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.
This is not a problem unique to the mathematical community.
What about software developer community? AI has eliminated the need for junior software engineers. Almost no one is hiring junior software engineers. But companies still need senior software engineers. Without junior engineers how will there be senior software engineers in the future?
What is the solution? I don't think the solution is to say AI progress in software, mathematics etc. should be halted.
Junior software engineers not being hired is not the same as not needing them. Now I have to fight senior employees that do worse things than junior employees (and produce worse software than two years ago), because they delegate their work to the AI without checking or reviewing anything at all, or questioning the AI architecture "decisions", and we have more incidents than ever...
It's really depressing watching brilliant software developers and engineers producing the worst, unmaintainable code imaginable, and being okay with shipping it because it's passing the test suite. Assuming the test suite is any good anyway (because holy crap, the nonsensical tests AI writes...)
Your code used to be a masterpiece, so well crafted it's easy for AI to tweak and modify because you've got everything so logically organised and scoped... and now this is what you're producing? Hard to debug monstrosities that only an LLM can realistically bolt new features or tweaks onto, because it can do the kinds of refactoring necessary each time.
We use to talk about the fact that code should be readable because you spend more time reading it than writing it, but I think that misses the key part that readable code is also typically easier to debug. If you can read and understand the code, you can follow the logic when things are wrong in production, and you can more easily reason about the emergent properties of interactions between the complex systems that are involved.
I always like to say that LLM-produced test suites aren't for testing software correctness or validity, they're for testing to make sure that stuff that was previously in place stays unchanged. This, of course, is six-in-one-hand-half-a-dozen-in-the-other since the agent will often just update tests to match the updates it just made, but I do find value in providing some kind of continuity to a codebase that's being modified at breakneck pace. YMMV
> This is not a problem unique to the mathematical community.
Ahh that's OK then. Everyone's in this same boat simultaneously in multiple industries! Cool!
> What is the solution? I don't think the solution is to say AI progress in software, mathematics etc. should be halted.
I think the solution from the maths world is to not grant these AI papers (or their human sponsors) the normal courtesies of "regular order", just as you would not with an AI lawyer or someone who was just pressing enter at a law firm.
But in the software world, nobody gives a shit, apparently. We are collectively morally bankrupt and should not be granted the regular order to help other people to decide what to do with us.
If you have made it to the point of being a Junior Developer, I can assure you food and shelter is not a problem for them. You just have to adjust to a standard of living like the other 7 Billion people on this world.
Also, if a Junior Developer can show me(or anyone) they have built an entire system on their own and explain key concepts, there is no dearth of jobs for them
> There is nothing preventing Junior Developers to develop their own systems and understand it.
Eh? Apart from it not being what they are paid to do on their 9/9/6 jobs, when will they have the time to make it happen?
What is going to happen is that the remnants of the open source community will do the job of educating juniors for free, when the university degree system collapses. Just like it currently keeps a bunch of systems going with inadequate compensation.
The corporate world gets the problem off its balance sheet. Again.
The argument you respond to here is "it is impossible for anyone to be Junior Software Engineer because AI". That is a straw-man.
The actual argument is "there will be no jobs for Junior Engineers, so there will be far fewer, and as a result there will be a huge shortage of Senior Software Engineers".
You are responding to the problem as if it some kind of extinction event, like a rare bird, where if we can find a breeding population we save the day. A few curious people, self training for the love of the game, and as a result we still have a few Software Engineers so everything is fine. It is not like that, and I haven't heard anyone suggest that is the issue. The potential problem is a massive shortage of workers with skills that are currently essential to the functioning of a large fraction of the economy, whom we might still need in the future.
The continued existence of talented enthusiasts does not establish an adequate workforce pipeline. If paid entry level experience contracts, what replaces it, and why should we expect that replacement to operate at sufficient scale?
Or the broader reproducibility problem that’s been silently plaguing most of academia for decades with little to no mention. Many, many, many papers and theses and assumptions we build on may be bunk.
AI development should be harnessed in such a way that AI augments humans without replacing them. Tools that replace human intelligence altogether are not true progress for humanity.
I'm not old enough to have gone through the revolution that was programming languages that got increasingly more abstract and decoupled from the metal, but surely there's a lesson that can be learned from that era?
more importantly those abstractions were designed to try to make it easier to reason about what was going on for the author, build additional internal abstractions and to allow a reader to follow along and gain an understand of the structure. unless we believe that we can completely punt on having agency over the codebase, then llm code is only as valuable as it is readable.
The dream is that we keep agency, but also give up on reading code, by doing away with code as our level of abstraction and instead having humans edit human-readable spec files (including, say, depicting UIs directly with visual mocks). Like "no code" platforms, but for everything.
If by "human readable" you mean written in natural language, then those spec files will have ambiguities and imprecisions. If you make the spec precise and unambiguous enough, then it essentially just becomes a program written in code.
We know how this goes, at least in broad strokes. We've been through it before, just not with "knowledge" work. If there is demand for something then supply will show up to provide it.
Some jobs will stick around in vastly diminished numbers with tasks that are completely different than what they used to be to produce the same output (e.g. farmer). Other jobs will be eliminated entirely (e.g. switchboard operator). I'm guessing things like software engineering will go the way of the farmer, with the main unknown being just how much demand for software there is.
Why do people think that people displaced by AI in one industry will get a job in another industry?
The entire valuation of the AI industry is predicated on people not just losing individual jobs, but being taken out of the workforce entirely on an economic level.
They are talking about the workforce of the entire economy shrinking. People will lose their livelihoods for good.
This has the potential to be even worse than the second agricultural revolution to industrial revolution phase, which made ordinary workers lives absolutely miserable for maybe a hundred and fifty years.
This time, there will be no jobs. If you are displaced from one industry by AI, you will end up in another industry also being decimated by AI; if you get a job at all, you will do so by working lower pay than other workers, who will in turn be pushed down the ladder.
And that is if you are lucky: if you have only IT skills, why should you be the first to get a fruit picking or plumbing job?
I would argue that how it goes ends up with the main downstream effect of shifting knowledge growth and therefore expertise and therefore economic power away from the people who outsource it and to the people who do that outsourced work.
In this case with AI that power will shift to the companies that run the AIs
I think we will see the same trend as other industries. “Good enough” but produced cheap is better business than “really good” but expensive. I assume most software will go that way, or has gone that way already. AI will probably cover most of it and only a few senior engineers will be needed. Basically like any other industry where it went from everybody being a craftsman to a few people building the machines that then can be used by relatively untrained people.
I hope we discover a solution before innovation totally stalls, but I do not think any solution has been found yet. And I agree that halting AI is unlikely to be the solution because even if we halt the big companies China for example can still do AI.
Some people hope AI will get good enough in a few years that it can innovate without human experts. Maybe? But that remains to be seen.
By the progress of AI from ChatGPT to now is horrifyingly fast.
Trendlines and basic reasoning point to a most probable future where the AI is superior. We can’t just say “that remains to be seen” because the alternative is the least probable future.
AI models and tooling has advanced significantly in the last 6 months. Give it a couple of years and the companies will not need senior software engineers. They will need someone to steer the AI, maybe. Why would anyone need senior software engineers?
> Give it a couple of years and the companies will not need senior software engineers. They will need someone to steer the AI, maybe. Why would anyone need senior software engineers?
Right, companies won't need software engineers. They'll just need someone who can use tools to produce source code and maintain the generated artifacts, plus make domain-specific technical decisions like "what should the system do when two users update the same record as the same time" or "how should the system behave when a message in the queue cannot be processed".
We really oughta come up with a job title for these people.
I honestly don't think that these people will need to think in this level. `message in the queue` is an implementation detail..
I do not know or care what my if statement turned into in x86 assembly unless it becomes a performance problem and even then, I'm not profiling or debugging in machine language. Neither do most developers these days. A message in a queue becomes something akin to that in this era.
I see that I got downvoted there. This is not something I advocate or look forward to but I feel this is where it is going.
It may not be necessary to think in those terms exactly, but if you are not even able to think in those terms, you probably will be no good at prompting the LLM either. It's quite plausible that someone can be a productive dev with claude if they don't know exactly how the message queue is processed. But if they don't know there is a message queue at all, that is much less likely.
Likewise, you don't care exactly how an if statement gets converted into machine code, but you do know precisely what an if statement is and how it should behave, and could identify if it was buggy, and that that part of the codebase contains a bug. If you can't do that, then there is an impossible-to-estimate probability that at some point you get stuck and no progress will ever be possible. I don't see that as a winning strategy, in the long run (but it may work very well in the short term).
> I honestly don't think that these people will need to think in this level. `message in the queue` is an implementation detail..
No it isn't lol. Have you worked on any real systems with customers? Good luck telling your boss at AWS that a poison pill message stopped the payment queue from processing so they lost $100 million in sales but hey, it's an implementation detail, no big deal.
> No it isn't lol. Have you worked on any real systems with customers?
I have. Those systems already fail in spectacular ways and people tell their bosses that some worker process stopped working because its transaction IDs overflowed.
I bet that sounds like `the flux capacitor stopped reticulating splines` which is already an implementation detail for the boss anyway. Nothing changes.
Right, so who's going to ask Claude to investigate the worker processes and fix the transaction ID overflow? The CEO? Someone in marketing? The sales team?
Exactly these people will be experts at typing this:
“ Claude! what should the system do when two users update the same record as the same time, explain to me with full clarity”
or "Claude! how should the system behave when a message in the queue cannot be processed? Give me all the possible ways ranked from best to worst, also explain to me all these concepts so I can understand as I don’t have a cs degree".
If you think that there is no future where software engineers don’t matter then you are delusional. While the future is not set in stone the pace and trendline of AI point to this future as a MORE realistic future then the alternative.
Your example btw is ALREADY a solved problem. AI can answer it and design around it. Agents at my company already handle our infra.
> “ Claude! what should the system do when two users update the same record as the same time, explain to me with full clarity”
This isn't even the right question to ask, I think you've basically proved my point. You are in charge of deciding what the system should do when two users update a record at the same time. It's extremely dependent on what you're trying to do.
> Your example btw is ALREADY a solved problem. AI can answer it and design around it.
What's the one-size-fit-all solution for concurrency management that works for every single domain and application? I'm curious.
> Claude! how should the system behave when a message in the queue cannot be processed? Give me all the possible ways ranked from best to worst, also explain to me all these concepts so I can understand as I don’t have a cs degree".
I have a data pipeline with 6 steps, A -> B -> C -> D -> E -> F. I asked Codex to make some specific optimizations to step B and benchmark them. It did what I asked. Then it decided to also benchmark the entire pipeline, and after noticing that step E was slow it decided to make some optimizations that I had not asked for on step E. It was at this point that I wondered why it was taking so long, saw what it was doing, and stopped it.
What do you think "steering the AI" means? It is not like we need someone to sit at a desk and type "yes, implement it". Of course if you are a sane person you mean someone who will determine if the AI is doing "the right thing" and change its direction if it is wrong. That person is almost by definition a senior engineer.
Someone making sure that the business requirements are implemented properly and correctly. Basically a project manager. Maybe also someone testing the output and providing feedback. Not someone that says `we might have a race condition here, lets implement a distributed lock`.
I think that person does not need to know about locks anymore.
At the moment yes, you are absolutely right. The argument was about a couple years into the future. Nobody can predict this though. I feel this will slowly steer that way. We’ll live and see.
Hopefully, there are some sustainable, profitable companies that keep a low profile now and will take over after the "self correction" happens, and whoever invested in them will become very rich.
Tons of corporations rely on the fact that human interaction within software production will be as minimal as possible, and no one actually cares who trains the seniors of the future.
> Without a thriving mathematical community to point out these things it would have stayed broken.
And that's a bad thing. If the math community didn't exist or was weak, OpenAI would still benefit from the prestige of these results they were forced to withdraw. Withdrawing these papers has harmed OpenAI's investors, and that's totally unacceptable.
> With automated math that community as tao pointed out is at risk.
Good to hear. The problem they represent needs to be eliminated.
OpenAI: "Here are the answers to every math problem. Now mathematicians are obsolete. Just send the prize money and prestige to Sam Altman. BTW gonna need some mathematicians to check these answers."
The people who released the papers weren't randos either. OpenAI has a ton of mathematicians on staff, including Jacob Tsimerman, a fields medal winner.
Scientific progress used to be people debating and correcting other people. Now it's going to be people with AI assistance debating and correcting other people with AI assistance.
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.
Tweeter checked it with Astra. It seems like OAI could have pointed their own instance at it before launch. Because the source of the tip is likely someone at OAI, my guess is that they actually did check. But after the launch.
LLMs are unpredictably complex with potentially sigbificnaly different reaults based on random seed and seemingly insignificant prompt details) in the ideal case and nondeterministic in practice, so someone finding an error with a given LLM is not strong evidence that the result was not checked with an LLM, even with the very same LLM, previously.
No, not modern foundation models. This isn’t gpt-3.5-turbo. Although they are causal autoregressive, they have self consistency. You just have to verify multiple times to ensure you have averaged out any sampling errors.
I can throw Opus 5.5 at my code three times for code review and get three different sets of things it considers to be issues. I imagine all of them were checked with Astra at least once, but were they checked enough times?
> What makes you think that nobody checked the [ai output] first?
Because this is what they say all the time. It's like a badge they have to wear and tell everyone they are wearing, even though we see it.
You can see the same thing with ANT. Had they looked at Mythos output, they would have realized there were only 76 items, not 79 like the bot claimed. Or the ones that were just a "it crashed" and nothing else (not a cve imo).
Because people are finding errors using other LLMs. This implies that if they spent a miniscule fraction of the enormous pile of money they spend making this pile of slop they'd find the errors. They didn't want to find errors. They want to build hype for an IPO.
My assumption is that they checked the proofs vigurously, but now a way broader community is taking a look with professionals from the relevant subfields, and different agent setups / models.
> My assumption is that they checked the proofs vigorously,
Perhaps with AI.
A manual human check of each one would take a few month at least. In peer review, there are horror stories in math about more than 1 year before the journal accept the paper. So 3 reviewers x 700 pdf = 2000 mathematicians, that is 10%-20% of the community according to an unreliable count printed by Gemini after scrapping r/math.
Also, in most cases the only people that can understand the proof in a so short time (let's say a few months!) is the small group of people working in similar problems, i.e. the same group of 20-100 guys/gals that you meet in every conference.
Why would the tip be from someone within OpenAI? If they knew it they would have surely omitted that result, there’s no way this is a desirable outcome for the capitalists either.
Presumably the tip would be from someone who’s familiar with the area but doesn’t want attention. Which is unlikely to be someone in OAI.
1. This is expected if you only use a single model family like Claude, eg. we use a different model family for code review than authoring, OAI could have done this too for their math dump
2. Ai needs a good human driver beyond the trivial or mundane, they are expert enhancing machines, not expert creating machines. This is where the community comes in. Reading Tao's ChatGPT session reveals this: https://news.ycombinator.com/item?id=49010345
3. OAI is not trying to be a member of the/any community, this is not the first story to shows this, nor do I expect it to be the last. Perhaps this is them being effective altruists today? /s
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.
> assumes local maxima don’t exist and greedy short term optimization always leads to long term benefit.
Even if your stated assumption was baked into the original comment, which is doubtful: the historical record shows that we will keep relearning The Bitter Lesson and each community will pretend what they do for a living is exceptional and immune because of xyz. The screams will get louder when the "greedy" and "dumb" automation comes knocking and it turns out nothing was truly immune or "nuanced ".
Getting some new hobbies may be in order, it's a Brave New World.
"Greedy" is not a moral statement, it's a description of an optimization strategy focusing on short term improvements without a view to the long term consequences or state of the system.
Bringing it back to math explicitly: you are essentially betting that the singularity is here, today, and that there are absolutely no downsides to breaking the pipeline which trains mathematicians (meaning that in 5-10 years at most there will be zero humans capable of assessing AI math output or independently advancing the state of the art).
"Who will advance [X] field or check on the work of the AI that surpassed us in 5-10 years?" is not a question that is unique to math, and the answer is pretty obvious if we get past the grieving process some are going through.
The CS101 lesson in the first paragraph is appreciated, you should do it more often for us simpletons.
> “If they can be automated, they are not necessary.” That’s a pretty interesting take as eventually everything could be automated.
It's great that we're starting to see the light at the end of the tunnel, and will some day achieve a perfect market without humans. If you think about it, all the market really needs is a people to own everything, everything else can be automated, and all those annoying human workers can be eliminated.
Will it also be "arson" if OpenAI dump on us solutions to more practical problems, for example, a blueprint for a better photolithography machine, or a nuclear power plant?
No that would be irony. Use up all the chip foundries and power plants to make more plans for chip foundries and power plants so we can build more chip foundries and power plants and use them to run AI to design more chip foundries and power plants.
The fact that humans are needed to correct mistakes is only an ephemeral status quo that is being eroded away as we speak. We all can see it happening in front of our very eyes. AI is getting better.
It is pointless to call out the little wins humans still have because again, those wins are temporary.
We need real concerted effort into asking: what is the point? For me the only answer I came up with is: fun.
I'm sorry but you don't actually need the mathematical community to check any of this. You just need autonomous verification, which already exists at scale and speed vastly beyond the entire human mathematical establishment. OpenAI simply rushed these out without completing that for every paper. These mistakes have nothing at all to do with the mathematical community and are 100% just the result of market pressure incentivizing speed at 1,000,000x the pace of human mathematicians. Frankly, a couple mistakes, trivially found not by humans but by humans using AI, is almost completely irrelevant. Human mathematicians have essentially nothing to contribute to this effort aside from prompting verification agents, which any of us can do if we cared to spend the time (most of us don't).
There is no such thing as knowledge that has never even been written down a single time by anyone or anything. Those are simply called ideas, they are not unique to humans, and they are more likely to be wrong than right compared to anything OpenAI just produced. It would be bold and almost certainly spectacularly wrong to assume that multi-trillion-parameter AI models could not possess their own such ideas, generated during the training process as part of their internal model of the world. Beyond that, if we assume that such knowledge does exist in humans, its marginal value is clearly nearly zero now, as AI systems without access to it are vastly outperforming all human mathematicians combined by multiple orders of magnitude.
This feels like a very rigid ontology. I know what type of food my dog prefers. An executive assistant has intimate knowledge of their boss’s needs. Neither of these would become knowledge if they were written down for the first time; they already are.
You’re distinguishing “knowledge” from “idea” in a particular way that doesn’t correspond to common usage (see my counter examples). Without you being explicit about your definitions, I can’t tell whether what you’re saying is meaningful. It feels tautological.
Given that an executive assistant has unwritten knowledge that is necessary to do their job, where your evidence that no mathematician has analogous knowledge (using the word in the common way, not whatever way you mean it)?
It’s possible, but it’s not as obvious as you seem to think.
I don't know that any of this really matters. I could just as well say that you don't know anything at all about the internal experience of your dog's mind. All you can do is read behavioral patterns and attempt to make inferences. At best you have an approximation, and approximations tend to be wrong. Math is correct knowledge, not approximations of reality. Correctness is not a property of the idea or inference itself, since ideas and inferences can be wrong; it's the result of a verification process which you cannot possibly carry out in its entirety relating to the internal conscious experience of your dog.
We can dig into the philosophy of these definitions, but I think the far more interesting point is that even if we grant the existence of this kind of knowledge in the minds of human mathematicians, we have passed the threshold where that "knowledge" can keep up with systems that do not have access to it. Moreover, to claim humans have a "vast amount of mathematical knowledge" that is apparently valuable and that AI systems don't have, you'd have to prove that this "knowledge" is not implied or cannot be reverse engineered from the entire corpus of mathematical writing on which AI systems are trained. You'd also have to demonstrate that this "knowledge" leads to actual results that AI systems cannot generate without it. Given the results AI systems are producing, which are far beyond human ability at this point, it is more likely that AI systems have already internalized the entirety of this so-called "tacit knowledge" and then went much further, much faster, without humans in the loop at all.
Those are simply called ideas, they are not unique to humans, and they are more likely to be wrong than right compared to anything OpenAI just produced. It would be bold and almost certainly spectacularly wrong to assume that multi-trillion-parameter AI models could not possess their own such ideas, generated during the training process as part of their internal model of the world. Beyond that, if we assume that such knowledge does exist in humans, its marginal value is clearly nearly zero now, as AI systems without access to it are vastly outperforming all human mathematicians combined by multiple orders of magnitude.
They aren't just ideas, i read that in semiconductor manufacturing these old heads have a tremendous amount of process knowledge that's never been written down.
I'd need to see specific examples. It's not clear to me that I'd consider this knowledge about the world but rather agreed upon conventions for how humans work together.
Is the risk here like "people will fund math research less because of AI"? I agree that would be bad, and we should try and stop it (along with e.g. funding for the humanities, which is in a much worse place than math!), but I'm not sure OpenAI are the right people to be mad at.
But they are the ones releasing an unverifiable (no model release) and massive and unchecked body of mathematics into the public while making exaggerated claims about its capabilities to replace human work. And they are the ones doing it in advance of a fractional sale of the company to the public.
Based on what I've heard from my math friends in academia, every talented undergrad who was set on going to grad school for math has switched to something like consulting internships or fintech, even if they were really passionate about math, because they don't want to spend another 7 years or so just to wind up jobless.
This has always been the risk with majoring in math. AI is making it worse but there was never a time where studying math didn't have an extremely high opportunity cost.
Or at least, we’re pretty sure that it’s a proof! There’s a Lean certificate, as there are for some of the other 372 breakthrough results (not all of them). But it also appears that no human has understood just about any of these proofs yet
It seems that the obvious thing to do would be to release in TWO parts: the ones that are verified, and the ones that might have some good ideas but also might have some mistakes. Presumably the latter would be much more epxensive for humans to verify.
I think that on closer inspection, a lot of these fully AI generated proofs will fall apart. Even in Lean, you can build theories which compile but nonetheless state something different than what you actually intend. It's just that the volume of proof is so staggeringly large that it will probably take years before we find the issues, a la abc conjecture
I feel this comment is based on a misunderstanding of how Lean works. In Lean you don't need to inspect the proof. There is no "closer inspection". All the human needs to verify is that the statement of the theorem is translated correctly from natural language to Lean. That usually covers a very small surface of the Lean code.
> All the human needs to verify is that the statement of the theorem is translated correctly from natural language to Lean. That usually covers a very small surface of the Lean code.
That's exactly what the navier stokes paper posted yesterday pointed out where the LLM bends the Lean code to make it "compile", because the NL might be wrong to begin with or because it missed a detail:
For complex / tedious proofs I can easily see how small details like this can lead to a valid lean proof (or valid "code"), but missing the important details that got lost.
Oh I fully understand how Lean works, how minimal the kernel is etc. I just think that just because "it compiled", we don't actually know that the autoformalization proved all the right stuff along the way. After all, LLMs can produce correct proofs for statements that don't align with the original intended theorem [1]. I just think we should be a bit more skeptical in general before saying these seminal results are fully true. What's the rush?
That is an idealized caricature, and far from the reality. One needs to validate the statement of the theorem and the boundary conditions needed to prove it (definitions, axioms, kernel soundness, etc), a la dependency injection. Mathlib is a common shared platform of vetted truths, but not all proofs restrict themselves to Mathlib AFAIK, and neither is Mathlib perfect -- particularly subtle mismatches in the definitions.
A tiny fraction compared to the proof, I'm guessing.
But the point is that you don't need to check the proof. But a lot of people seem to misunderstand what's happening and think you still need to check the Lean proof that AI outputs.
None of the papers withdrawn were formalized in Lean, only about half the papers in the repo are formalized. I don't think we yet have an example of what you're suggesting actually happening.
I also don't think there's been nearly enough time for peer review of what was actually formalized vs what was intended. How many humans out there actually have a deep enough understanding of the background to be able to check the work? I understand that Lean checks the mechanical steps, but if it's building a ladder to some other result entirely, nobody (certainly nobody on HN) will know for some time.
I'm probably wrong, but what's the point of throwing away all skepticism?
Yeah the one i glanced was the ‘matrix multiplication is nlogn^0.9999999 for many more 9s’ therefore less than nlogn
The proof explicitly hand-waves some complexity by assuming lookup tables to avoid some calculations which isn’t actually possible since it’s dealing with such large numbers and it only works on incredibly large numbers.
The complexity being so close to nlogn and the handwaving by assuming lookup tables in parts should be a really really obvious smell. At the very least worthy of holding back from the broader announcement.
It us proven in lean as-is with these assumptions and it’s not one of the ones retracted but those assumptions are doing some heavy lifting. I think it’s worth adding back in those ‘by using a lookup tables for x’ complexities and seeing if we really are below nlogn on that one.
Many of the statements were already there and looked over by the community in lean prior to the work though, the statement can get formalized before the proof of it.
I just think that with the vast amounts of compute involved and the tendency to reward hack, we can't assume the steps towards that formalization are without error until full human understanding of the formalization.
It doesn't have to be the statement, see the recent incident where someone used an LLM to generate a lean refutation of the collatz conjecture, the lean proof exploited bugs in the lean kernel.
That proof was artificially constructed specifically to show the exploit. It wasn't a real attempt at a proof that was later shown to be using an exploit.
I'm unaware of any serious proofs that have been shown to have a kernel exploit in them.
1. why can’t the so called “real mathematicians” (as if mathematics does not belong to all of us) write the lean theorems by hand and then we let the machine fill the rest in? They are very upset that they can no longer contribute to frontier mathematics. This would let them contribute.
2. Why shouldn’t math progress happen in the open, commit by commit? Why is it so horrible if a proof is 95% of the way there but we later find that it needs to be refined? Mathematics previously was optimizing for an antiquated publishing and distribution scheme. There is no need for the first print to be correct. We have the internet now. We can and should publish incomplete results and correct things on the fly. Maybe mathematicians would have solved some of these problems years ago if they didn’t hide incomplete almost solutions in their filing cabinet because it wasn’t yet ready to be published.
You don’t hate the pageantry of mathematics and academics enough.
What are you even saying. Mathematics largely happens “commit by commit” as insufferable as that is a way of saying it, via conferences and meetings and prepublications. You’re attributing some bizarre to morality how mathematicians operate. You’re just upset people aren’t playing at your playground enough to your liking.
Also “real mathematicians” aren’t the people who “math belongs to”, you’re a mathematician if you do math, that’s it.
I mean 95% of a proof is not a proof, and the fact that we got 95% of the way there isn't necessarily an indication that we'll ever get there. There's also a big difference between publishing a mostly-done proof as such and publishing a proof as complete only to retract later.
There's a lot to hate about the academic world, but the solution isn't spewing out terabytes of crappy half-baked results.
I find the paper about beating O(n log n) for integer multiplication also quite fishy, not sure but it seems like too good to be true, I feel like there must be a subtle flaw in that. Maybe that's just me hating these small numbers in the paper, but it seems wrong, unnatural even! I would be similarly skeptical about a physics paper that claims to be able to exceed the speed of light by a tiny fraction. There's no reason n log n is the natural limit here but I see a few good intuitions so having something else that can't be represented in an elegant form seem very "unmathematical" to me.
Yes i talked about that in a different thread here. It has fishy ‘assume we have a lookup table for x’ assumptions in it. These are relevant to the main body of the loop. The numbers it deals with are outside of any possible lookup table capability (not enough atoms in the universe for such a table).
The lean proof uses these assume ‘a lookup table’ assumptions. The paper smells with the nlogn^0.99999999 (many more nines actually) and unbelievably close to nlogn statement and then the literal talk of lookup tables pushes it over the edge clearly for me.
Maths can generate weird numbers out of nowhere but it really really looks like an nlogn result with some tricks to get past leen to me
I'm not familiar with the paper you mention. But it's also worth pointing out that afaik the n log n algorithm itself isn't particularly practical. It's one of these "galactic algorithms" that is asymptotically more optimal, but is so complicated that it's only a real improvement for comically large n. And that's without even considering the mental overhead of implementing and maintaining the thing.
Of course, that's not to say the research is necessarily useless. It's still theoretically interesting to find "better" algorithms if only to shed some light on lower bounds, and so on. And who knows, maybe the line of research could lead to more practical algorithms later on.
The whole point of that paper is to show that it's possible in principle. Now people (and AIs) can think of better algorithms, etc.
Regarding elegance, take a look at Graham's number. It was not some meaningful constant - it's just a big-ass number which could be used in existence proof. Human mathematicians have been using this approach for quite some time, it's not really AI doing things odd
Surely it's a galactic algorithm that you can't physically run? You wouldn't get a constant as small as 2^{-182} without some other numbers elsewhere being incredibly large.
From the "Introduction" section of that paper: "The constants and thresholds in the construction are extremely large".
(And verifying if the algorithm multiplies correctly or not is the less-interesting part of this, anyway. Gets you no closer to verifying the complexity result).
Isn't it possible that all of the integers that have been or will ever be encountered, anywhere, any time, in human history, number less than 2^182? In which case you could argue that integer multiplication is O(1) via LUT :)
Everything is a lookup table in non-standard arithmetic but that's not useful for someone writing the code b/c they don't have access to non-standard integers & have to write an algorithm to reconstruct it.
I look forward to OpenAI reviewing all papers in the field.
It'll be a good test to separate those earnestly trying to advance human knowledge, from those wasting my tax dollars. The later group ought to be publicly shamed and ridiculed without mercy. We need a more invective word than 'pseudo-intellectual.'
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?
I can prompt ChatGPT right now and ask for mountains of more "mathematical work"; thousands and thousands of pages of nonsense for you to review. So you can "be informed".
But you couldn't make me review it. Anyway I think you're just straw manning what I was trying to say. I probably didn't express it terribly clearly and I'm not invested enough in this debate to put any more time in.
He’s not strawmanning you as much as taking OAI at their word. Plausibly the majority of the work was done with a fractional amount of human oversight, and maybe he’s sort of operating on the assumption they’re running “every” open problem continuously, which is pretty sensible. If you’re a mathematician working on an open problem which other people know about (how much of actual mathematics work is this kind of workflow varies from field to field) you can be pretty certain that an AI lab is prompting at it.
Just dropping a comment here to let y'all know I'm all out of time, but yeah, I would definitely put more time into reading hundreds of pages of slop proofs if it was my field, but sorry I really have to run right now.
But you can't do it with their internal model that is the same or a successor to the one that solved the navier stokes millenium prize problem.
With 40% formalized they probably have a good idea of how many were found to have fatal issues in the formalization attempt, and they hired some mathematicians to verify some of them, especially the big headline ones.
That's not what this is about. The person I was responding to said "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". That's what I was responding to. They were basically suggesting that the amount of mathematical slop in the world should be maximized, and then it would be up to humans to choose what they would want to read. You know, a needle in a haystack type of thing, where you're maximizing the size of the haystack.
Nobody solved the navier stokes problem, Jesus. A subproblem was possibly solved (still being verified) based on context in an actual mathematician’s chats with ChatGPT. These models on their own are still incapable of producing anything but slop.
Mathematicians are in no rush. And they are less likely to review math vomit that hasn't even been formalized and verified. Especially among the now thousands of vomit papers out there.
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.
The write-ups are one thing and more of a cherry on top but I would say the more pressing matter is the lack of Lean formalization which means you can't really say it has been (dis)proven or not.
I think the obscurity is a feature, not a bug. They don't want a headline where 250 of these results are invalidated overnight. They want rejections to trickle out and be buried.
My man, there are more than 100,000 professional mathematicians in the world.
Are they all too busy having brilliant ideas? Doubt.
OpenAI math paper dump should be considered like a hint from 200 IQ eccentric genius - unreliable but perhaps insightful. If it was not "ugh AI" people would be happy about it.
I don't have a problem with them publishing. I don't have a problem with the process and how they are interacting with it. I am delighted that they are actually acting as stewards of these works.
All that aside, they should be paying the people verifying the problems. The thing that really gets me is that we know anything published in the process of verifying this is going to be vacuumed up into the next training session.
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.
You have the frontier labs who are marketing that it’s over and they’re building intelligent machines and you’re saying the mathematicians should ignore it? Ok
I'm not sure how you construed that, so let me be more precise.
Mathematicians, as autonomous entities with no formal connection to any AI lab, have zero obligation to do any work for those labs. OAI can't do anything if all the mathematicians band together and say "Sorry, we're not interested".
If they do chose to engage, they are doing so entirely voluntarily, and it would strongly indicate, if they are voluntarily doing it for free, that there is value (i.e. compensation, payment, barter, worthwhile, whatever) to be had by digging in.
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?
Why's that? Do you think that institutions and funding agencies won't cover researchers' use of advanced models, or what? The group I worked in in undergrad had millions of dollars of equipment for doing experiments. I'd have to imagine they could get funding for a few thousand dollars in tokens for the theoreticians to have AI assistance.
The symbiosis here isn't I'll read your paper and you read mine. It's I'll publish my results and you publish yours. Groups share results and cross-pollinate ideas. If people don't want to read OpenAI's papers, no one's going to make them. If no one's interested in the ideas that OpenAI is coming up with, everyone can just ignore them.
The problem people are having is they clearly are interested. They think the ideas are good. In fact, too good. If they thought otherwise, they would just say it's all slop, no one cares, business as usual. And you can tell that there's this phase change in their behavior because previously you could ask chatgpt about math and it would just give you word salad and everyone knew that. Now we can all see that it's not just word salad and people are scrambling to figure out what to make of that. Obviously an accurate answer oracle is still strictly useful even if it makes no attempt to tell you why (you can even use it only to help prove your boring technical lemmas when you have ideas!), so obviously this is an emotional reaction, not a rational one.
Okay? Again, when I was in my group, money would flow to Nvidia to buy GPUs that we would use to run simulations (in addition to the experimental devices I mentioned). The researchers could also request money to use for openrouter or build their own GPU cluster if everyone thinks it's good use of funds.
Shouldn't we pay for the best tools if it helps researchers to be more effective?
yes, but in this case, openai does a lot of PR how their models solve important math problems. if it goes unchallenged, parts of society would think that is true. what would happen if we scale it and 10k companies dump 10k papers every month claiming solved math problems. how is this scalable?
We need the companies to humanly review their papers. in the same way as at other companies we use humans to review the papers.
Well, per another comment in the thread, some 20% of their solutions come with formalization, so there's a very high chance (probably higher than typical asks of research mathematics) that they did solve the problem. And that also presents a pretty easy solution to the scaling issue: demand formal proofs.
(If you're going to object that it's difficult to validate the statement of the problem, please first state your level of experience doing so. It's getting tiring seeing people raise this objection and claim that a statement is just as hard as a proof over and over who don't seem to actually know any math and have never tried to write anything in Lean)
> 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.
Like I was reading some about adele rings last night, which is already going to be quite a concept for a layman to be able to even slightly describe. Then you can layer on that apparently they're locally compact, so we can talk about harmonic analysis on the additive group. Like, come on now, 99.99% of people have no hope of ever following along, and this is stuff from 75 years ago.
> Anyone with access to a sufficiently advanced model has the capabilities of analyzing these papers/proofs.
But they don’t. What they have is the ability to ask something else to do the analysis. It’s an important distinction. If the asker has the skills to evaluate the results, that’s one thing, but too many don’t and act as if whatever they got is unambiguous truth.
> This hardcore gatekeeping of math (and by extension STEM) fields MUST stop.
What must stop is the overuse of the word “gatekeeping”. Anyone is free to study these fields and work on problems. What people rightfully object to is uninformed research flooding everything with hard to verify junk.
The discourse around "gatekeeping" is so poisonous. I think a lot of non-mathematicians are looking at this situation as if this was a guild of medical doctors or some other profession with a regulatory monopoly trying to "gatekeep" access to math from a new upstart in order to preserve their own pricing power. That's not how the math community works, it welcomes all and there is no barrier to contribution.
Mathematicians do have some vested interest in keeping the profession from collapsing into an intellectual oligopoly, where one or two commercial players with early access to their own internal models continuously scoops everyone else and pollutes the field with externalities, and the profession itself collapses, only leaving AIs and hobbyists able to stand. At that point it'll be the AI firms who become rent-seekers. That's not really "gatekeeping" in any conventional sense of the term, it's protecting a healthy economy of ideas and the long-term development of mathematics.
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.
The product at the end is important, but so is the process. Few of the things that would happen along the way are happening here, so it's harder to justify the value of the deliverable when there is a failure.
Exactly, the scientific method is what it is for a reason. Sure the institution of academia around it is not perfect, but in general, science, especially general research such as this is not about just bragging about how many papers you have published, it is a process that might help us find out things we might have not known otherwise.
Extrapolating the rate, there won't be any left by the end of next quarter. I jest, but reading these is arduous and finding holes in them is going to take time for anyone daring to.
3 non-formalized papers withdrawn, 6 non-formalized papers formalized. Extrapolating the rate there won't be any non-formalized papers left by the end of November, but because 2/3rds of them will remain as formalized papers.
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.
I can assure you that a lot of mathematicians are spending time on this, but research level maths just don't move that quickly. As of writing this, the initial drop happened 41 hours ago, that is under normal circumstances not a lot time for reading and understanding a proof paper, and it is most certainly not enough time for publishing a rebuttal. One does not claim that someone else's paper is wrong lightly, you sleep on it, you discuss it with colleagues, you discuss it with the author (not sure how that part works in this case) before posting stuff on the internet that you might come to regret.
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
Except Mathematics and science is not done this way, its not code that you can just release bugfixes to, its not a numbers game, its about furthering our shared knowladge. If it is done by flooding everything with a bunch of paper that have not been peer reviewed and verified, and are known to be error prone, that just takes away a bunch of mental capacity from scientists, and time, to manually verify all 400 of them. The issue here is how openAI approaches the science, not their hitrate.
I got the impression that indeed mathematics is done exactly this way. People used to write proofs, somebody would find issues in them that don't invalidate the entire work (or they do), the mathematician would work to correct the issues and resubmit.
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 happen 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 peer review should be understood as what’s going on now as mathematicians look over the papers and find flaws.
I don't know why so many people are dunking on this. This is essentially just peer review, mistakes happen all the time in human written papers as well.
flooding the system with parts that may be incorrect hurts the whole process and will get people to tune out (like politics). Can't see the International Mathematical Union making a similar mistake because it would do reputational harm. But the models don't care about their reputation. Bad for the layman - like me - to know what to make of all this.
“Good writing and the ordering of things, [the thread]—this distinguishes the master from the bungler, even in trifles” — Leopold Mozart‘s advice to his son, Amadeus
So mathematics is having the same issue all of the open source projects/maintainers have been dealing with for the past few years. Exciting times indeed.
I think this is now an interesting part about LLM based automation. The scientific community is quite strict on references. Even with its most advanced model ChatGPT isn't reliably able to tell me if an online shop has an item in stock. Then the other part is peer review which isn't optional either.
When You See One Cockroach, There's Probably More.
This can and should erode our trust in every single proof OpenAI published. The model is clearly faliable despite the lean proof, and clearly the output was't actually checked properly before release. Once these proofs are peer reviewed and published in a journal we might be able to trust them again but until then they are just slop, sadly.
I think OpenAI actually did the right thing by sharing everything with the whole community right now but I also hope that some significant credit will now go to the reviewers who confirm these 'proofs" actually work.
Fantastic. Let’s also apply this reasoning to math papers written by humans too?
Humans produce flawed Lean proofs. Indeed LLMs were successful at finding and fixing many issues in the “core” standard library if I recall correctly. Humans regularly produce flawed papers and have minor issues require fixing. And when it happens it often isn’t as prompt and clear as this.
I think you are implying that my suggestion is unreasonable and exceeds the standards applied to science produced by "normal" human processes.
In fact we already follow exactly this process for human papers and have done for a very long time. Publications without peer review are treated with great suspicion. This is how we end up with journals of varying levels of prestige and rigour.
The process isn't flawless and there are huge problems with retractions, as well as weird financial incentives and rent extraction but there is definitely an increased level of trust in a paper published in Nature.
Super-intelligence that’s going to end mathematics as we know it surely must be held to a higher standard than puny humans?
More seriously the problem is the complete utter lack of care OpenAI has shown in their desperation to demoralize mathematicians with their new LLM. In their words, it took 3 hours of ChatGPT pro per result, why not spend a hundred hours per result formalizing it, checking if the formalization matches the natural language proof, and whether the argument could be made more simpler and readable. Any human paper has hundreds of hours of work put into it, but OpenAI who is absolutely adamant in demoralizing the mathematical community and demonstrating their superior “intelligence” will only spend 3 hours, write unreadable, inscrutable proofs, not formalize all of them, and then dump it on the mathematical community for some reason.
This whole "AI solved X math problems!" Articles were always just advertisements. Thats why you read about these "breakthroughs" in every AI themed space, but if you read the mathematics news you don't notice anything happened.
The papers were all in a 'preprint' directory in GitHub. Academic mathematicians seem to think all research should happen in secret until it's completely proven.
But how much more progress would have been made in the last 100 years if they collaborated in real time? Watching the work someone is doing and spotting errors, or making suggestions would be a good thing. Unless the goal is simply to claim credit for a discovery vs the discovery itself.
It's a little strange to write a comment attacking strawman "academics" with the structure of a partisan political attack ad in response to OpenAI making a mistake.
My intention wasn't to attack academics. I was just trying to point out that being wrong is something that happens all the time, especially when something is in-progress (pre-print). How many papers written by people are withdrawn during peer-review, or while in the preprint state?
If someone had a blog about their research on a math problem, and they figure out one day that what they wrote a week before was wrong (retracting it), would that be a bad thing? I don't think it would be bad, but that's not how academics approach things.
What are you on about. The papers are held to scrutiny, this is how it works. If you put something out there, you should have done the due diligence of checking it (which is how these errors were found, with their own weaker model!). Being a smug prick about checking results that were announced as progress is less than worthless.
Was surprised at how messy and uncurated the release was/is. I frankly expected a major drop of like the Riemann Hypothesis or something from another lab yesterday. Cause otherwise they just dumped a pile of proofs of varying quality and let everyone else figure out whether they're right.
Picture a remake of Good Will Hunting, where Will is an AI and, instead of getting the mathematical formulas correct, he just mass dumps a bunch of nonsense and the professors have to go through it all, pointing out where it is wrong. The professors know that AI Will isn’t as smart as people say, but their funding depends on it, and if they prove it, which they can do easily, it may just tank the whole economy, causing a depression, all because they have history’s dumbest President in office.
I guess I feel two ways about this. It does could be a "working with the garage open" sort of thing where these are known to be unverified and they're just letting people see the sausage being made.
But that also means marketing and PR should shut the fuck up until things are verified. And they should more clearly annotate lack-of-verification status on their repo.
I believe this is nice marketing trick. Don't have human names have following effects
- AI can work alone and produce value
- There no person whose career on the line, and who is responsible.
- You can skip lot of time on verification of papers, and just show as it is.
Goals of marketing people obviously don't aligned with science goals.
Sure, unverified claims are unverified so there's a real risk of reputational tarnish. Why is it anyone else's job to verify a papermill? Would any journal accept an article that doesn't name people who are accountable? It should correctly be viewed as abuse of peer review. Let them rot.
Without the expertise needed to evaluate this information, it really reads like a "business KPIs have gone up! All is well!"-type communication. Their ability to spout technical jargon at scale is like a firehose that no one can really consume. I'm losing trust in any announcement of LLMs having 'solved' anything novel at this point.
People keep calling this "a PR stunt", but from a PR perspective, it seems they went about it in the least PR way possible.
No announcement, no press blast (big orgs have press contacts that they feed big story tips to), they just quietly dropped a blog post and a link to the repo on a tuesday evening.
I get we really want to have some kind of negative framing here, but lets at least not lose track of the ground truth around it. In a parallel universe this was easily headline news that made it to water cooler chat the next day.
Those results were not dumped to advance math. Those results were dumped to generate positive press for OpenAI.
Now it's on actual mathematicians to figure out whether the proofs are bogus or not. But the mistakes will never reach the same level of public attention as the original positive press, so for OpenAI this is good anyway, consequences be damned.
In a sense this is a microcosm of AI usage in the wild, ignorance is laundered through LLMs, and it is left for those that still have knowledge to figure out what makes sense.
OpenAI is a horribly negligent company. The threat it poses to humanity is not that their models will be a superintelligent singularity that will take over the world, is that their negligence and greed has real world consequences that they really don't give a fuck about. Like right now, their shitty math bruteforce is just keeping actual specialists occupied trying to figure out what is bullshit from what is not. For free, mind you.
Tao and most anti/critical ai math folks remind me a bit of the brhamins in the hindu caste hirarchy system... whilst others fought (kshatriyas), farmed/traded (vaishyas), built things, cleaned roads etc (shudras), the brahmins were the high priest doing science, stronomy, religion ...
AI is this strange modernist machinary that kind of threatens that brhaminic role... its almost like the vatican vs post industrialization world .. where they still have to keep making the case for why religion/priesthood/god is important... even as the tech/science world starts operating on totally different terms...
This metaphor might be applicable if the AI slop machine was in fact producing novel output. It seems to be getting invalidated as people dig through the wall of meaningless text surrounding the actual results.
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.
It's so funny to see people on Hacker News talk about academic communities that they clearly are not part of. To be clear to anyone reading, no, retracting papers is _not_ standard in math. In math, people submit papers after they have checked with colleagues, they give seminars, they submit it for peer review, etc. It is not shotgunning papers and retracting incorrect ones on the regular. Retracting papers is rare and embarrassing.
Wait, what? Well, yes, you're correct, AND flipping a sign in a draft paper that your buddy catches in a pre-read is SUPER common. People don't do math in a vacuum. Well, many do not. Some do.
First of all, people retract papers all the time. I can't give you the exact figures, but surely at least half of all academic researchers have retracted a paper at least once in their lives... Second, is it so hard to believe we are going through a complete paradigm shift in academia? People can now produce hundreds of high quality papers in a matter of weeks/days (with enough compute). Even if the error rate goes up (which it likely won't) we're still being exposed to a monstrous amount of novel information.
Even Einstein retracted one of his earlier papers re the cosmological constant... And he is one of the greats. Although not purely math related, it still counts.
It is wild to me how much stock mathematicians put into the social aspects of math. The whole social framework you are describing _did not exist_ for almost the entire history of math. It might very well be seen as a historical anomaly, like renaissance mathematicians challenging each other to solve cubic equations.
What do you mean by "the social aspects of math" here? Even some of the earliest known mathematical texts (like the Rhind Papyrus) contain evidence of a social aspect of math. And certainly mathematical discussions occurred among the ancient Greeks. People have been exchanging mathematical ideas for millennia. If you mean to say that the current academic organization of mathematics is a recent phenomenon, that's certainly true. But pretty much all the math history we know has been people communicating with each other, evaluating each other's ideas and developing them further. Given this, I understand why people are worried if the field should suddenly take a non-social form.
Thanks for the question. It's difficult to quantify but it basically comes down to how many obvious errors LLMs produce amortized by the processing time.
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.
Irresponsible is an adjective that means lacking a proper sense of responsibility, or acting without thinking about or caring about the potential consequences of one's actions.
They do not care if they waste everyone’s time or flood the common with slop. They did not spend their own time to verify that the Lean proofs correspond to the natural language proofs. They did not even spend their own time to verify that all of these proofs are well written.
They instead are mining the unrenewable resource of open math problems.
However, seeing it another way is easy if you are financially motivated by their upcoming IPO (see how easy it is to invent motivations for comments?).
Actually they sat a highly illustrious group of mathematicians down to advise them before releasing -- illustrious enough that I am certain that they have more global standing than you do to make a good call. That group advised open release, which is what they are doing. It lets mathematicians interested and skilled in each area look at what we have. It is by no means irresponsible.
You invoked the idea of political/legal/regulatory action to stop this type of thing. That's not commensurate with the type of irresponsibility you're describing i.e. publishing slop and wasting people's time.
What you suggested is however commensurate with some sort of personal animus.
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.
No, it's not how math works at all. Math is not experimental science. Results take years to formulate and are generally known to be true by colleagues via correspondence and seminars before a paper is even written. Retraction is very rare.
I don't know why people are talking about something like this that they are clearly not familiar with.
The greatest proof ever written by man, Andrew Wiles' FLT, was published with a flaw before being retracted and reworked. It's _completely_ normal in mathematics to find flaws in the argument. That's what peer review in mathematics is _for_.
Besides which it's not clear if these papers are considered published or preprint since they appear in no journal, so it's not really a retraction.
It's also very very normal to post preprints on Arxiv before peer review, so it's not the case that mathematics is kept private during review.
Not true. Wiles presented his proof in a series of lectures in 1993. The error was found by a reviewer, and he spent over a year trying to fix it. Once he did fix it, he asked colleagues to review it again, and only once it passed that review did he actually publish it.
Withdrawing it isn't irresponsible. I don't even think releasing it is, because that is often the best way to find problems with it; expose it to the wider research community. Doing PR victory laps based on unverified, unfinished work, on the other hand, is. It is well known, even scientifically demonstrated, that retractions or refutations get much less attention than the initial exuberant PR announcement. And thus this practice contributes to misinformation.
And just to preempt the kneejerk whataboutism: Yes, all of academia does this to varying extents, and the mainstream media are also complicit. And that is also irresponsible. And no, that is not an excuse for OpenAI. Especially when you consider that OpenAI actively portray themselves as some kind of moral arbiter on AI and "doing good for humanity". They should be held to the extraordinarily high moral standards they purport to hold themselves to.
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.
Because they have hundreds of potential proofs they were sitting on, and lack the internal expertise to judge them. It seems like they're working to formalize all of the in Lean, but that takes time.
What about software developer community? AI has eliminated the need for junior software engineers. Almost no one is hiring junior software engineers. But companies still need senior software engineers. Without junior engineers how will there be senior software engineers in the future?
What is the solution? I don't think the solution is to say AI progress in software, mathematics etc. should be halted.
Your code used to be a masterpiece, so well crafted it's easy for AI to tweak and modify because you've got everything so logically organised and scoped... and now this is what you're producing? Hard to debug monstrosities that only an LLM can realistically bolt new features or tweaks onto, because it can do the kinds of refactoring necessary each time.
We use to talk about the fact that code should be readable because you spend more time reading it than writing it, but I think that misses the key part that readable code is also typically easier to debug. If you can read and understand the code, you can follow the logic when things are wrong in production, and you can more easily reason about the emergent properties of interactions between the complex systems that are involved.
https://warhammer40k.fandom.com/wiki/Tech-Priest
Ahh that's OK then. Everyone's in this same boat simultaneously in multiple industries! Cool!
> What is the solution? I don't think the solution is to say AI progress in software, mathematics etc. should be halted.
I think the solution from the maths world is to not grant these AI papers (or their human sponsors) the normal courtesies of "regular order", just as you would not with an AI lawyer or someone who was just pressing enter at a law firm.
But in the software world, nobody gives a shit, apparently. We are collectively morally bankrupt and should not be granted the regular order to help other people to decide what to do with us.
In fact, the world is always filled with curious people who like to go one level below.
This hysteria about losing "Junior Software Engineers" -- most of them in it for money, promotion rather than craftmanship, is over-rated.
People who love solving puzzles will always find ways to sharpen their mind.
People who love understanding things, will always find ways (AI will help them tremendously).
People who love taking shortcuts will always find ways for it (AI or not)
If you have made it to the point of being a Junior Developer, I can assure you food and shelter is not a problem for them. You just have to adjust to a standard of living like the other 7 Billion people on this world.
Also, if a Junior Developer can show me(or anyone) they have built an entire system on their own and explain key concepts, there is no dearth of jobs for them
Eh? Apart from it not being what they are paid to do on their 9/9/6 jobs, when will they have the time to make it happen?
What is going to happen is that the remnants of the open source community will do the job of educating juniors for free, when the university degree system collapses. Just like it currently keeps a bunch of systems going with inadequate compensation.
The corporate world gets the problem off its balance sheet. Again.
The actual argument is "there will be no jobs for Junior Engineers, so there will be far fewer, and as a result there will be a huge shortage of Senior Software Engineers".
You are responding to the problem as if it some kind of extinction event, like a rare bird, where if we can find a breeding population we save the day. A few curious people, self training for the love of the game, and as a result we still have a few Software Engineers so everything is fine. It is not like that, and I haven't heard anyone suggest that is the issue. The potential problem is a massive shortage of workers with skills that are currently essential to the functioning of a large fraction of the economy, whom we might still need in the future.
The continued existence of talented enthusiasts does not establish an adequate workforce pipeline. If paid entry level experience contracts, what replaces it, and why should we expect that replacement to operate at sufficient scale?
Some jobs will stick around in vastly diminished numbers with tasks that are completely different than what they used to be to produce the same output (e.g. farmer). Other jobs will be eliminated entirely (e.g. switchboard operator). I'm guessing things like software engineering will go the way of the farmer, with the main unknown being just how much demand for software there is.
The entire valuation of the AI industry is predicated on people not just losing individual jobs, but being taken out of the workforce entirely on an economic level.
They are talking about the workforce of the entire economy shrinking. People will lose their livelihoods for good.
This has the potential to be even worse than the second agricultural revolution to industrial revolution phase, which made ordinary workers lives absolutely miserable for maybe a hundred and fifty years.
This time, there will be no jobs. If you are displaced from one industry by AI, you will end up in another industry also being decimated by AI; if you get a job at all, you will do so by working lower pay than other workers, who will in turn be pushed down the ladder.
And that is if you are lucky: if you have only IT skills, why should you be the first to get a fruit picking or plumbing job?
In this case with AI that power will shift to the companies that run the AIs
Some people hope AI will get good enough in a few years that it can innovate without human experts. Maybe? But that remains to be seen.
By the progress of AI from ChatGPT to now is horrifyingly fast.
Trendlines and basic reasoning point to a most probable future where the AI is superior. We can’t just say “that remains to be seen” because the alternative is the least probable future.
Anticipate the change and act prior.
Right, companies won't need software engineers. They'll just need someone who can use tools to produce source code and maintain the generated artifacts, plus make domain-specific technical decisions like "what should the system do when two users update the same record as the same time" or "how should the system behave when a message in the queue cannot be processed".
We really oughta come up with a job title for these people.
agent herder!
If that comes to pass, I will have to re-evaluate my career options
Who do you think the will be choosing whether the database uses a pessimistic or optimistic concurrency strategy? The CEO?
I do not know or care what my if statement turned into in x86 assembly unless it becomes a performance problem and even then, I'm not profiling or debugging in machine language. Neither do most developers these days. A message in a queue becomes something akin to that in this era.
I see that I got downvoted there. This is not something I advocate or look forward to but I feel this is where it is going.
Likewise, you don't care exactly how an if statement gets converted into machine code, but you do know precisely what an if statement is and how it should behave, and could identify if it was buggy, and that that part of the codebase contains a bug. If you can't do that, then there is an impossible-to-estimate probability that at some point you get stuck and no progress will ever be possible. I don't see that as a winning strategy, in the long run (but it may work very well in the short term).
No it isn't lol. Have you worked on any real systems with customers? Good luck telling your boss at AWS that a poison pill message stopped the payment queue from processing so they lost $100 million in sales but hey, it's an implementation detail, no big deal.
I have. Those systems already fail in spectacular ways and people tell their bosses that some worker process stopped working because its transaction IDs overflowed.
I bet that sounds like `the flux capacitor stopped reticulating splines` which is already an implementation detail for the boss anyway. Nothing changes.
Or maaaaaybe.... an engineer?
“ Claude! what should the system do when two users update the same record as the same time, explain to me with full clarity”
or "Claude! how should the system behave when a message in the queue cannot be processed? Give me all the possible ways ranked from best to worst, also explain to me all these concepts so I can understand as I don’t have a cs degree".
If you think that there is no future where software engineers don’t matter then you are delusional. While the future is not set in stone the pace and trendline of AI point to this future as a MORE realistic future then the alternative.
Your example btw is ALREADY a solved problem. AI can answer it and design around it. Agents at my company already handle our infra.
This isn't even the right question to ask, I think you've basically proved my point. You are in charge of deciding what the system should do when two users update a record at the same time. It's extremely dependent on what you're trying to do.
> Your example btw is ALREADY a solved problem. AI can answer it and design around it.
What's the one-size-fit-all solution for concurrency management that works for every single domain and application? I'm curious.
> Claude! how should the system behave when a message in the queue cannot be processed? Give me all the possible ways ranked from best to worst, also explain to me all these concepts so I can understand as I don’t have a cs degree".
Who's going to make this decision? The CEO?
I have a data pipeline with 6 steps, A -> B -> C -> D -> E -> F. I asked Codex to make some specific optimizations to step B and benchmark them. It did what I asked. Then it decided to also benchmark the entire pipeline, and after noticing that step E was slow it decided to make some optimizations that I had not asked for on step E. It was at this point that I wondered why it was taking so long, saw what it was doing, and stopped it.
This is GPT-6.1 Sol High.
I think that person does not need to know about locks anymore.
In the age of extraction capitalism where building sustainable, profitable companies is not the goal, no one will care.
And that's a bad thing. If the math community didn't exist or was weak, OpenAI would still benefit from the prestige of these results they were forced to withdraw. Withdrawing these papers has harmed OpenAI's investors, and that's totally unacceptable.
> With automated math that community as tao pointed out is at risk.
Good to hear. The problem they represent needs to be eliminated.
Scientific progress used to be people debating and correcting other people. Now it's going to be people with AI assistance debating and correcting other people with AI assistance.
but do these 'people' need to belong to a thriving community or not to be able to do those things?
This concerns the Hodge conjecture (millennium prize related) paper. Seems to me like PhD nerds weren't confident bosses pushed ahead anyway.
Because this is what they say all the time. It's like a badge they have to wear and tell everyone they are wearing, even though we see it.
You can see the same thing with ANT. Had they looked at Mythos output, they would have realized there were only 76 items, not 79 like the bot claimed. Or the ones that were just a "it crashed" and nothing else (not a cve imo).
https://www.youtube.com/watch?v=NnV_cWeoo5Q (Linux Kernel team sharing their side of the Mythos "hacking" story)
Perhaps with AI.
A manual human check of each one would take a few month at least. In peer review, there are horror stories in math about more than 1 year before the journal accept the paper. So 3 reviewers x 700 pdf = 2000 mathematicians, that is 10%-20% of the community according to an unreliable count printed by Gemini after scrapping r/math.
Also, in most cases the only people that can understand the proof in a so short time (let's say a few months!) is the small group of people working in similar problems, i.e. the same group of 20-100 guys/gals that you meet in every conference.
Presumably the tip would be from someone who’s familiar with the area but doesn’t want attention. Which is unlikely to be someone in OAI.
1. This is expected if you only use a single model family like Claude, eg. we use a different model family for code review than authoring, OAI could have done this too for their math dump
2. Ai needs a good human driver beyond the trivial or mundane, they are expert enhancing machines, not expert creating machines. This is where the community comes in. Reading Tao's ChatGPT session reveals this: https://news.ycombinator.com/item?id=49010345
3. OAI is not trying to be a member of the/any community, this is not the first story to shows this, nor do I expect it to be the last. Perhaps this is them being effective altruists today? /s
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
As much as anything can be infallible.
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.
Even if your stated assumption was baked into the original comment, which is doubtful: the historical record shows that we will keep relearning The Bitter Lesson and each community will pretend what they do for a living is exceptional and immune because of xyz. The screams will get louder when the "greedy" and "dumb" automation comes knocking and it turns out nothing was truly immune or "nuanced ".
Getting some new hobbies may be in order, it's a Brave New World.
Bringing it back to math explicitly: you are essentially betting that the singularity is here, today, and that there are absolutely no downsides to breaking the pipeline which trains mathematicians (meaning that in 5-10 years at most there will be zero humans capable of assessing AI math output or independently advancing the state of the art).
The CS101 lesson in the first paragraph is appreciated, you should do it more often for us simpletons.
It's great that we're starting to see the light at the end of the tunnel, and will some day achieve a perfect market without humans. If you think about it, all the market really needs is a people to own everything, everything else can be automated, and all those annoying human workers can be eliminated.
To witness an arson and rejoice reveals an ugly kind of sadism.
It is pointless to call out the little wins humans still have because again, those wins are temporary.
We need real concerted effort into asking: what is the point? For me the only answer I came up with is: fun.
An absolutely ridiculous statement. There is a vast amount of mathematical knowledge that hasn’t even been written down, much less formalized.
You’re distinguishing “knowledge” from “idea” in a particular way that doesn’t correspond to common usage (see my counter examples). Without you being explicit about your definitions, I can’t tell whether what you’re saying is meaningful. It feels tautological.
Given that an executive assistant has unwritten knowledge that is necessary to do their job, where your evidence that no mathematician has analogous knowledge (using the word in the common way, not whatever way you mean it)?
It’s possible, but it’s not as obvious as you seem to think.
We can dig into the philosophy of these definitions, but I think the far more interesting point is that even if we grant the existence of this kind of knowledge in the minds of human mathematicians, we have passed the threshold where that "knowledge" can keep up with systems that do not have access to it. Moreover, to claim humans have a "vast amount of mathematical knowledge" that is apparently valuable and that AI systems don't have, you'd have to prove that this "knowledge" is not implied or cannot be reverse engineered from the entire corpus of mathematical writing on which AI systems are trained. You'd also have to demonstrate that this "knowledge" leads to actual results that AI systems cannot generate without it. Given the results AI systems are producing, which are far beyond human ability at this point, it is more likely that AI systems have already internalized the entirety of this so-called "tacit knowledge" and then went much further, much faster, without humans in the loop at all.
https://en.wikipedia.org/wiki/Tacit_knowledge#Definition
If so, why did they mix proofs that were verified with Lean, and proofs in natural language?
I was wondering that while reading Aaronson's blog:
https://scottaaronson.blog/?p=10169
Or at least, we’re pretty sure that it’s a proof! There’s a Lean certificate, as there are for some of the other 372 breakthrough results (not all of them). But it also appears that no human has understood just about any of these proofs yet
It seems that the obvious thing to do would be to release in TWO parts: the ones that are verified, and the ones that might have some good ideas but also might have some mistakes. Presumably the latter would be much more epxensive for humans to verify.
https://arxiv.org/html/2610.08144v1#S2
For complex / tedious proofs I can easily see how small details like this can lead to a valid lean proof (or valid "code"), but missing the important details that got lost.
[1] - https://arxiv.org/abs/2610.08144
But the point is that you don't need to check the proof. But a lot of people seem to misunderstand what's happening and think you still need to check the Lean proof that AI outputs.
I'm probably wrong, but what's the point of throwing away all skepticism?
The proof explicitly hand-waves some complexity by assuming lookup tables to avoid some calculations which isn’t actually possible since it’s dealing with such large numbers and it only works on incredibly large numbers.
The complexity being so close to nlogn and the handwaving by assuming lookup tables in parts should be a really really obvious smell. At the very least worthy of holding back from the broader announcement.
It us proven in lean as-is with these assumptions and it’s not one of the ones retracted but those assumptions are doing some heavy lifting. I think it’s worth adding back in those ‘by using a lookup tables for x’ complexities and seeing if we really are below nlogn on that one.
This is just a Rice Theorem problem, right?
https://lawrencecpaulson.github.io/2026/07/30/Collatz.html
I'm unaware of any serious proofs that have been shown to have a kernel exploit in them.
2. Why shouldn’t math progress happen in the open, commit by commit? Why is it so horrible if a proof is 95% of the way there but we later find that it needs to be refined? Mathematics previously was optimizing for an antiquated publishing and distribution scheme. There is no need for the first print to be correct. We have the internet now. We can and should publish incomplete results and correct things on the fly. Maybe mathematicians would have solved some of these problems years ago if they didn’t hide incomplete almost solutions in their filing cabinet because it wasn’t yet ready to be published.
You don’t hate the pageantry of mathematics and academics enough.
I bet you enjoy when a peer asks you to find the issues in a fully AI generated PR that’s 95% of the way there.
Also “real mathematicians” aren’t the people who “math belongs to”, you’re a mathematician if you do math, that’s it.
There's a lot to hate about the academic world, but the solution isn't spewing out terabytes of crappy half-baked results.
The lean proof uses these assume ‘a lookup table’ assumptions. The paper smells with the nlogn^0.99999999 (many more nines actually) and unbelievably close to nlogn statement and then the literal talk of lookup tables pushes it over the edge clearly for me.
Maths can generate weird numbers out of nowhere but it really really looks like an nlogn result with some tricks to get past leen to me
Of course, that's not to say the research is necessarily useless. It's still theoretically interesting to find "better" algorithms if only to shed some light on lower bounds, and so on. And who knows, maybe the line of research could lead to more practical algorithms later on.
Regarding elegance, take a look at Graham's number. It was not some meaningful constant - it's just a big-ass number which could be used in existence proof. Human mathematicians have been using this approach for quite some time, it's not really AI doing things odd
From the "Introduction" section of that paper: "The constants and thresholds in the construction are extremely large".
(And verifying if the algorithm multiplies correctly or not is the less-interesting part of this, anyway. Gets you no closer to verifying the complexity result).
repo - https://github.com/swapnil-jain/integer-mult-kappa
The latest model even finds mistakes in previously published math papers!!!*
* so far, only OpenAI's math papers were faulty and needed retraction.
It'll be a good test to separate those earnestly trying to advance human knowledge, from those wasting my tax dollars. The later group ought to be publicly shamed and ridiculed without mercy. We need a more invective word than 'pseudo-intellectual.'
With 40% formalized they probably have a good idea of how many were found to have fatal issues in the formalization attempt, and they hired some mathematicians to verify some of them, especially the big headline ones.
Are they all too busy having brilliant ideas? Doubt.
OpenAI math paper dump should be considered like a hint from 200 IQ eccentric genius - unreliable but perhaps insightful. If it was not "ugh AI" people would be happy about it.
It would be ridiculous for anyone to say "hey man you really shouldn't even have posted these unless you have an ironclad proof".
I don't have a problem with them publishing. I don't have a problem with the process and how they are interacting with it. I am delighted that they are actually acting as stewards of these works.
All that aside, they should be paying the people verifying the problems. The thing that really gets me is that we know anything published in the process of verifying this is going to be vacuumed up into the next training session.
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”
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.
Ironically though, what I imagine will happen, is that the researchers will pay OAI to use chatGPT to help themselves eval the proofs.
You have the frontier labs who are marketing that it’s over and they’re building intelligent machines and you’re saying the mathematicians should ignore it? Ok
Mathematicians, as autonomous entities with no formal connection to any AI lab, have zero obligation to do any work for those labs. OAI can't do anything if all the mathematicians band together and say "Sorry, we're not interested".
If they do chose to engage, they are doing so entirely voluntarily, and it would strongly indicate, if they are voluntarily doing it for free, that there is value (i.e. compensation, payment, barter, worthwhile, whatever) to be had by digging in.
That's right, and the difference is that this one is parasitic.
If reading each others work is symbiotic it makes sense OpenAI is parasitic: whose papers are they reading in return? No-one’s.
The problem people are having is they clearly are interested. They think the ideas are good. In fact, too good. If they thought otherwise, they would just say it's all slop, no one cares, business as usual. And you can tell that there's this phase change in their behavior because previously you could ask chatgpt about math and it would just give you word salad and everyone knew that. Now we can all see that it's not just word salad and people are scrambling to figure out what to make of that. Obviously an accurate answer oracle is still strictly useful even if it makes no attempt to tell you why (you can even use it only to help prove your boring technical lemmas when you have ideas!), so obviously this is an emotional reaction, not a rational one.
Shouldn't we pay for the best tools if it helps researchers to be more effective?
We need the companies to humanly review their papers. in the same way as at other companies we use humans to review the papers.
(If you're going to object that it's difficult to validate the statement of the problem, please first state your level of experience doing so. It's getting tiring seeing people raise this objection and claim that a statement is just as hard as a proof over and over who don't seem to actually know any math and have never tried to write anything in Lean)
Someone still has to read the formalization.
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.
Like I was reading some about adele rings last night, which is already going to be quite a concept for a layman to be able to even slightly describe. Then you can layer on that apparently they're locally compact, so we can talk about harmonic analysis on the additive group. Like, come on now, 99.99% of people have no hope of ever following along, and this is stuff from 75 years ago.
But they don’t. What they have is the ability to ask something else to do the analysis. It’s an important distinction. If the asker has the skills to evaluate the results, that’s one thing, but too many don’t and act as if whatever they got is unambiguous truth.
> This hardcore gatekeeping of math (and by extension STEM) fields MUST stop.
What must stop is the overuse of the word “gatekeeping”. Anyone is free to study these fields and work on problems. What people rightfully object to is uninformed research flooding everything with hard to verify junk.
Mathematicians do have some vested interest in keeping the profession from collapsing into an intellectual oligopoly, where one or two commercial players with early access to their own internal models continuously scoops everyone else and pollutes the field with externalities, and the profession itself collapses, only leaving AIs and hobbyists able to stand. At that point it'll be the AI firms who become rent-seekers. That's not really "gatekeeping" in any conventional sense of the term, it's protecting a healthy economy of ideas and the long-term development of mathematics.
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
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 happen 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 peer review should be understood as what’s going on now as mathematicians look over the papers and find flaws.
If you want to see paper retractions, you ain’t seen nothing yet.
This heuristic indicates that at most a handful of them will be of marginal value.
That’s almost certainly due to things like captcha or something. What’s the actual shop you are referring to?
This can and should erode our trust in every single proof OpenAI published. The model is clearly faliable despite the lean proof, and clearly the output was't actually checked properly before release. Once these proofs are peer reviewed and published in a journal we might be able to trust them again but until then they are just slop, sadly.
I think OpenAI actually did the right thing by sharing everything with the whole community right now but I also hope that some significant credit will now go to the reviewers who confirm these 'proofs" actually work.
Humans produce flawed Lean proofs. Indeed LLMs were successful at finding and fixing many issues in the “core” standard library if I recall correctly. Humans regularly produce flawed papers and have minor issues require fixing. And when it happens it often isn’t as prompt and clear as this.
In fact we already follow exactly this process for human papers and have done for a very long time. Publications without peer review are treated with great suspicion. This is how we end up with journals of varying levels of prestige and rigour.
The process isn't flawless and there are huge problems with retractions, as well as weird financial incentives and rent extraction but there is definitely an increased level of trust in a paper published in Nature.
More seriously the problem is the complete utter lack of care OpenAI has shown in their desperation to demoralize mathematicians with their new LLM. In their words, it took 3 hours of ChatGPT pro per result, why not spend a hundred hours per result formalizing it, checking if the formalization matches the natural language proof, and whether the argument could be made more simpler and readable. Any human paper has hundreds of hours of work put into it, but OpenAI who is absolutely adamant in demoralizing the mathematical community and demonstrating their superior “intelligence” will only spend 3 hours, write unreadable, inscrutable proofs, not formalize all of them, and then dump it on the mathematical community for some reason.
But how much more progress would have been made in the last 100 years if they collaborated in real time? Watching the work someone is doing and spotting errors, or making suggestions would be a good thing. Unless the goal is simply to claim credit for a discovery vs the discovery itself.
If someone had a blog about their research on a math problem, and they figure out one day that what they wrote a week before was wrong (retracting it), would that be a bad thing? I don't think it would be bad, but that's not how academics approach things.
https://www.smbc-comics.com/comic/equations
But that also means marketing and PR should shut the fuck up until things are verified. And they should more clearly annotate lack-of-verification status on their repo.
Goals of marketing people obviously don't aligned with science goals.
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.
No announcement, no press blast (big orgs have press contacts that they feed big story tips to), they just quietly dropped a blog post and a link to the repo on a tuesday evening.
I get we really want to have some kind of negative framing here, but lets at least not lose track of the ground truth around it. In a parallel universe this was easily headline news that made it to water cooler chat the next day.
Those results were not dumped to advance math. Those results were dumped to generate positive press for OpenAI.
Now it's on actual mathematicians to figure out whether the proofs are bogus or not. But the mistakes will never reach the same level of public attention as the original positive press, so for OpenAI this is good anyway, consequences be damned.
In a sense this is a microcosm of AI usage in the wild, ignorance is laundered through LLMs, and it is left for those that still have knowledge to figure out what makes sense.
OpenAI is a horribly negligent company. The threat it poses to humanity is not that their models will be a superintelligent singularity that will take over the world, is that their negligence and greed has real world consequences that they really don't give a fuck about. Like right now, their shitty math bruteforce is just keeping actual specialists occupied trying to figure out what is bullshit from what is not. For free, mind you.
People won't want to seriously peer review an AI study unless it's already out there potentially spreading misinformation
AI is this strange modernist machinary that kind of threatens that brhaminic role... its almost like the vatican vs post industrialization world .. where they still have to keep making the case for why religion/priesthood/god is important... even as the tech/science world starts operating on totally different terms...
This metaphor might be applicable if the AI slop machine was in fact producing novel output. It seems to be getting invalidated as people dig through the wall of meaningless text surrounding the actual results.
3 results out of 400 is nothing.
* 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.
Even Einstein retracted one of his earlier papers re the cosmological constant... And he is one of the greats. Although not purely math related, it still counts.
Or is it the kind of research you'd prefer to keep shrouded in mystery?
Publishing a math paper and then unpublishing it is not "irresponsible". It's just a math paper.
They do not care if they waste everyone’s time or flood the common with slop. They did not spend their own time to verify that the Lean proofs correspond to the natural language proofs. They did not even spend their own time to verify that all of these proofs are well written.
They instead are mining the unrenewable resource of open math problems.
However, seeing it another way is easy if you are financially motivated by their upcoming IPO (see how easy it is to invent motivations for comments?).
https://agmai.org/statement-oct6/
https://terrytao.wordpress.com/2026/10/07/ahm-statement-on-o...
You can appeal to authority all you want, but you should actually read the opinion of the authority you're appealing to.
What you suggested is however commensurate with some sort of personal animus.
In one case by asking Astra to review it.
Not exactly encouraging that they did their homework before publishing results.
I don't know why people are talking about something like this that they are clearly not familiar with.
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.
Besides which it's not clear if these papers are considered published or preprint since they appear in no journal, so it's not really a retraction.
It's also very very normal to post preprints on Arxiv before peer review, so it's not the case that mathematics is kept private during review.
And just to preempt the kneejerk whataboutism: Yes, all of academia does this to varying extents, and the mainstream media are also complicit. And that is also irresponsible. And no, that is not an excuse for OpenAI. Especially when you consider that OpenAI actively portray themselves as some kind of moral arbiter on AI and "doing good for humanity". They should be held to the extraordinarily high moral standards they purport to hold themselves to.
The headlines keep the hype train arunnin