Without a thriving mathematical community to point out these things it would have stayed broken. With automated math that community as tao pointed out is at risk.
The bigger question is why there was internal pressure to rush such a historic launch without having someone in the company, anyone, check the proofs first.
This concerns the Hodge conjecture (millennium prize related) paper. Seems to me like PhD
nerds weren't confident bosses pushed ahead anyway.
What makes you think that nobody checked the proofs first? It's not like someone checking it once without spotting any mistakes means that nobody else will find any mistakes either.
Proof of what? There is a sign error in one of the proofs, OpenAI acknowledged it and withdrew three papers (two relied on the result).
I agree LLM review is also fallible (as is human review) but the interesting part to me is that finding this sign error before publication should have been table stakes for OpenAI, it’s their own model that found the sign error.
I’m curious what was in the original prompt and what was in the prompt that led to finding the sign error, I think it matters a lot for understanding the dynamics here
> With automated math that community as tao pointed out is at risk.
If they can be automated, they are not necessary. If they are necessary, they won't be fully automated. It's a pretty simple experiment to run, the math "community" should bear with us. Darwin would be proud.
If you do a dump like this all of it should be formalized, there's simply too much material to review by hand and additionally it is AI-written which makes it hard to read compared to human work.
Not a mathematician but surely if a problem I was working on had an AI also working on it, I would want to know as early as possible - even with flaws or gaps. What advantage is it to me to be less informed?
Apparently the write-ups are garbage (as in very hard to read). I feel like they could've had AI fix that up at least somewhat. Maybe they'll reinvest more in writing ability now.
I’m conflicted. I guess we’ll see what the final total is once an enormous level of unpaid human effort is expended verifying the AI outputs. A little sad if that’s the future of math.
It kind of reminds me of when tech giants open source a project as a means of putting a positive spin on abandonware. “Here’s the source! Any problems are yours to fix now. You’re welcome”
Where are you getting unpaid from? Almost all people who are qualified to analyze the results are paid researchers. And if it is unpaid, then it sounds like they're looking it over for their own reasons, and that's fine?
I also fail to see the issue you have with releasing abandoned source. In what world is that bad? That obviously is a gift and should be encouraged. e.g. id software's history of doing that has meant their work stays alive forever.
Researchers normally don't pay each other to read each other's work. It's a symbiotic relationship. If they think the AI results are nonsense, they could ignore it like any other crank. If they think it seems plausible and it's relevant to them, they can try to understand it. Seems fine?
> Almost all people who are qualified to analyze the results are paid researchers.
This _might_ have been true somewhat in the past (although it wasn't), but it's completely false today. Anyone with access to a sufficiently advanced model has the capabilities of analyzing these papers/proofs. It's no different than reading a codebase you might not be fully familiar with, and checking it for correctness (give an engineering analogy).
This hardcore gatekeeping of math (and by extension STEM) fields MUST stop.
I mean, I have a decent math background, but I would struggle greatly to attempt to even tell you what most (or any) of the conjectures in e.g. number theory are about at even the highest level. I can't imagine a layman would have any hope.
I’m unsure. The whole academia is built on unpaid human efforts. Journal writers are unpaid, and institutions paid for their papers to be published by for-profit publishers. Journal reviewers are paid the bare minimum, certainly unproportional to their efforts and expertise.
well, it might be that these proofs are correct or it might be that people aren't bothering to spend a lot of time checking whether they are correct. OpenAI already has a pretty bad reputation in the mathematics community for how they are approaching this process, they seem to be more interested in creating a story for their IPO than advancing math.
But can the others even be "disproven", given that they apparently are so messy and awful that no humans can follow them? Shouldn't the onus instead be on OpenAI to prove that they're right, instead of hundreds of mathematicians wading through slop?
Exactly, I was glad to see these withdrawals, its a natural part of a healthy ecosystem of scientific review, hypothesis, claim, test, refute, extend, withdraw, its the heart of science.
IMO If you take out all the stupid human aspects mostly related to fear, egos, etc, we should brace the imperfect and helpful tools, whatever they are, improve them so they are as easy as possible to review, and keep that core scientific discovery loop going
Retraction and withdrawal are different. Retraction is when you publish something, it passes peer review, is published, and some time later its publication is undone, often by an editor or some other person because some fraud was uncovered.
Withdrawal is akin to submitting a paper to peer review and then when you’ve noticed mistakes, you decide to take the paper back and correct it.
Reject is when someone else notices the mistakes and tells you to take it back and correct it.
Withdrawal and reject happens all the time in a scientist’s career. They don’t necessarily mean the scientist is doing bad research, just the research was not ready. Retract usually means something more.
By dumping the papers, OpenAI skipped the typical peer review process, so that should be understood as what’s going on now as mathematicians look over the papers and find flaws.
This is pretty standard. Important to note that these "errors" (* not really errors) themselves were caught by an LLM, further proving their usefulness.
* The reason you shouldn't consider the withdrawals to be caused by errors is because this is pretty standard in math and development. "Errors" like this are a core aspect of science and it happens _all the time_. And from my research LLMs have a far lower error rate than even the best human scientists.
I wonder why the heck were they provided / uploaded then. Perhaps just a fast and loose play-out on their part. What I don't understand is how come engineers / scientists working on these are okay with this kind of attitude.
This company is just irresponsible. We (at least, Americans that vote and can therefore decide indirectly what’s legal) should not allow them to continue.
it's like if you vibe coded something and the onus is now on the reviewer and the reviewer tells you your work contains bugs and is messy - that is not acceptable from the reviewers pov - why should the reviewer spend all his human effort, a scarce resource, reviewing your code while you've spent barely a fraction of his effort generating this. OpenAI is a trillion dollar company, surely they can verify stuff before pushing it out? The problem is not that they are solving the problems, they don't care at all about the actual process of doing mathematics. Using compute to mine problems and throwing results in github and letting human reviewers spend effort to correct these is not going to win them any favor. If OpenAI really cared about math, they would have someone on their side who actually understood the results they produced and was able to verify their correctness and educate others.
Without a thriving mathematical community to point out these things it would have stayed broken. With automated math that community as tao pointed out is at risk.
Have you got a link to someone pointing it out? It looks like they're still going through formal proofs so likely found the problems that way.
Yes: https://x.com/ElliotGlazer/status/2108026240582246600
So someone ran a different LLM to find an issue they'd find anyway during formalisation? That's not the same as relying on thriving community.
The bigger question is why there was internal pressure to rush such a historic launch without having someone in the company, anyone, check the proofs first.
This concerns the Hodge conjecture (millennium prize related) paper. Seems to me like PhD nerds weren't confident bosses pushed ahead anyway.
What makes you think that nobody checked the proofs first? It's not like someone checking it once without spotting any mistakes means that nobody else will find any mistakes either.
That’s not proof though is it? If the original LLM output is fallible surely the LLM review of that output is also very much fallible?
Proof of what? There is a sign error in one of the proofs, OpenAI acknowledged it and withdrew three papers (two relied on the result).
I agree LLM review is also fallible (as is human review) but the interesting part to me is that finding this sign error before publication should have been table stakes for OpenAI, it’s their own model that found the sign error.
I’m curious what was in the original prompt and what was in the prompt that led to finding the sign error, I think it matters a lot for understanding the dynamics here
> With automated math that community as tao pointed out is at risk.
If they can be automated, they are not necessary. If they are necessary, they won't be fully automated. It's a pretty simple experiment to run, the math "community" should bear with us. Darwin would be proud.
“If they can be automated, they are not necessary.” That’s a pretty interesting take as eventually everything could be automated.
If you do a dump like this all of it should be formalized, there's simply too much material to review by hand and additionally it is AI-written which makes it hard to read compared to human work.
Not a mathematician but surely if a problem I was working on had an AI also working on it, I would want to know as early as possible - even with flaws or gaps. What advantage is it to me to be less informed?
Apparently the write-ups are garbage (as in very hard to read). I feel like they could've had AI fix that up at least somewhat. Maybe they'll reinvest more in writing ability now.
Almost like they care less about the maths and more about a deadline for marketing purposes.
And added 6 new ones. Might want to add that to the headline.
Looks like those are new formalizations of existing proofs, not new ones
Imagine how many wasted hours in peer review these AI math papers will cause for the 1% chance of reaching a transformative idea.
All that AI compute and resources and they couldn't hold onto releasing the papers until a legitimate peer review was performed?
Just had to get that PR stunt out to bump their valuation.
Vibe coding math research is just next-level AI slop.
Mind you, this is a competent AI company that's making these mistakes.
I can only imagine what non-technical people are putting out in production via vibe-coded AI slop.
I think it's equal parts PR stunt and negging.
People won't want to seriously peer review an AI study unless it's already out there potentially spreading misinformation
3 mistakes (so far) out of ~400 is still a pretty good hit rate
I’m conflicted. I guess we’ll see what the final total is once an enormous level of unpaid human effort is expended verifying the AI outputs. A little sad if that’s the future of math.
It kind of reminds me of when tech giants open source a project as a means of putting a positive spin on abandonware. “Here’s the source! Any problems are yours to fix now. You’re welcome”
Where are you getting unpaid from? Almost all people who are qualified to analyze the results are paid researchers. And if it is unpaid, then it sounds like they're looking it over for their own reasons, and that's fine?
I also fail to see the issue you have with releasing abandoned source. In what world is that bad? That obviously is a gift and should be encouraged. e.g. id software's history of doing that has meant their work stays alive forever.
Unpaid by OpenAI. In service of their PR goals they’re creating a bunch of work for others and not contributing to compensating that work.
OpenAI isn’t paying mathematicians to verify all these papers. It’s dumping the papers trying to nerd snipe them into checking it for free.
Researchers normally don't pay each other to read each other's work. It's a symbiotic relationship. If they think the AI results are nonsense, they could ignore it like any other crank. If they think it seems plausible and it's relevant to them, they can try to understand it. Seems fine?
> It's a symbiotic relationship
That's right, and the difference is that this one is parasitic.
> Almost all people who are qualified to analyze the results are paid researchers.
This _might_ have been true somewhat in the past (although it wasn't), but it's completely false today. Anyone with access to a sufficiently advanced model has the capabilities of analyzing these papers/proofs. It's no different than reading a codebase you might not be fully familiar with, and checking it for correctness (give an engineering analogy).
This hardcore gatekeeping of math (and by extension STEM) fields MUST stop.
I mean, I have a decent math background, but I would struggle greatly to attempt to even tell you what most (or any) of the conjectures in e.g. number theory are about at even the highest level. I can't imagine a layman would have any hope.
I’m unsure. The whole academia is built on unpaid human efforts. Journal writers are unpaid, and institutions paid for their papers to be published by for-profit publishers. Journal reviewers are paid the bare minimum, certainly unproportional to their efforts and expertise.
We are all reverse centaurs now.
I would say not. For a mathematicians, having to retract more than 2 papers in a lifetime is already a big issue in their career.
But is it equivalent to withdrawing post-publication or is it more akin to not passing peer review with major revisions requested?
Most mathematicians don't produce 400 papers in a 48 hour window either so I'm not sure comparisons are helpful
well, it might be that these proofs are correct or it might be that people aren't bothering to spend a lot of time checking whether they are correct. OpenAI already has a pretty bad reputation in the mathematics community for how they are approaching this process, they seem to be more interested in creating a story for their IPO than advancing math.
But can the others even be "disproven", given that they apparently are so messy and awful that no humans can follow them? Shouldn't the onus instead be on OpenAI to prove that they're right, instead of hundreds of mathematicians wading through slop?
The onus is on formal verification when it comes to computer generated results. So far only 22% of the papers have it.
Exactly, I was glad to see these withdrawals, its a natural part of a healthy ecosystem of scientific review, hypothesis, claim, test, refute, extend, withdraw, its the heart of science.
IMO If you take out all the stupid human aspects mostly related to fear, egos, etc, we should brace the imperfect and helpful tools, whatever they are, improve them so they are as easy as possible to review, and keep that core scientific discovery loop going
How many mathematicians need to retract ~1% of their papers?
Retraction and withdrawal are different. Retraction is when you publish something, it passes peer review, is published, and some time later its publication is undone, often by an editor or some other person because some fraud was uncovered.
Withdrawal is akin to submitting a paper to peer review and then when you’ve noticed mistakes, you decide to take the paper back and correct it.
Reject is when someone else notices the mistakes and tells you to take it back and correct it.
Withdrawal and reject happens all the time in a scientist’s career. They don’t necessarily mean the scientist is doing bad research, just the research was not ready. Retract usually means something more.
By dumping the papers, OpenAI skipped the typical peer review process, so that should be understood as what’s going on now as mathematicians look over the papers and find flaws.
It would turn out to be a pure energy and time wasting exercise … the math community would want to keep away from it.
Whose names are on these papers?
They try to be clever and put company name as the author.
Proof by authority works until human mathematicians actually run the code. Back to prompt engineering.
This is pretty standard. Important to note that these "errors" (* not really errors) themselves were caught by an LLM, further proving their usefulness.
* The reason you shouldn't consider the withdrawals to be caused by errors is because this is pretty standard in math and development. "Errors" like this are a core aspect of science and it happens _all the time_. And from my research LLMs have a far lower error rate than even the best human scientists.
Would you care to share your research? What was your methodology? Did you write it up? Is it published?
Or is it the kind of research you'd prefer to keep shrouded in mystery?
Another discussion: https://news.ycombinator.com/item?id=50002650
"a sign error" LOL
So much for the "it's lean verified" defense.
The withdrawn papers were not lean verified nor claimed to be.
I wonder why the heck were they provided / uploaded then. Perhaps just a fast and loose play-out on their part. What I don't understand is how come engineers / scientists working on these are okay with this kind of attitude.
I suspect they are not okay with this way of working.
I’m sure the outsized pay packages help quite a bit
They’re okay enough to do the work and collect a paycheck and stock options. I don’t think their arms are being twisted that hard.
How come mathematicians are ok with human mathematicians are ok with that kind of sketchy submissions? That's pretty bad too.
... they're not? Why would you think mathematicians are happy about sketchy or bad submissions.
Lies travel around the world before the truth has time to put it’s sneaker’s on…
The headlines keep the hype train arunnin
But that's the argument that was used when people here were skeptical about the results.
not these results
Can you point to where that defense has been made?
This company is just irresponsible. We (at least, Americans that vote and can therefore decide indirectly what’s legal) should not allow them to continue.
This type of sentiment is almost always motivated by fear over the potential negative personal economic impact from AI (e.g. losing employment).
Publishing a math paper and then unpublishing it is not "irresponsible". It's just a math paper.
How is withdrawing a paper irresponsible?
They only withdrew it after someone pointed out that it was a flawed paper.
In one case by asking Astra to review it.
Not exactly encouraging that they did their homework before publishing results.
This is how science is meant to work.
Most good scientists work hard to prove results to themselves before going public.
Peer review is then done _in private_ before publication as a check on quality and significance.
Retracting a paper is pretty embarrassing. And not considered science as usual.
Retraction is after publication and peer review, no?
Yes. A researcher who achieves a reputation of making mistakes carries that reputation.
it's like if you vibe coded something and the onus is now on the reviewer and the reviewer tells you your work contains bugs and is messy - that is not acceptable from the reviewers pov - why should the reviewer spend all his human effort, a scarce resource, reviewing your code while you've spent barely a fraction of his effort generating this. OpenAI is a trillion dollar company, surely they can verify stuff before pushing it out? The problem is not that they are solving the problems, they don't care at all about the actual process of doing mathematics. Using compute to mine problems and throwing results in github and letting human reviewers spend effort to correct these is not going to win them any favor. If OpenAI really cared about math, they would have someone on their side who actually understood the results they produced and was able to verify their correctness and educate others.
Withdrawing it, in itself, might not be, but it kind of skips over the part where they have a paper that warrants it in the first place.