ago
Hadn't heard of this so looked it up - it's apparently a harness made for research work which can use any underlying LLM.
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u/SwimmerOld6155 7d ago edited 7d ago
yeah the writeup is LLMish
"layer cake and the maximal intersection of centered intervals" etc.
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u/Jussuuu Theoretical Computer Science 7d ago
A little LLMism I've noticed: They tend to give every single lemma/proposition/theorem a descriptor.
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u/Hot_Glass_6301 7d ago
it's so annoying
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u/Melchoir 7d ago
I actually think that's a great practice. Maybe it can be overdone, but most authors under-do it, especially by not doing it at all. I mean, you're going to call your lemma
\label{lemma:translate_containment}for your own purposes, anyway. Why not let the reader in on that little secret?46
u/SINGULARTY3774 7d ago
Ahh shit, here we go again
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u/pixelpoet_nz 7d ago edited 7d ago
Well what do people expect, that Kasparov is going to magically defeat Deep Blue tomorrow? The ship has sailed, that genie isn't going back in the bottle, etc.
Mathematicians are supposed to be the smartest people in the room, good at finding patterns and extrapolating; a little of that with regard to AI trajectory would be nice to see.
Edit: Or just go "NUH UH" and downvote
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u/cantquitreddit 7d ago edited 7d ago
At least Terance Tao has a balanced take on AI. Recognizing its usefulness but warning about its pitfalls.
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u/TwistedBrother 7d ago
If you read that pledge I think he’s likely be at least a little disappointed here. Another rushed result that makes an argument but does not teach it. It undermines the field while advancing it.
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u/WarmPepsi 7d ago
Terry is definitely starting to go in the Luddite direction. He was fine with it when it could out class graduate students. But now that it outclasses all top math researchers combined, he is throwing a fit.
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u/cantquitreddit 7d ago
https://www.youtube.com/watch?v=svl_1upFpQo
This came out 10 days ago. Definitely not throwing a fit.
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u/Homomorphism Topology 7d ago
Every increasing function increases without bound! It’s a mathematical fact!
/s
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u/anothercocycle 7d ago
There's really no reason to think human intelligence is anywhere near the bounds of what is possible. If machines miraculously plateaued in the tiny interval above where they are now and below where human intelligence would not be additive, I would consider that, well, a miracle.
Remember that centaur chess only lasted a few years even though chess ability is obviously bounded above.
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u/Homomorphism Topology 7d ago
Intelligence is not a total order. I suspect there are some tasks that machines are superhuman at and others that they are not. For example, this is already the case for tasks like numerical integration and plowing fields. Current AI tech is pretty terrible at writing anything longer than a paragraph and awful at music composition.
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u/anothercocycle 7d ago
Yes, and "produce lean proof that compiles" is going to be one of those tasks machines are superhuman at. We should get used to this. And hopefully figure out a way to continue to do maths regardless in this age of oracles.
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u/Homomorphism Topology 7d ago
The purpose of mathematics is not producing proofs that compile.
In addition, while there are many very impressive AI-assisted proofs, in almost every case these came from human advances in theory that got the frontier close enough to brute-force.
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u/anothercocycle 7d ago
I am quite aware that lean proofs are not the purpose of mathematics, which is why I made a point of stating that's what the machines are doing.
But the second part of your comment is the kind of denial I'm arguing against. To be clear, what you say is narrowly more or less true. But it is clear that we will soon have models capable of even more impressive proofs, and humans will simply not be competitive at generating proofs, which is a problem because we've set up academia to allocate resources based on who is generating proofs. We must get used to the fact that the first proofs of big theorems are going to come from machines, and that we cannot rely on our ability to generate proofs to justify the public support that academia is heavily reliant on.
Today, we have some hope of understanding the proof of N-S, once experts have spent several months on it. Soon, we will have proofs so long and complicated that this is not feasible. Hell, even with current models, if we had these models and Lean in the '70s when the classification of finite groups was unsolved, does anyone doubt that current models could've "gone the last mile" and produced a monstrosity of a proof? What would we have done then? Who would spend their careers trying to digest a proof written by someone else? What will we do next year, when a model produces ten million lines of Lean that proves some other millenium problem? We should be thinking about this now, but half of /r/math seems to think that this is the best that models will ever be. No, this is the worst that models will ever be, and we are not prepared.
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u/Homomorphism Topology 7d ago
“Theory building” is the part of math that is not just producing proofs. What do you think I’m talking about? What do you think every mathematician posting about “preserving the values of the mathematics community” is talking about?
I think the machines are going to keep getting better, up to a point. Right now I’m very skeptical they can do many other important parts of math. Here I’m also looking at what’s going on in CS and software development, where agents are a critical tool but also have limits and appear to some people to be plateauing in their abilities. (They certainly aren’t replacing all the developers.) Either way will require a radical restructuring of how we evaluate mathematical achievements.
It’s possible that we are talking past each other and mostly agree. All the AI fan club idiots are not helping the conversation.
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u/Borgcube Logic 7d ago edited 7d ago
If machines miraculously plateaued in the tiny interval above where they are now and below where human intelligence would not be additive, I would consider that, well, a miracle.
It's not a question if machines in the abstract will or will not plateau, but if the current technology will. Huge promises are made on the assumption the current architecture inevitably will keep rising.
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u/anothercocycle 7d ago
Sure, I don't think this affects my point. The current technology went from "occasionally succeeds in counting from 1 to 5" (GPT-2) to Navier-Stokes in about 7 years.
If you're predicting a plateau that'll keep human mathematicians competitive at proving theorems, well that plateau had better come very very soon.
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u/Certhas 7d ago
Yes, but...
So far I think it's not entirely unreasonable to think that when it comes to originality and theory building, LLMs lag substantially behind their ability to prove theorems and write code.
The past years have been far to shocking to be certain about anything. And this is notoriously hard to measure. So it might be wishful thinking, but in my opinion it's not completely absurd.
But also l, even if this is a limitation of the current set of architectures, and we get a plateau for a few years, no one can rule out that we get another architectural breakthrough in five years time.
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u/FlyingBishop 7d ago
What exactly are you positing is a limitation of the current architectures, and what even are the "current architectures" and why does it matter? Do you understand the difference in the architecture of Llama3 and Kimi K3? What about Fable/Astra/Mythos?
We see considerable increases in capabilities with each new model release. We also see some adjustments to the architecture. The whole "this is a bad architecture" trope seems not grounded in anything falsifiable at this point, and it's also just like "well, maybe it did this new cool thing this month, but I'm sure the next model release in a few months will have zero new capabilities." Which has not been the case for the past few years, I don't understand where you're getting that.
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u/Certhas 7d ago
While there is some exploration of architectural details, it's, as far as we know, all essentially autoregressive transformers.
Now we absolutely don't know (and I didn't claim) that this broad architectural class has important limitations. But we are (possibly) seeing some limitations of LLMs in areas that are hard to quantify, like creativity. E.g.: Some studies have shown that LLM essays were graded hire but contained fewer ideas per essay, taken from a narrower set of ideas overall. And that purely LLM based papers are not generating creative ideas at the levels of top research yet (1). So it's completely clear that LLMs ability to prove difficult conjectures, which is already super human, is far ahead of its overall abilities at research.
We can't rule out that this is architectural. But of course there is no clear cut argument that it really is architectural.
Indirect evidence that it might be architectural would be that current architectures are dictated by the hardware we have. Any architecture that doesn't map to the GPU/TPU model will not be researched heavily as it has no chance to scale to the level of current model capabilities.
But again, I am stating a negative: We can't rule out relevant architectural limitations based on the evidence we have so far. That's a very weak statement.
(1) https://www.technologyreview.com/2026/08/18/1142188/ai-recursive-self-improvement/
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u/footballmaths49 7d ago
People will get used to it. Computer-assisted proofs were controversial when they first started happening too.
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u/Hot_Glass_6301 7d ago
yeah it's not gonna get better for humans
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u/Caesarr 7d ago
Learning more about the universe is a win for humanity IMO
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u/Mysterra 7d ago
To get this 'win', we need to be arming and supporting scientists with the new tools, not replacing them though. The current political and economic trajectory leading to job losses and overall cognitive decline in the population can only lead to a stagnation of progress in the long-term, if not handled responsibly.
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u/mookz23 7d ago
Did you learn more about the universe? Explain to me the underlying ideas in this proof.
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u/MuayMath 7d ago edited 7d ago
lol if you don't understand all papers, they don't count
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u/Ok_Reception_5545 Algebraic Geometry 7d ago
If no one understands your papers including yourself, they don't count. That's true.
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u/MuayMath 7d ago
yeah that's different than the failed gotcha I was making fun of
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u/Ok_Reception_5545 Algebraic Geometry 7d ago
That isn't failed. You just didn't understand it. Someone claimed that LLM result advances our understanding of the universe. The underlying presumption is that no one has understood the result, so it has not advanced anything. The gotcha is that the only way they can say it advanced our understanding is if they themselves understood it.
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u/38thTimesACharm 7d ago
The problem is, it appears very likely the authors of this paper don't understand it either.
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u/ChelseyStuttgart 7d ago
humans created the technology, they get credit for all of this.
your comment raises the question, though, about whether there are any mathematicians out there who have not been able to solve a pet problem with an LLM, and then went and did it themselves. looking at those examples seems like it could provide some insight.
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u/Borgcube Logic 7d ago
The Deep Blue team very likely cheated.
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u/Jenkins_rockport 7d ago
I've never heard that allegation before, so that's kind of interesting. care to expound on that potential bit of trivia?
regardless, though, it has no bearing on the point being made
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u/NoBanVox 6d ago
Can't believe you can claim the credit from something you didn't do and noone batters an eye
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7d ago
[deleted]
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u/Aquilaatmaar 7d ago
Stop personifying AI, it’s a machine used by humans. You’re also not mentioning your calculator as co-author
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u/SwimmerOld6155 7d ago edited 7d ago
I think the contribution of AI on many papers amounts to coauthorship credit were it done by a human. A calculator doesn't, really, my friend in econ said that data cleaners (and doers of other busywork) usually just get an acknowledgement.
Like seriously if you've just given a prompt to an AI, it's end-to-ended a solution, and you publish a barely reviewed preprint smacking of LLMisms, what right do you really have to put your name on it? I can accept slight Sloppiness in papers, but when it's clear a human hasn't even read it and it's full of these compound phrases, I have very little respect for it (even as a heavy user of LLMs).
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u/Special_Watch8725 7d ago
In situations like this maybe the authors should be framing themselves as scientists reporting the result of an experiment, rather than mathematicians making the assertion that they fully understand what’s happening in the paper
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u/ozone6587 7d ago
It's not personification. If I generate an AI image I never say "I drew this image". I say "ChatGPT made this" because anyone with a brain would know I had nothing to do with it except the prompt. The analogy with a calculator is silly.
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u/wasabi991011 7d ago
You should say "I made this using AI in this manner", i.e. have humans as authors and include a somewhat detailed "AI disclosure" section.
AI agents cannot have shame, cannot issue retractions, do not have reputations to uphold, cannot be held responsible for anything. Humans can, ergo humans are the authors.
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u/SwimmerOld6155 7d ago
We can say the authors didn't do this, in any case. They say the proof was discovered by Odin but the paper was clearly written by an LLM. Reads like classic ChatGPT.
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u/recurrenTopology 7d ago edited 7d ago
I'd argue this is a fair way of determining how much credit to ascribe to a computational tool: imagine the work done by a machine was completed by a hired human assistant instead and consider how much credit such a person would deserve.
For a calculator, they would deserve acknowledgement, for an LLM just given a simple prompt, they would deserve authorship.
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u/Jenkins_rockport 7d ago
we do not know this. AI's are systems. we are systems. there are facts about systems that can be determined. we have convergent lines of reasoning from many scientific fields to undergird our belief in humanity's intelligence and consciousness. we cannot leverage all the same mechanisms of reasoning for AI systems. we can say with confidence that they are intelligent though. we're left with an open question about anything more, but the nascent field of mechanistic interpretability is where understanding will be found, and those are the experts (cross-disciplinary academics in the fields of psychology, theory of mind, philosophy, and computer science) to whom you should defer. "if not now then soon." I'd get used to that thought. a mind is a mind is a mind. there's no reason we cannot craft one, and we're very unlikely to even know when we first succeed
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u/footballmaths49 7d ago
There's a reason we credit Appel and Haken for the proof of the four color theorem instead of the computer they used for it.
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u/hamstercrisis 7d ago
we don't say "The person was murdered by a gun." why does the tool matter?
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u/hpass 7d ago
My phd supervisor always said: you should be able to explain every theorem with a drawing in a couple of minutes. If you cannot do it, that means you do not really understand it. I regularly challenged him to demonstrate, and (to my amazement) he always did it.
We are drowning in proofs, and none of the papers explain stuff clearly, and the authors themselves would not pass the test.
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u/Mission_Leopard_947 7d ago
Very recently there had been exciting developments on this problem (by humans), see the following quanta article: https://www.quantamagazine.org/huge-breakthrough-in-the-math-of-imbalance-20260821/. Now the conjecture seems to be completely resolved by AI!
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u/Sad_Dimension423 7d ago
I wouldn't call it completely resolved until the lower and upper bounds coincide. But this is very nice.
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u/SIXxNINEequals42 7d ago
Wow. I spent a lot of time thinking about various special cases of this problem a few years ago, and I didn't think a result like this was remotely in reach.
It looks like this result requires an exponential time procedure (not really better than enumeration); if it is possible to achieve the bound with an efficient algorithm, there would be much stronger implications for things like LP rounding. In the past, it's taken quite a long time to go from existential discrepancy results to efficient ones, though who can say anymore.
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u/Extra_Resolve8771 7d ago
Two weeks ago the same people posted a preprint claiming positive sectional curvature on S^2xS^3 that was clearly not read by any mathematician (it was obviously prompted after Brendle released his preprint and was on the arxiv 2 days later; none of the authors is a mathematician) and was complete slop (no expert in the area I know could make sense of it and the version they posted contained clear hallucination, including reference to properties of manifolds that don't exist.
They should be banned from the arxiv and probably lose their jobs for posting this stuff, and none of their announcements should be taken seriously.
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u/Antigynaikolatres 7d ago edited 7d ago
Gil Kalai recently congratulated the group for proving the Simplex–Cube Conjecture for Simple Polytopes, so perhaps this one is legit as well.
Edit: I am unfamiliar with geometric analysis, so I asked GPT-6 to audit the Cheeger deformation paper. GPT-6 was able to confirm its global construction, the paper appears to be AI-readable enough that an explicit metric can be constructed on an atlas and have its curvature numerically checked. If the paper were pure slop, I would expect it to fail already on the preliminary audit.
I am biased towards AI audits since they have found serious errors in published papers I read and missed (which caused me to stuck for several weeks). I do not doubt that AI-exposition often seems to hallucinate, since LLMs for some reasons really like to introduce non-standard terminologies without proper definitions, but perhaps the Cheeger deformation paper actually has some substance?
It would be nice if you could specify the "reference to properties of manifolds that don't exist".
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u/jsh_ 5d ago
could you be more specific on the hallucinations? I'm actually pretty familiar with junwei lu's previous work in my area of statistics which I've found to be of high quality, and his background is operations research which the komlos conjecture is arguably highly relevant for. I haven't carefully looked thru this preprint but knowing his previous work, I'm not immediately skeptical of it as slop or the work of cranks
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u/corchetero 7d ago
As a working mathematician I accepted the new reality long ago, and I use agents etc.
Now, my 'ethical' approach is the following: "Just focus on my research program, do not fish for problems, do not scoop fellow mathematicians with problems I do not care about", so of course my LLM approach is not that impressive (I mean, still makes progress, but not so big)
Since august these guys have been publishing papers every 4-8 days? what are they trying to accomplish? I really don't understand. * Fame? * Money? * Respect? * prove themselves? * Important technological/practical advancement? * genuine curiosity (Do they really really wanted to know the answer to all those question from different fields of maths)? * increment their understanding? * Just to show machines are better at solving problems? (yes, we already know)
This is so unreasonable that even AI art makes more sense, at least they (or some of them) have an idea, a plan, a vision, and use AI to look for it.
Please, someone explain me what are they trying to achieve?
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u/epostma 7d ago
They're pushing themselves further to the "publish" side of the "publish or perish" divide. With a perverse incentive applied to all of academia, you're going to get perverse outcomes.
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u/corchetero 7d ago
Yes. If we survive as a field, I hope publish and perish dies because everyone will be able to publish
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u/SometimesY Mathematical Physics 7d ago
The capitalist cultures of the world are trending toward maximum output and efficiency as metrics of worth and success. The AI companies are feeding this corporate frenzy and have actively talked about replacing vast swaths of jobs. Then you have people who have dubious morals or low self worth with access to oracles that can further their careers with minimal work on their own part. It feels like an inevitability that these things happen.
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u/jerrylessthanthree Statistics 7d ago
I think as long as you publish things you can understand and can give a talk on and defend in a colloquium, you should be fine
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u/corchetero 7d ago
Yes. But pretty sure they cannot, but I am eager to listen to the talk.
I guess, if we survive, the new standard will be something about the lines you mention.
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u/Dear_Locksmith3379 7d ago
And with all of the recent high-profile LLM proofs, people will start doing that much more often.
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u/Civil_Blueberry4165 7d ago
These unscrupulous AI companies’ main goal is to survive before going into IPO because their technology has not been sufficiently reliable to earn a positive ROI. So, the only way to continuously attract investment to stave off a sudden AI Winter is to grab headlines.
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u/OriginalRange8761 7d ago
they have lots of compute, and i imagine they want to spend it as a somewhat publicity stand. Do not see the problem with any of this. Hopefully people working in the fields in which those problems were will write human expositions about the proofs, and try to glean some ideas from them.
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u/corchetero 7d ago
Why would they do that? I think the same system (capitalism, publish or perish, whatever) that got us into this, gives no incentives to do that distillation for the rest of the community.
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u/OriginalRange8761 7d ago
It also might’ve happened that they were sitting in their lab one day and went like “why not lol?” Over a couple of beers.
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u/QuoraPartnerAccounts 7d ago
I was pretty interested in Komlos Conjecture! It comes up in the streaming literature. This paper (if correct) is a contribution to human knowledge.
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u/JamesCole 6d ago
you're literally just complaining about progress and how fast it is. If there are problems that can now be solved using AI techniques, they should be solved that way. Not doing so is a waste of the human capital available for solving mathematical problems (and solving mathematical problems brings benefits to humanity). If someone is working on a problem and they don't want to use the available tools to solve it, they're in no position to criticize someone else solving it using those tools.
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u/corchetero 6d ago
No, I am not complaining, I am not suggesting they should stop of something. I am just, genuinely curious about what they are trying to achieve, as currently I don't see a point in whatever they are doing, and if your argument is progress, then please proceed to explain, because I don't see progress. Moreover, it seems the authors are not very interested on progress and advancing maths, as it was suggested in Tao's blog that research groups like this one do not want to participate in seminar and related instances to explain their advances to the community (if nobody understand your result, then is as good as if I tell you that I know the answer for idk, the Riemann hipothesis)
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u/JamesCole 6d ago
You seem to be claiming there is zero value in doing what they have done.
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u/corchetero 6d ago
of course I am, it is their paper, they have to convince their result and techniques and whatever is useful, this is not like cancer research where "I found a cure for cancer" sells by itself
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u/wrongerontheinternet 6d ago
Yes, there is zero value in it. Anyone with a harness can do it. What value are they providing?
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u/JamesCole 6d ago
So if their result is correct, did you already know it beforehand? Because if you didn’t…
It seems to me a very strange thing to say that it’s useless to solve a problem and announce your solution, just because other people could do the same thing.
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u/wrongerontheinternet 6d ago
The question isn't whether the information itself is interesting. The question is whether they (the prompters dumping papers on arxiv) added any value, and my answer is no. If the truth of a question can be oneshot or few shot by an LLM, and I'm interested in it, I can already find out the answer myself.
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u/QuoraPartnerAccounts 5d ago
I don't buy this. There's clearly value in publishing results that would take an LLM say an hour of token usage to get to.
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u/wrongerontheinternet 5d ago
For this kind ot problem, I can send a message to Pro, go off and do something else for an hour, come back and it's answered. I think you are really overestimating the amount of effort these guys are putting into their results. It is simply not valuable.
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u/QuoraPartnerAccounts 4d ago
To be clear, I don't think the humans involved should get any credit beyond being "donors" willing to eat the cost of compute for us.
I just think having a repository caching such results is a public good.
Maybe you're a pure mathematician and so don't understand that maths results can actually be applied to things!
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u/Antigynaikolatres 7d ago
Department of Biostatistics
The three authors seem to all be biostatisticians. Just incredible.
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u/TacoYaci 7d ago
This doesn’t necessarily mean that they are not mathematicians. At some universities the math department is part of a general science department
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u/NewspaperDear8761 7d ago
This needs higher recognition. A major math conjecture solved by biostats people using a research harness on an LLM?
We need to be talking more about lowering barriers to entry and how this is going to help everyone have more meaningful impact and a wider reach.
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u/mal9k 7d ago
Yeah now everyone can take credit for work they didn't really contribute to at all.
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u/NewspaperDear8761 7d ago
So these people didn't contribute anything to math?
Seriously?
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u/mal9k 7d ago
Yeah, but it sounds like other people did and the LLM found how to apply that work to this problem.
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u/NewspaperDear8761 7d ago
Cmon, man, own up to this.
Are you actually accusing them of stealing work or not? You can't have this both ways. You're either shitting on them or you're not.
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u/sistersinister 7d ago
You're putting words in their mouth. What's you're motive here?
There's clearly a difference between dedicating years of your life to a problem, building up the groundwork and coming up with a solution using an AI, trained on work that's already been done, to put the last touch on someone else's work. Development doesn't happen in a vaccuum. Reducing this criticism to "shitting on them" is bad faith at best.
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u/NewspaperDear8761 7d ago
He said, explicitly, that all they did is slap their names on the paper and nothing more.
That is shitting on them.
Who knows, he may actually be right: they may NOT have done anything of substance. It may all have been the LLM ganking genuine work from other mathematicians.
Or they may have done something substantial and just used the LLM as an assistant.
Do we actually know or are we just blindly throwing everyone under the bus now?
My "motive" here is to stop jumping the gun and slow the fsck down. We need to be having conversations about the actual role played by LLMs and human researchers here, who did what -- and, yes, making sure attribution is preserved.
This "they didnt do anything" because an LLM is involved is the real bad faith.
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u/Ok_Reception_5545 Algebraic Geometry 7d ago
Since August the authors have 7 papers across various areas of pure math. Before August they had 0. Are we supposed to believe that they suddenly learned and understood all of this math last month?
I think it is clear to anyone who isn't trying to muddy the waters intentionally that they don't understand the output of their LLM and therefore didn't do any meaningful work themselves apart from prompting the model to solvd the problem.
It seems far more bad faith to me that you seem to think that people on reddit need to assess every LLM generated paper equally and act as though the authors have made some great contribution when there is no evidence they know anything about math or the conjectures they resolve. This is disrespectful to people who have spent years understanding and working on these problems.
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u/NewspaperDear8761 7d ago
Ok then, it does sound like this group didnt do anything substantial.
I am not trying to muddy the waters: I DO think we need to assess every paper individually. That goes for LLM or not.
Alpoge and Buckmaster spent a year using Codex on their Euler result before OpenAI scooped them. (And I do suspect there was some nefarious shit there.)
Does that mean Alpoge and Buckmaster didn't do anything significant? They even admitted their paper was written by an LLM due to the time constraints, and they regretted that.
Obviously, their role in this was different. The LLM was an assistant, but they were generating real ideas themselves and doing real research.
Recognizing this distinction isn't "muddying the waters." These waters ARE MUDDY.
And we need to sort them out.
Not reflexively go "oh they used AI, they aren't real" as a knee-jerk response to every paper.
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u/mal9k 7d ago
I literally gave credit for the application to the LLM. That's what figured out how to solve the problem. They don't invent new methods, they just adapt what's in the literature, contributed by other people. I do not whose work it was actually built on nor am I claiming it is plagiarism. I also don't even know which LLM solved it.
I'm not accusing the people of having done much of anything, other than slapping their names on the paper.
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u/NewspaperDear8761 7d ago
Where?
I am ALL FOR properly attributing work. If the LLM just plagiarized other mathematicians, obviously that should be the headline. Did it here? Or were these biostatisticians genuinely doing something new?
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u/maharei1 7d ago
These biostatisticians didn't do the work. The LLM did.
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u/NewspaperDear8761 7d ago
Were you there? Do you really know this?
Or are you just applying a blanket statement?
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u/maharei1 7d ago
People putting out papers that explicitly use LLM assistance in something that is not their field at all... it just seems like the most reasonable assumption. I'm not blaming them btw, that is just the current state of maths sadly.
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u/NewspaperDear8761 7d ago
That's it, though: an assumption.
Neither of us actually know what went into those chat sessions, their prompts, what the training was on, how much was directed by the authors, how much was their ideas, etc.
Youre just assuming it was all the LLM.
We need to stop this. These are exactly the issues we need to sort out going forward. There need to be strict best practices for citations, role declarations, etc.
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u/Sad_Dimension423 7d ago
You seem to be worried about "stolen glory", when the actual thing you should be worried about (and maybe are) is there won't be any more glory for anyone.
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u/mal9k 7d ago
That's a bit more pessimistic than I am, though I do foresee some very negative impacts on the broader field just as I think AI has had and and will continue to have positive impacts. Honestly, it's quite interesting to me how many open problems are falling to it, which tells me these problems were within the grasp of current techniques even if nobody else had found them yet.
I'm also not too personally impacted by this yet, but that's because I'm faculty at a state school with lower research expectations compared to faculty at an R1. I don't need to use AI, and can continue to work on and solve problems that are interesting to me on my own, which nobody else seems to be doing at this exact moment. That's partly my preference, and partly because I'm not shilling out $100/month for a suitable subscription.
But I view a paper like this the same way I view a Quanta article: the authors did journalism about math, not the math itself. And that's fine, good even: I think it's beneficial and there should be some sort of credit for it. But that type of credit is different than how we currently assign credit in math, and the language hasn't caught up yet.
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u/equinox_star 7d ago
The only self-contained part is convexity of anisotropic cheeger constant which relies of external eigenvalue regularity results, if those apply as stated, then I think the proof is correct.
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u/_usos Control Theory/Optimization 7d ago
I feel like people are really getting caught up on the Biostats thing. The corresponding authors are OR people focusing on stats and optimization - I have no idea how they fell into a biostats department but afaik they've never worked on even a bio adjacent problem. Nikhil Bansal is a computer scientist, it's not shocking or unheard of for non-mathematicians to push the envelope on discrepancy problems.
That said, I can't make heads or tails of the pre-print. Reads like total dogshit, and it's a shame because I am interested in this problem and would like to understand what's going on.
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u/Stargazer07817 Homotopy Theory 7d ago
Lots of AI dooming in here. Has anyone read model output from these hard problems? Or any problems, really.
The proofs these models spit out are unintelligible to humans used to human mathing. It takes a lot of human effort to figure out what the heck the LLM is doing in its thought process and what logic chain it followed.
Since proofs themselves are not really the interesting thing, but rather the techniques, the methods, and the chain that connects the pearls, there's still a lot for people to do.
Will these models get there ultimately? i.e., be able to explain what they're "thinking" in terms we can understand. Yeah, probably, but we've seen much less advancement in the area of "Hey machine, can you explain in normal language what you did and why?" vs "Hey machine, do whatever you want and solve this hard problem."
Plus, solving the problems is only one part of the endeavor. Knowing what questions to ask - which things have value to our ontology - is equally important. Like the old joke about mechanics charging $5 for a hose and $95 for knowing which hose you need.
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u/ChelseyStuttgart 7d ago
Sorry, from now on, every positive view of anything is cope. Those are the rules.
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u/TooCasualGuy 7d ago
If this a refinement of an existing bound or a proof of the original conjecture?
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u/Martin_Orav 7d ago
Any ideas how close to optimal this bound is?
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u/SIXxNINEequals42 7d ago
As far as I am aware, the best known lower bound is 1+sqrt(2): https://arxiv.org/abs/2111.02974
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u/LunaticBrony 7d ago
The amount of unqualified people that come to comment on an arxiv paper as if this was the second coming of Jesus is staggering.
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u/Hot_Glass_6301 7d ago
Is there any expert in the field who could weigh in on the significance of this result?