OpenAI, the Partition Principle, and Mathematics
karagila.org
karagila.org
Yes, the situation sucks overall and mathematics as a whole is in a turbulent time now.
But it also sucks when mathematicians, who are considered experts on a particular problem, refuse to engage with breakthrough results about that problem. #2 above is still true regardless of where it came from or how hard it can be to absorb.
While reading "The Mathocalypse" post [0] by Scott Aaronson, Scott described his wife Dana's reaction to one of the newly solved results in her primary domain of expertise, on which she'd been working for decades.
After her initial shock, and annoyance with the format/style, she decided to start using Astra - for the first time - to help her understand the new result. And he reported in the comments that she had made a lot of progress understanding it in one day, and may be even excited to give a talk about it!
That seems like a much healthier attitude towards these new results.
Yes, everything else sucks about this messy period. But there are still diamonds (in the rough) in this drop that perhaps should be looked into. If the author is too busy, perhaps one of their students can take a look? Someone will, eventually.
If some mathematicians complain about OpenAI sucking, that is fine actually, and if others are more “mature” about it, that that is fine too. Neither of these reactions should be at put as an equivalence to the blame OpenAI deserves for this stunt.
You might argue that these aspects of math are less important in the new AI accelerated math world, because agents will inevitably be smarter than humans, but I think clear framing and communication is even more important than before because with this technology we can choose to augment our intelligence instead of defer it
I don't believe this myself. But I do believe that if you've formed your very ideas about what is good and desirable on the basis of a culture that has held certain values dear for hundreds of years, and have fought against every doubt and difficulty in life for decades to mold yourself into that image, that it does not 'suck' that you are unable to adapt to a new reality overnight.
Very few people that would love to be craftsmen would love to be factory foremen. It is far too insensitive to the human experience to expect people to just deal.
Forgive me if I have no sympathy for current mathematicians who think this way. It's a pretty ugly kind of arrogance.
Some people told themselves they were the pinnacle, the first-rate mind, as opposed to all the second-rater. Well guess what, now your first-rate mind is a commodity and exposition is more valuable. They'd better learn to live with it.
Thankfully, very few mathematicians share Hardy's opinion, just as very few share his opinion that "mathematics is a young man's game" (and indeed we now have prizes like the Abel Prize with no age limit).
In fact, many of the greatest mathematicians throughout history have taken exposition very seriously, e.g. Euclid, Euler, Lagrange, Cauchy, Dirichlet, Kolmogorov etc. all wrote textbooks. Many mathematicians today carry on that tradition of taking exposition seriously and write books and freely share their lecture notes.
So we should not take Hardy's opinion as representing the opinion of all mathematicians or even most mathematicians. In fact, Hardy's statement is somewhat self-contradictory since he himself wrote several expository books (e.g. "A Course of Pure Mathematics").
It might be a shock for you but they are very few in numbers. Most of researchers I know are always busy with something. They cannot just drop other responsibilities for something like this. They will take their own time getting through the proofs (if they want to).
> That seems like a much healthier attitude towards these new results.
Another thing to consider is not all mathematicians are from US or with good funding. The PI or graduate students cannot afford to pay 200/month.
TFA was about a niche topic that OpenAI doesn't have in-house expertise in.
Otoh Aaronson is the co-author on Lijie Chen's (reasoning lead at OAI) top cited paper. OAI have deployed their resources more effectively against UGC that some of their staff are already familiar with
I wish they take a bit of more time to communicate the findings effectively.
There are good reasons not to delay publishing at all:
> They should release all their results immediately. (Imagine working on one of the problems they already solved.)
This is the most popular answer to a question regarding AI advisory group and immediate access on a popular website for professional mathematicians: https://mathoverflow.net/a/515442/473286
The whole debate regarding the behaviour of OpenAI is a red herring. Mathematics need to redefine their profession and how they work (like us software developers too). There are very good reasons to believe mathematics has an important role to play. If they could just stop talking about OpenAI and get back to work - they are very much needed, in particular now!
This kind of phrasing sounds particularly empty. We are not in WWII researching the nuclear bomb. What are they so urgently needed for to drop everything and work on understanding openai's proof on partition principle and axiom of choice?
Says who? The professional mathematician writing the article disagreed. Why should people start dancing the tune that openai wants to play for their own reasons and interests? And I do not see how taking the time and effort to write a proper exposition makes it "a very elitist science" when this exact effort and time is needed to actually get other experts understand and build on a result. Unless you equate spending time and effort learning math as "elitism", which is the ai-shilling moto some time now with everything time and effort related. I cannot see how spending time and effort to understand a field and then spend time and effort to make a proper exposition so that other people can also understand it as "elitist" vs throw everything out there "in raw form".
The root issue is OpenAI et al.'s thoughtlessness in their engagement with a field.
OpenAI has resources.
That they fail to allocate enough of those to cleaning up pre-print papers (that seem to be a corporate PR priority for them to release) so they can be consumed and engaged with by the field they're targeting is... acting like a jackass?
It's the same "Meta / Alphabet can't vs won't hire more human reviewers" problem.
OpenAI could, at an immaterial salary level to them, pay a ton of PhD students and mathematicians just to clean up their proofs and papers.
Not doing so is a leadership and financial choice.
What do you think is gained, if AI companies manage "cleaning up"? Tax money?
For me the problem is that rigth now the structure of incentives that has been built (e.g. you publish more = you get a grant; good exposition < solving a conjecture) is now broken. So, for instance, you would be very irresponsible if you throw your student into one of those AI papers, it's too much the risk. This part is mathematician's responsability, they need to change this incentives structure.
In any case, OpenAI is being a dickhead here. They throw millions of dollars at these problems, but they can't afford basic literature reviews (the drafts barely cite previous work)? Or checking that Lean's formalizations really correspond to what they claim to prove (even for Navier-Stokes they made this mistake)? It's obvious that for them this is just a PR stunt.
There's also the case of ethical violations, straight up scientific misconduct, as when OpenAI steals results of others (their customers) and present them as their own.
One particularly bad one came yesterday: https://arxiv.org/abs/2610.10072
> The result is also contained in a paper [8] released by OpenAI on October 6, 2026, in which the proof strategy and specific choices of notation are identical to a preliminary version of the present paper that was uploaded to ChatGPT on September 8, 2026.
Of course it's hard to say what to make of that without knowing what exactly went into the machine, but it certainly looks bad. And there's obviously a non-zero probability that it is indeed another instance of plagiarism, given that that's how they operate.
In this case, the author is a grad student, so what we're looking at is a company willing to steal from a student, ignoring whatever impact that could have on their career prospects, for a tiny piece of marketing material.
No it doesn't. Hundreds of open problems in a STEM field getting solved at once does not suck at all.
You would have to be deeply jaded and cynical to conclude that.
Nice idea.
People who are invested in the idea that we've invented a general intelligence, now, which includes all these companies that are literally financially invested in this claim they are making, will tend to believe that its results can already be trusted in domains like this. Some mathematicians seem to believe some of the proofs written by their models, and some, like this one, don't. I do think it's valid for an expert to push back against the claim that the best use of their time right now is to verify the poorly written work of everyone who's claimed to solve the problem
That's not true. [0]
> On July 25, Ramana Kumar published a repository containing a sorry-free "disproof" of the Collatz conjecture, produced with AI assistance. It is not a valid proof because it exploits a bug in the kernel's handling of nested inductive types.
Even in this dump we're talking about, it hasn't been true. [1]
> In “Algebraicity of Weil classes on split abelian eightfolds” a sign error invalidates a stabilization-trace cancellation argument and the construction used by two dependent papers.
[0] https://leodemoura.github.io/blog/2026-8-24-postmortem-for-t...
2. None of the results Open AI retracted had an attached lean proof
If you just strip mine the answers and Sam Altmans magic button solves 100/100 problems, what's next? Who is left to come up with a new interesting question for the magic button to solve?
Lastly, life and the present moment is all there is, if there is no enjoyment in anything we do, then what's the point of all the "living for ever" Altman et al want to achieve.
We will live forever to read boring papers generated by LLMs? Literally sounds like an eternal hell.
He's tracking the community progress on sub-n log n multiplication. OpenAI started with 1 - 1.63e-55. The result has been now improved on 115 times, and the current record is "rohanarun"'s 1 - 9.87e-5. I'm sure by tomorrow it'll have improved again.
Does this look like people aren't having fun? Does it look like they aren't discovering stuff? It looks like it's spurred a cascade of interesting community activity. It doesn't really seem much different from what happened with the twin primes conjecture. Isn't that supposed to be the point of all this?
In fact, I can't remember a time when I was more excited about the future of science. This could herald an end to the replication crisis, and kill off bullshit science completely. The danger of course is that we end up with two companies effectively dominating cutting edge research in every field, but it remains to be seen if that's even possible given the pace of improvement in open weight models.
However, there are always smarter, hungrier people out there and this is a buffet.
Some output is going to be wrong or incomplete. I am willing to bet even those have nuggets that can be used elsewhere.
Like people enjoy racing in front of a stopped train? As soon as they turn on the engine again, they will run you over. The questions that remain will be only the low value ones, not worth the effort to vacuum up.
So no, the smarter, hungrier people are not the ones that are going to swoop in. It will be the most desperate.
> Some output is going to be wrong or incomplete
This is a very human take on the situation. No, the Lean proof is not going to be wrong, and it will be incomplete only in the sense that OpenAI didn’t try to push the results further.
This is like "no one is forcing software engineers to use AI tooling" or "no one is forcing you to show your ID in the airport" or "no one is forcing you to own a car in your small midwestern city" - there can be no law requiring something and the practical consequences of not doing so can be so painful that you're effectively forced anyway.
That’s why it doesn’t make sense to present AI companies as dumping or burdening the scientific community into doing labor for them; the scientific community is self motivated to do so.
I just imagined that instead of math papers, they released 700+ feature length films, and the only way to tell if one of them is any good is to watch it in its entirety.
That feels pretty unappealing to me.
I know it's the same for human made films, so what's the difference right? But those are good enough most of the time that it's a decent bet, and the people that made them had real skin in the game.
Contrast that with something made by a nondeterministic slop machine with no skin in the game where small details can be off in a way that's jarring. Right out the gate I have an aversion to committing that much time to something that very well may waste it.
As someone who uses LLM tech occasionally, this is why I prefer using open local models. If I’m making myself obsolete, at least I’m not making some asshole richer and their closed model better.
(See https://agmai.org/general-sep29/ for the recommendation in question.)
People seem to have very misguided ideas about why OpenAI is doing this at all. It is not to brag or to torture mathematicians. It is an eval. OpenAI is known to be willing to pay large amount of money to get a good eval, think FrontierMath. FrontierMath is now saturated, so they need a replacement eval for math. Open math problems are actually a fairly good eval, although a proper eval is better (eg FrontierMath has known difficulty and have tiers from 1 to 4).
Mathematicians would prefer if OpenAI didn't use open math problems as an eval, but OpenAI is not obliged. I actually think OpenAI wouldn't point AI to open math problems if unsaturated FrontierMath Super Duper is available, as it just angers mathematicians, but such eval is not in fact available. Given OpenAI used open math problems as an eval, they could just throw out the result (this is in fact better as an eval since it will keep problems useful longer), but mathematicians preferred to see the result. So OpenAI released them.
> supported by a clear plurality of respondents
was referring to?
This is a misleading characterisation of the mathematicians' position.
The very first paragraph of the AGMAI recommendations explicitly states:
"we do not endorse this practice, and we ask them to stop testing advanced mathematical problems on proprietary models." You appear to have acknowledged this by saying “Mathematicians would prefer if OpenAI didn't use open math problems as an eval…”.
The mathematicians did not ask OpenAI to produce these results. They explicitly asked AI labs to stop producing them in this manner. Their subsequent recommendations concern what labs should do if they have already produced significant results, not an endorsement of the practice.
Furthermore, the recommendation was not simply to release the results, but to responsibly release already existing results. Section 2.B, Step I, explicitly recommends "...labs that have AI mathematical output that is not understood by the people who prompted the AI systems", to search the literature for relevant prior work, provide appropriate attribution, and improve the exposition of AI-generated proofs before releasing them, rather than leaving this work to mathematicians afterwards.
OpenAI published the results on GitHub while still exploring repositories that meet the committee's guidelines. So they followed some of the recommendations, but not all of them and hence, did not release the results as requested by the mathematicians.
I do not think it is a settled matter whether this was done out of goodwill. This is because releasing these results as they were can benefit OpenAI more than releasing them according to the AGMAI recommendations. AGMAI recommended in section 2.B, Step 1.5 that "Each time a solution to a problem is released, it should be clearly documented how exactly AI came to be used on that particular problem. If many results are released at once, then in addition to the results themselves a further document should be written and made public that references all of the released results and explains how many other problems of comparable difficulty the models tried and failed to solve, as well as how the problems were chosen." If the results are released, it is easy to expect that the media will discuss the capabilities of the AI used in the work, as indeed happened. If this AGMAI recommendation was followed, the media would plausibly have also discussed the number of failed attempts and then the overall attitude would not be as favourable to OpenAI as it is now when it comes to the capabilities of the AI that was used. OpenAI did release on GitHub that approximately 4,000 problems were attempted and resulted in 719 manuscripts (after 3 containing suspected errors were removed by OpenAI) across 372 families of problems, but this does not give a calculable number of problems it failed to solve. I do not claim to know OpenAI's intentions or reasoning when these results were released and am not arguing that it was done with improper intentions, only that whether it was done out of goodwill is not a settled matter.
AGMAI's October 6 statement explicitly clarified that its advisory role should not be interpreted as an endorsement of OpenAI's process, and that it was up to the mathematical community to assess how successfully its recommendations had been followed.
Recommending how to responsibly handle the outcomes of something you oppose is not the same as asking for it to happen.
> Mathematicians did not ask for this work to be done. The Advisory Group on Mathematics and Artificial Intelligence, from whom OpenAI has claimed to derive its legitimacy, opened their initial advisory statement by saying that frontier AI corporations should not test advanced mathematical problems on internal models. In ignoring the central premise of the Advisory Group’s position, OpenAI has indicated total disregard for the norms of scientific research — norms that guarantee that mathematics remains trustworthy, ethically researched, and in the public interest.
It looks like people are enjoying themselves, having fun with the new results, and generally doing all of the things you say "science" is supposed to be about. So what's the problem?
https://www.youtube.com/watch?v=LKiBlGDfRU8 https://www.youtube.com/watch?v=shFUDPqVmTg
As the author of the post points out, there is no way this is “the best they could do”. It’s a write up that didn’t involve someone with the math + communication skills required to clearly explain the result.
They normally don't feel like they are in some kind of race to publish the results ASAP and claim priority. Cases like that are very rare (but they get media coverage because they are so unusual).
OpenAI did a publicity stunt, their motivation is not to make a good contribution to the field, which has very different standards and culture, compared to the AI labs.
They don’t have any more patience for this.
I even think it's plausible a lot of mathematicians are excited by it, but the sweeping confidence of the comment you replied to without anything to back it up leaves some to be desired
There's a "Silicon Valley-ism" for you. We offer a thing in whatever form we want and people "who are passionate" will gobble it up, should gobble it up, 'cause they're "passionate".
It is entirely possible that one day progress just stops or slows down, but with current evidence, I don't find that too likely - at least not in the near future. The sheer amount of resources being put into this (AI) race is mind-boggling.
So while past performance does not guarantee future results, I'm just going to kick back, and assume that many of the current issues will be fixed with future models.
Maybe this is just a matter of what model developers choose to invest training resources in, but I don’t think it’s inevitable unless clarity is made a higher priority
The problem is that right now mathematicians don't have the economical incentive to read these AI generated results. Even if you love mathematics and all that, it's always more important to get a job, and for that it doesn't seem like a good idea to invest time around problems that AI touches because you can't compete with it and you don't know if tomorrow they'll improve by x10 the sota.
Of course, it's not clear at this point whether reporting such a result even matters, but still. In its own right, it's a very cool result.
But providing the answer in gibberish along with a certificate is not that, it's at best a cruel way to do it, but I'm leaning towards the idea that it's a fundamental misunderstanding of what it means to do math and what it means to communicate a result.
If you think sending an answer in gibberish is acceptable just because it's true then SSdtIG5vdCBzdXJlIHdoYXQgdG8gdGVsbCB5b3UsIGJ1dCB3ZSBkaXNhZ3JlZSBvbiB0aGF0.
If you did’t bother to write it, I shouldn’t be bothered to read it.
Perhaps AI agents can have their own publications and magazines where they are the chairs and associate editors and reviewers.
If AI can solve such grand, outstanding math problems, and mathematicians argue these pure math problems are important, what’s the problem with them needing to read the output if they want to understand it?
The alternative you are proposing implicitly is even crazier. OpenAI should not release a proof that is most likely correct so that it doesn’t burden others. What? It’s not about that guy dude. It’s about the society TM. One can’t delay progress because a guy may be burdened.
“Guys plz don’t release this thing that is absolutely correct but I’m kinda busy with other things ok?”
The alternative is that they do the work to properly present the results. They spend billions of dollars in AI training and inference but can't afford to even cite the literature properly? They're doing the bare minimum because they're inly interested in doing a PR stunt.
Bare minimum is still _solving_ the open problem standing there for years. Nobody owns math. Nobody owns giving enjoyable proofs to someone else.
If you don't like to engage with OAI proof dumbs in current state, don't. Maybe others will. Or maybe _these_ mathematicians are afraid that _other_ mathematicians will do it. Just elitism and gate keeping.
Ok, I don't see the point of discussing with you. It's clear that you decided what to believe in and no evidence will convince you that reality is more complex. The proof is that you ignored all the nuances expressed here by simply sticking to your simplistic interpretation, without any explanation of why such nuances are invalid.
You don't think this changes when the thing in question is a proof of a STEM problem no human has ever been able to solve?
Academics have always been required to engage with hacks and cranks to some extent; the deluge of AI proof writing has only exacerbated the problem.
English speakers generally use this word in a very broad sense “and now Netflix is forcing ads on paying users”, “because there was no sink, I was forced to drink the whole thing”. It is only when you are literally describing a crime where this word has this strict meaning you are alluding to.
> forced; forcing
> transitive verb
> 1 :to compel by physical, moral, or intellectual means
> A player was forced out of bounds; They forced the CEO to resign; I forced myself to finish.
Can you provide some evidence of this claim? "Nobody says nothing" probably works on reddit but I generally expect higher quality discourse on hackernews.
Were you satisfied with the paper?
Having read the paper, do you understand "what you missed" in those 3000 hours?
This part I don't understand. Not that anyone should read the entire Lean code of any proof, but if the statement of the theorem to be proven in lean seems to be correct, then I would think there would be at least some interest if in fact there was a formal proof (which might or might not correspond to the written proof) of something I was working on. That to me would be interesting. Or you are saying you doubt the validity of the formal proof, which would also be interesting. But saying it is of no consequence doesn't make any sense to me.
It would be like trying to look at a completed video game's assembly code, being told that it was call of duty, and then being asked questions about the high level code architecture.
AI models are perhaps unsurprisingly good at low level translation (see the progress being made for decomp games)
These models have surpassed human capabilities at math/machine code, but they can't "simplify" yet - in part because they don't have the same need to due to their comparative lack of cognitive constraints. AI Slop code is getting better, but it takes time. At the moment, its embarrassing frankly. It will come eventually, but right now OpenAI is not handling this with the care, respect, or concern that it deserves.
If you have a 20-40 IQ points gap with another developer, this happens a lot.
The baseline of "simplify" is wildly different based on your IQ points. That's precisely why exceptional students are usually bad in teaching. They try to break things down, simplify, but things still go over the head of normies.
However, we can intervene/train the models. So it should be possible to focus on the simplification, and as you said, it will come eventually.
I sympathize with those who've worked on some problem for years and now don't have something to work on; it's been a part of their identity. I also especially sympathize with those whose career tracks and plans were thrown in disarray.
That being said, I absolutely cannot understand how one can't be excited and happy and enthused about these advances in one's field. Assuming just that the ones with formal lean proofs are actually true, these are reportedly huge advances. Even if folks don't understand it YET.
They got into math for the love for mathematics but if they couldn't make a living from it (tenure) then they would have done something else just like everybody else who is not a starving artist. So, no, they won't celebrate it and neither would you if you were honest. (note also that starving has a short time limit before you die so "if all of it leads to some form of superabundance" won't work in that circumstance)
Work this abstract almost certainly has no value outside the community that is (was) interested in the result. OpenAI should engage with the community to realize the value (beyond PR).
All of these comments seem to suggest that if papers are not 100% abiding by readable books their standards, they are basically the same as literal noise. This is highly dishonest.
I’m just a dude and even I’m able to understand the paper after using ChatGPT to help me through it.
??? That's literally what everyone does. You are creating a hypothetical that is nonsensical. Here's your hypothetical:
1. Agent gives you 5000 lines of slop
2. You reject it and just do it yourself
This is reality
1. Agent gives you 5000 lines of slop
2. you realise that it has done a lot of research and is mostly in the correct direction and you ask it nicely to refine it
3. verify that you understood it and push it to prod
Are mathematicians babies that they need a completely different approach?
Do you rely on the tests/Lean to accept correctness or not…
That would be nice, but the rest of the world wasn't interested in the results before and they won't be interested after.
I wonder what this means long term. Maybe mathematicians will keep plodding on as usual except sporadically when an AI company need a marketing boost so they spend millions of dollars to dunk on them. Because the mathematicians sure don't have that kind of money.
Dismissing results on the basis that Lean code is too long disqualifies this opinion. It is not hard at all to read the Lean result statement, even with very superficial Lean knowledge.
A few papers have been retracted, but it looks like many are withstanding intense scrutiny. Lean is making the results more likely to be correct, but I think making them harder to understand.
The world has changed and you’ll know a math department is making a serious attempt to adapt when it teaches a required Lean course in freshman year.
The one for the quasi-Riemann Hypothesis is half a million.
...
>So, no, I will not be sending Sam Altman a bottle of whisky anytime soon, nor I am planning on spending my time reading through that paper and trying to make sense of it.
Think about a hypothetical circumstance where we get radio communication with some aliens on another planet. They send over tons of math to help us advance our tech, we know the math they're sending us is correct, but their explanations are really hard to work through because they aren't humans and the math is so different from anything we've done. Should we whine about the results they sent to us and refuse to engage with it?
The major discussion is about whether this will in fact advance our tech.
In the Three Body Problem, the alien race shows us “miracles” in an attempt to discourage us from the pursuit of science. Consider that possibility.
it won't be long before there's no more low hanging fruit like this to complain about, and the writing / explanations of the results are superhuman as well
separately, i really liked the author's denial-of-service analogy. super useful practical framing
> This is why I generally avoid using AI for mathematics (I am happy to ask LLMs to consolidate information for me, or to generate a useful infographic, or to proof read an email, etc.)
In other words, the author is OK with using LLMs to replace data analysts (that could consolidate information), to replace graphic designers (that could generate infographics), and to replace editors (that could proofread an email). But don't you dare use LLMs in their mathematics.
Imagine being someone who is working on one of these problems. You have no good guarantee that the problem was solved, but you will have the horrible homework of reading the AI slop. Also, if you do have something interesting to say about the problem, people will have less enthusiasm about it now
When I am tasked with reviewing that code. First, I don't know if it's valid. The person who wrote it doesn't know if it's valid. In order to validate it I must step back and understand the full problem space. Then, when I ask for revisions or clarifications, it's seen as either
A - Slowing progress, being resistant to change... or... B - Thanks for catching that (Claude fix PR 532 with the review comments)
It's 100% removed the enthusiasm.
Perhaps, there is a point where we just "give up" the understanding and accept AI output as the ground truth, because the sheer amount of generation is too much for our puny human minds to comprehend, and a lot of the times it IS right, even if a little wonky.
I know the model that produced these proofs is still private, but it’s worth a shot tackling the proofs with the current consumer-available frontier.
This was always the essence of mathematics, and it will stay this way whichever statement by whomever is made.
As much as I personally despise altmans, "darios", and their bootlickers, this is one aspect which is undoubtedly "good for the mathematical community" as a whole. The fact that the validity of your statement does not depend any more on an expert opinion of some person with grants, but as it always should have had been, just on the validity of the chain of deductions.
For what's worth it, this batch of results are not very tight intentionally by OpenAI and promising mathematicians already started to consume them and improve the results, while someone is still complaining on it.
The lack of emotional maturity and empathy is very on par with my experience thus far.
Excellent point.
I don't blame the AI for this - I blame OpenAI.
Literal slop grenade (see https://fortune.com/2026/09/17/shopify-tobias-lutke-ai-slop-...)
If Mr Tao had submitted a shitty, poorly-written proof of a famous outstanding problem, no journal would reject it. That extends to anyone with sufficient credibility. They might ask him to keep at it and fix it up, but nobody would begrudge him putting his shitty (but ultimately correct) draft of arXiv while he did so.
We're all getting disrupted, we all have feelings about it, but from the perspective of a software engineer who's been dealing with all of this for several years now, this post is just cope.
It’s clear from the author’s tone about lean, emails, infographics, etc. that he thinks automating those away is fine. Why should math be any different?
In fact, the academic system is a kind of worldview created by humans. And as it is shared and the community grows, the problem will gradually become more complex. Because when a discipline develops sufficiently, just as in a mine where rich veins are easy to extract early on but become very hard to extract once much has been dug out... in that sense, as things gradually become more complex, once a certain threshold is reached, won't scholarship surpass the limits of human understanding? Of course, scholarship is entirely for humans, but at some point the system itself may face its limits, and then wouldn't it again reduce the existing normalized minimum within that discipline and establish a new normalization of a new logical system?
In my view, perhaps for very complex work like today, AI will do it, and then there will be work that normalizes and further simplifies the results of that AI. Then, coming back to the human fold, if humans create the initial skeleton, the LLM will learn that again and it will become complex work again, and won't this create a continuing cycle?
I think verification and understanding can be separated. If the proof targets a correctly formalized proposition and passes a reliable proof checker, isn't it valuable? We have obtained knowledge justified as true, but there is simply no new theory that understands that knowledge. As was the case with the Four Color Theorem...
I am always curious what shape the newly compressed new discipline will take. At that time, I hope even people like me, who are intellectually behind, will be able to learn that discipline.
No.
But its worth a lot less than one that can be understood.
They really should be trying to partner with the mathematics community to add maximum value.
Their current approach is reckless and risks doing more harm than good.
Sorry, but I don't get why mathematicians are so upset. Like, just accept the knowledge and insights and acceleration in your field! If it isn't "fit for human consumption" because an AI produced, okay... it soon will be explained ELI5 by even better models.
Most software developers (or people in any field, working for anyone) rarely own anything they do at work.
And the entrepreneurs running their own companies (which there's an explosion of atm largely because of AI) do indeed "own" the higher-level products and things they're producing, even if AI writes the code.
What is supposed to have changed?
The same could go for mathematics or any field; there are lots of people who enjoy the process and aren't satisfied by being handed and opaque final result
Their field is at the stage where the humans are “debugging” the AI slop.
They are still imagining how to escape from having to read the generated code. Hopefully they find a way.
> I took a brief look at the preprint released by OpenAI. It sucked. It is unclear, muddled, and has a strange structure.
https://img.getfn.io/images/e3245d47a159592b06570ffbd64d5af8...
This is a strawman. OpenAI didn't say they are expecting all mathematicians to read the solutions, incomprehensible or not.
So mathematicians are upset with OpenAI for solving "their" math problems. Software engineers are even more affected by AI, yet mathematicians seem to be reacting more strongly. I don't get why.
It looks like the spent $20 on writing the actual papers.
If they actually wanted to do good for the world, they wouldn't have released these as the slop grenades they are.
In their current state, they are actively damaging the mathematics community.
It shows a lack of respect and care for the impact that their technology has.
It shows that they cannot be trusted for things like private data, AI safety, and company partnerships.
In math/science, repeatability and review are critical to the process.
The right way to handle this would have been to work with the mathematics community to co-develop and create meaningful proofs rather than slop grenades.
If they proceed in the current state, we'll just get a bunch of spaghetti math that won't do anything for helping people build an understanding.
Maybe some day, we won't need people to understand things, but that's certainly not the case at the moment, and likely won't be for several more years.
Perhaps this is projection, and the staff at OpenAI doesn't understand their work anymore? Not a great sign regardless.
The mathematics community can finish the job OpenAI started. Or are you saying the community has no incentive to do that because there is no reward/recognition for doing that?
They didn't just "start" it though - they released slop papers.
That's finishing it - not starting it as far as scientific publishing is concerned.
> Or are you saying the community has no incentive to do that because there is no reward/recognition for doing that?
Not exactly - but that is part of it.
I think what would have went over better is:
1. Immediately announce a solution has been found.
2. Do not publish the solution.
3. Put out an open request for anyone with experience in the area who wants to get involved to help collaborate on a construction and human-comprehensible paper. Accept anyone who can demonstrate potentially useful work/experience in the field/problem. Share the solution with them after they sign some kind of NDA that they won't independently publish or share the solution/work.
4. Work with people until a paper is ready (I mean actually ready - not the kind of slop that they released).
5. Publish. Include names of everyone who made meaningful contributions to the paper (not just the proof).
EDIT: Notice the incentive with my proposed second path is that it gives OpenAI an incentive to improve the interpretability of its proofs. This is a good thing! The maths community would be thrilled to actually gain understanding from such releases, and OpenAI would be happy because they could more quickly and independently publish their results. At the moment the "value" of their mathematics research "product" is low because of the lack of this interpretability, and this current approach is simultaneously destroying the opportunity value of the community as well as the incentive for OpenAI to ever improve on what's missing.
OpenAI is doing science the right way. Making the information available as widely as possible so that anyone can check and verify it.
That is the scientific process working exactly as it should.
If that "damages the mathematics community" then all it means is the mathematics community is not doing science and should be ignored.
I cannot stress this enough. If you are complaining about "how they released it" or calling this stuff "slop cannons", you're an unscientific hack that's dragging down humanity.
Engage with the actual claims. Prove them or disprove them. Nothing else matters here.
The amount of time the OP attacks OpenAI for errors of form and not substance is unfortunate. Do they also attack amateurs who try to contribute like this?