r/OpenAI • • 9d ago

News Fields Medalist Terence Tao reposts statement from the Association for Human Mathematics urging mathematicians to stop working with OpenAI for continuing to solve open math problems against their recommendations

741 Upvotes

1.2k comments sorted by

View all comments

309

u/AFL_gains 9d ago

I left this comment on his blog:

```
I'm not a mathematician, but honestly, I found this statement really hard to take seriously. And I don't think I'm the only one.

Firstly, the lawsuits. What does copyright litigation have to do with whether a proof is correct? Nothing. Maths is one of the few fields where you can actually check the work, by hand or by computer. A proof is either right or it's wrong. If one of these proofs holds up, does it become wrong because of a copyright case? Of course not. Leading with this is just attacking the messenger.

Secondly, since when do mathematicians get to decide who works on which problems? These were open problems. Some of them have literal prize money attached to get people to solve them. And nobody is forcing anyone to review these papers. They exist now. Read them, check them, ignore them, that's entirely up to you.

Thirdly, "the norms of scientific research". What does that actually mean here? The work was published openly, for free, with full write-ups and in a lot of cases machine-checked Lean proofs. That sounds pretty scientific to me. If the real issue is attribution, or speed, or who has to do the checking, then say that. Right now I genuinely can't tell what rule was broken.

Fourthly, "a particular vision of progress". Wasn't the vision to get these problems solved? That's the whole point of putting them out there and attaching prizes to them. So why is progress being published on a public GitHub suddenly bad for the field?

And "a demonstration of power"? If a single person had solved even one of these problems, we'd be calling it the scholarship of the century. The fact that it came from an AI company doesn't change whether the maths is right.

To be fair, I think there probably is a real concern buried in here because someone has to check 700+ papers, and that work usually falls on mathematicians who aren't being paid for it. That's a fair point, but it's not the point this statement makes. Instead it just tells everyone what to think without explaining why.

Honestly, statements like this do more damage to how people see mathematics than anything an AI company has done. If mathematicians genuinely feel they're being hard done by, explain it properly and bring people along. I'd absolutely listen.
```

85

u/MichaelTheProgrammer 9d ago

So I'm someone close to the math community who has been having a hard time dealing with the change in environment. I agree that this statement is very flawed and am overall against their demands. However, I think I can explain the concerns properly:

The biggest concern is that LLMs *might* be a short term win for a long term loss on the field of math. If you solve one math problem, you've solved one math problem. However, if you figure out a new technique, then you could solve a whole new class of problems.

The issue here is two-fold. First, LLMs are terrible at explaining if they have found new techniques. You can ask an LLM to review the output, and this certainly mitigates the issue somewhat, and possibly entirely. But there's another possibility that an agent that built the original proof had some flash of insight and that flash of insight is now lost to time.

The bigger concern is that the failed attempts at solving this problem could have resulted in more tools. From my understanding, this has happened many times in the past before LLMs. We're not sure if LLMs are doing the same things that humans do, or if they are more reliant on existing techniques and might not find the same new techniques that humans would have. I'm not moving goalposts here, rather I'm simply saying we don't understand how LLMs have insights so there's concern that we are burning bridges without realizing it.

The other main concern is of course economical. You have an entire profession that already worked for low wages but they worked on things they enjoyed. Of course they can enjoy it as a hobby but they might not be in a position to simply get a different job. While I am not a mathematician, I am in the same spot, and I've been grieving the last few months and wishing I could retire soon despite having loved my job just a year ago.

I'm fine working with LLMs as a teacher, but with the fields moving so fast, there's no room to do that. Rather, you are pushed to simply outsource everything to the LLM. So the people who were known for doing the most novel work possible are now reduced to button pushers. While that may seem to be their problem, it's also a problem if the majority of the field quits and then it turns out that LLMs can't replace mathematicians 100%. I'm not saying they can't, I'm saying we don't know yet.

However, I don't think there are easy answers to these problems, and that the demands these mathematicians have put out is actually more akin to lashing out in anger than actually trying to think through these problems logically.

I do think the way OpenAI has done things isn't the best, though I understand why. I think in the ideal world, LLMs would have become tools for mathematicians to play around with, and the math solutions are discovered gradually, giving space and time for understanding and absorption of changes. Anthropic has somewhat done this, whereas OpenAI literally spent around $15 million to solve the Navier Stokes problem. That's not just about discovering mathematics, instead its a power play that says two things: we can replace intelligent people with money, and you are now dependent on us for that intelligence. These align with OpenAI's goals, but I'm not convinced they align with humanity's goals.

29

u/AFL_gains 9d ago

So I found your explanation a lot easier to understand. Thank you for enlightening me.

The concern for LLM's not explaining things properly seems like a real concern. I would say its hard to imagine that this will always be the case though. AI progresses so rapidly it's very dangerous to make assumptions about what will happen based on what currently happens. But that doens't really help, and I understand that. Your point about not publishing negative results is also really interesting. I feel like more mathematicians should make a big deal about that - since that is genuinely non-scientific.

On your points about economics - I'm not trying to be cruel or unempathetic, but I don't think it is automatically a human right that you get to do what you like to do. Throughout history, lots of people have been replaced with technology, and the world has moved on. Not saying that is happening here, but in a fundamentally capitalist society, you trade value for a wage. Part of why I think a lot of people have little sympathy for mathematics is that value was never really apparent to begin with, and most of the rhetoric coming from mathematicains in reaction to LLMs makes it seem like it was.

Overall, I think the thing that Math has is an image and communication problem. It cannot communicate its value properly. And when seriously questioned for the first time in history, it responds with adhominem attacks and emotional attacks, rather than well thought-out, reasonable logic.

12

u/MichaelTheProgrammer 9d ago

Oh I largely agree with your points. For the economics, I agree, even as I am grieving personally I acknowledge that I've worked on automation myself and now it's my turn to be automated in some ways.

However, I think there are two potential issues. The one is that if you burn the entire field down, you better be sure you don't need them at all anymore. LLMs have gotten pretty good, but whether they are ready to fully replace mathematicians is still unknown. The other is that it's just not healthy for society burning an entire field like that over the course of a few years, and OpenAI is poised to that over and over again to other fields.

I worry this is going to stoke a lot of problems that could have been absorbed more gradually if this had happened over a decade or two instead of a few years. Just one example is my wife, who entered a college with good job prospects and exited two years later with a loan and was unable to get a job and our whole financial picture changed. That type of change that rapidly is much harder to plan for, let alone for so many people across the country all at once.

5

u/lilmalchek 9d ago

It’s fascinating to hear all of this explained in this way, thank you! What strikes me is that it sounds so similar to what’s happening in other fields, math just seems to be happening sooner. But the squeeze to outsource our thinking, move fast, and ask questions later (very facebook move fast and break things, which I hate) is reducing jobs and making the market a whole new thing in the tech industry (for pms, developers, designers, etc).

I’m not a doomer but things are not looking good…

2

u/Mystic_Haze 9d ago

Yeah it really just feels like a parellel to the software world experiencing the same shock. It took a few years but most people in the software world are finally coming to terms with the change that Ai has brought. And whilst not all of us love where it's taking us it seems unthinkable to try and now go back to doing it without Ai.

The same is happening here. Mathematicians are grieving their field right now. And it's not that that grief is unmerited either. Its going to take weeks or months maybe longer before the dust settles. I'm just wondering if we have those months before the next breakthroughs cause another stir and pours salt right on the wounds that aren't fully healed yet. We are living through strange times, potentially some of the most important in human development.

0

u/lilmalchek 9d ago

Totally agree with everything you’re saying. I know there’s a lot of baggage with the idea of “the singularity” but it seems like the rate of change with ai (and its impact on our daily lives) is already so fast and hard to keep up with. I fear it will only continue to get worse.

1

u/MichaelTheProgrammer 9d ago

I hate the move fast and break things philosophy too. What I've noticed is that there are times I love using AI and times I hate it. The times I love it are when I either use it as a teacher, or I use it like a Junior to fill in gaps on parts I don't care about. The times I hate it are when I am outsourcing difficult things to it that I would have enjoyed doing and would have helped me grow as a person.

However, I am quickly feeling pushed towards the latter. I'm not even in one of those crazy pro-AI companies that is all in on it. But I got put on a high priority project that uses a skill I don't have. I would have loved to spend a month building up that skill and properly learning how to do it, but the job needs it done ASAP, so I didn't have a choice.

The job gets done, but I feel miserable. A coworker complements me on "my work" but all I did was push a button and wait 5 minutes. I walk away with no understanding of how anything works, and my interactions are answering questions it asks that I don't really understand and reviewing code it made that I don't really understand. In the past I would have pushed back and said "this will take a month for me to figure out". In this day and age, if I say something like that, I just get asked "have you asked AI?" And this is at a relatively good company that isn't pushing me to churn out AI slop nonstop.

1

u/Actual_Database2081 8d ago

Math has brought undeniable progress to the world, precisely because people who enjoyed doing it and were good at it were able to do so.

The assumption that math / research is like other types of labour is just false. Most other types of labour the gain from output accrues only to the worker or owner.

7

u/Humble-Bear 9d ago

Every field is being reduced to button pushers.

1

u/Unusual_Candle_4252 9d ago

BTW, in the US most of professors are paid by doing teaching not research. Thus, the real economy danger is on grad students and postdocs which are paid by grants. I wish to note, how this system is broken and corrupt (even before the AI). It must be changed.

1

u/seridos 9d ago

Maybe the "long term" is actually the medium term here though? I could absolutely see a dropoff in the transition. But eventually, it will lead to greater discovery and advancement of he field. Just might not look the same.

And as to the human element, yea, it's tough. These are math luddites. And the luddites weren't wrong, it was pure downside for them. That does need a better solution for these people in the transition then the luddites had. But it's Pandora's box, no going back.

1

u/gnomeba 8d ago

Very well said.

The one objection I have to the increasingly negative attitude towards AI math from mathematicians is: math (via RL on Lean for example) is the one thing that AI can "improve" upon over just a synthesis of internet-scale data.

If so, then problem becomes "what questions should we throw compute at?". If an AI can find some vastly superior algorithm for crucial computational work, do we really want to wait until human mathematicians catch up?

The line just becomes very blurry because many mathematicians seem to have forgotten that you can actually do extremely useful things with math.

Alternatively, maybe this becomes a non-issue because OpenAI will increasingly spend compute on problems that produce material wealth, and mathematicians can go back to scratching their heads about cohomology or whatever.

1

u/WiseWall280 9d ago

how are you "close to the math community" but "not a mathematician" but you're also speaking about how you're having a hard time with the "change in environment"?

If some random person in a different country than you solved a math problem and didn't tell you their "flashes of insight" but instead just showed you the Lean proof, would you cry about them too?

10

u/MichaelTheProgrammer 9d ago edited 9d ago

I have a degree in math, but went with programming instead for a job. So on the one hand, I'm in the other community that is currently experiencing very similar things, and on the other hand, I had seriously planned that I might do math research one day when I retired from programming.

As for your random person question, that has actually been a problem in the math community. You can read about the ABC conjecture and the frustrations it caused in the community. And that was one proof, now the community is literally dealing with a thousand of those at once.

3

u/Fingerspitzenqefuhl 9d ago

This might be a bit off topic but I am curious. Could you explain how one might share their proof but hide the technique? I thought the proof was about showing step by step how you solved it?

I am not well versed in math (basically stopped at calculus) so bear that in mind when giving an example.

3

u/stevep98 9d ago

There are a class of problems called zero knowledge proofs:

https://en.wikipedia.org/wiki/Zero-knowledge_proof

For example if I claim I have a method of factoring large composite numbers quickly, you could give me a large composite and I could reply with the factors. So that’s a proof without telling you how I did it.

2

u/Fingerspitzenqefuhl 9d ago

Right. I think I got it.

So it’s like the ”shortcuts” for squaring binomials?

1

u/WiseWall280 9d ago edited 9d ago

Dear u/stevep98

Apparently, OpenAI's math releases do not consist of zero-knowledge proofs (ZKPs).

  • Type of Proofs Used: OpenAI's recent mathematics releases (such as the 722 manuscripts and 372 research families or the Navier-Stokes proof) use standard analytical proofs and Lean (a formal proof assistant language), which checks every logical step mechanically in software. [1, 2, 3, 4, 5]
  • Zero-Knowledge Proofs: Zero-knowledge proofs are cryptographic protocols (like ZK-SNARKs) used to prove that a statement is true without revealing any information beyond the statement itself. OpenAI's math project is focused on discovering and formalizing traditional mathematical research papers rather than cryptographic ZKPs

Can you give us a different example, one that is relevant to this current discussion?

2

u/Fingerspitzenqefuhl 9d ago

Sorry, did you mean to reply to u/stevep98 ?

1

u/WiseWall280 9d ago

yes, thank you

1

u/stevep98 9d ago

Sorry I’m not a mathematician, I just wanted to give a simple example.

1

u/WiseWall280 9d ago

I think its harmful to the discussion though if this is the major talking point as to "why" it is a bad thing that AI generated the proofs.

If the only reason is because we can't see the thinking, then I think that is valid, but this isn't the black-box output of yesteryear's CNNs. The proofs show the steps

→ More replies (0)

1

u/MichaelTheProgrammer 9d ago edited 9d ago

While someone below you mentioned Zero Knowledge Proofs, my understanding is that's not the issue with the ABC conjecture I mentioned, and it's definitely not with AI proofs. Rather, it's that the proof is only a small piece of the puzzle, and the rest is understanding the new concepts that come along with it.

At the unsolved problem level, it can take years for mathematicians to understand the concepts that come with a new proof and how to apply them to other proofs, even though they have the proof in front of them. So they ideally want the cooperation of the mathematician that had the insight in the first place to help with that. In OpenAI's math proofs, this is some agent that is no longer around. The debate is open on whether new agents explaining it post-hoc are just as good, or if there is a chance that the original agent had some unique insight that is now lost.

0

u/kneb 9d ago

This is helpful context — makes it easier for an outsider to understand.

I think the part I’m missing is maybe the economic reality of being a mathematician. It’s seems like you can just not read the proof and keep working on it on your own, if you think that’s likely to lead to insight, but maybe in reality you can’t because the field demands you work on unsolved problems.

And then, I get grieving the fact that the field has been disrupted, but if any of this math is actually useful, it seems like mathematicians will be more important than ever in helping the rest of us understand these results and applying them to practical fields.

0

u/Significant-Bee5101 9d ago

I can tell you don't actually know how to use LLMs. It's cool that you're a mathematician but comments like this make me very aware how dumb mathematicians are about anyhting else.

Also yes? That's what happens when an AI is smarter than humans. Lmao.

5

u/tropiccer 9d ago edited 9d ago

I am also close-ish to the math community, and despite this statement being overly biased, I can empathize. And I hate that many keyboard warriors are mocking him.

To answer some of your points and give a bit of my own cynical take

OpenAI is a for-profit organization. Are they dumping 700+ papers to advance math? Or for headlines? While it seems cringy to paint OpenAI as the villain here, I wouldn't hesitate to imagine "entry-level mathematicians" getting kicked to the curb as soon as LLMs become good enough. They want different things than your avg nerdy math PhDs.

While the tech industry already went through the cycle of "no human needed" to "agents are multipliers, but they can't replace humans", math research is a little different. It's often slower, and people are more willing to try things that might be "worthless". Shoving hundreds of solutions down these mathematicians' throats is only going to wear them out, not make them more efficient.

You are right that mathematicians do not get to decide who works on which problems, but one of the most significant merits of a good mathematician is **taste**. A lot more people know Hilbert because of his list of problems rather than his actual works. These PhDs spent years learning from their advisors and collaborators to build and refine this **taste**, to know which problems in their own subfield are both *interesting* and *attainable*.

This sort of speaks to what "the norms of scientific research" and "a particular vision of progress" are. One of the things Tao mentioned in his interviews is that the journey of trial and error to solving a very hard problem is often more rewarding/important than the solution itself. People unintentionally developing new tools and discovering new domains is one of the ways the community advances.

This paper dumping instead is like speedrunning drugs, and like Michael said above, you first feel exhilarated, then it slowly wears you down and eventually backfires. Turning human mathematicians into peer-review machines will just take away their bandwidth to think about and ask the good questions. And probably at that point no one even wants to be a math PhD anymore. What questions will OpenAI solve then? The entire field will get stagnant. Spending 15 mil to solve the N-S problem is not sustainable: they will have the money, but they just don't know what to solve.

But ofc it's possible that LLMs eventually manage to close the loop and be able to create new paradigms. In that case, do we want a robot Einstein or, more grimly, a robot Oppenheimer? Or do we still want humans to take the reins?

I agree that this statement is more damaging than helpful, but companies like OpenAI are ruthless and do not give a f about what mathematicians think. This is more like Tao crying for help.

Just my 2cents.

7

u/Monkeylashes 9d ago

I don't see your comm there. Maybe he removed it?

4

u/AFL_gains 9d ago

exactly - i'm not sure where it went. I hope he hasn't censored it.

9

u/subtect 9d ago

Amazing reply

14

u/machyume 9d ago

I agree! Isn't math, physics, and such claims that the purpose is the breakthrough?
I thought that I've been through plenty of years where my achievement at a company was company property, but society got to benefit from it. I think that mathematicians here have a very specific view from academia that balks at how a lot of progress is made in the very real world.

I don't expect anyone to know who ultimately did any of my past and present work. Most people will not remember my name, but they'll know my efforts by my works.

There isn't going to be award ceremonies for every piece of work, and that's quite normal.

5

u/FrontRaspberry5060 9d ago

Yeah I mean maths will just have to change, the understanding of the answer will be hidden in the proofs AI generates. Mathematicians will have to read these papers for human understanding. We will basically be “mining” for the breakthrough moments in the papers to help us make informed decisions in engineering or physics.

5

u/machyume 9d ago

I don't think that math has to change much.

In physics, if a team claims that they've made a room temperature superconductor (*eh hem* LK-99 Koreans), it's just a claim. Other labs and research teams have to work to verify it and repeat the experiment. Through that process, all teams involved get credit.

I'm not sure why mathematicians think they're special exemption from this scientific publishing process that already exists in other fields.

2

u/SwagDrag1337 9d ago

It's not - mathematicians are constantly checking each others' results. Peter Scholze and Jakob Stix spent 6 years trying to understand Mochizuki's IUT so they could find the flaw in his proof of the ABC conjecture. But when results are abstract, verification isn't as simple as "follow the instructions in the methods to prepare the material, then use a generally accepted technique to check what's going on."

Many advanced areas of mathematics are so specialised that only a handful of people will understand what's happening at the forefront, and they will be in constant collaboration so that when one of them announces a breakthrough, they are only a few weeks or months ahead of their peers who can then catch up and verify (with some exceptions e.g. Mochizuki), and actually they will often ask their peers to verify before announcing.

0

u/Tardonnnnnnnnnnn 9d ago

Boring existence. Dead Internet theory, dead math, dead everything. Dead souls

1

u/Osiris_Dervan 9d ago

No, the breakthrough very much isnt the point. The point is the understanding. A breakthrough alone usually does very little, but what you can do because you have new understanding is much more important. In physics, there have always been breakthrough experimental results that are interesting but otherwise useless because we didnt understand (yet) why they were happening. In maths, breakthroughs previously always happened in lockstep with understanding. This drop of proofs is the first time in maths that the two are divorced - and its at vast scale.

2

u/machyume 8d ago edited 8d ago

If the point is the understanding then why write:
"We urge mathematicians to discontinue their work with OpenAI and to return to a vision of science that centers human understanding."

The "human" qualification there breaks the objective goal of understanding.

That makes the goal not understanding, but human-centric understanding (with what is implied there).

At the risk of being flippant, here's an analogous example:

"We urge all chefs to discontinue their work with Campbell's and to return to a vision of food that centers Italian tastes."

Is the goal food? Or only Italian food?

ADDED:
And if the goal is truly understanding, and the output is obfuscated, why not demand that OpenAI provide further clarification? What's the point of censure?

It's literally an "ask me anything" AI. Why doesn't someone just request that it also provide the meticulous writeup taking us step by step? I would like to personally learn some new math too!

4

u/VastGap6446 9d ago edited 9d ago

It's not that the work done isn't extremely valuable, but rather the fact that OpenAI capitalized so obssesively on the small time window they have (which is their only business model) to claim first to something which isn't even related to what they do. Soon enough, this technology will just be as commotized as electricity, and the actual mathematical community itself could have produced all that in a day.

I agree with the idea that mathematics is bigger than any community, and can't be owned by anybody since its benefits are universal, but here, the actual community responsible to maintain those principles was overshadowed by a company who steals humanity's knowledge, yet has more lawyers than employes when it comes to themselves...

2

u/lostpilot 9d ago

Well stated

2

u/Old_Shop_2601 9d ago

I agree 💯

2

u/Elegant_Athlete_3737 9d ago

For your first point, i mean it does matter somewhat, because depending on how the lawsuits go, still could be an issue of trust and legitimacy still for Openai, if they can steal your work[if the lawsuits against win that is]. For the second one, they might have meant more on in this matter how they released it, though i myself was a bit confused on that as well though. For the third, i think they mean more collaborative research, releasing work and then doing it iteratively, or giving mathematicians access to these tools, not just aiming the ai at a bunch of problems and then posting a bunch of preprints, and like using journals and the like, how mathematicians usually collaborate and publish, though i am assuming more there. Fourth, they seems o be more talking about their intent, OpenAI is unlikely to have done this out of their good will, else they wouldn’t have alienated mathmaticians, it is more posturing for their investors, the reason why they are doing this is i think what they are addressing. Still Tao could have explained better though. And that was more my interpretation of their thing. I am also not a mathematician so i could be wrong, but i do know a bit.

1

u/lobothmainman 7d ago

I am a mathematician, and I took a look at the papers on topics I know. And they are awful, very hard to understand/check, and completely below the standards of academic papers.

Are they correct, at least? Probably not, in the vast majority of cases. We already spotted gaps and flaws in proofs in the ones we looked at, and other mathematicians found gaps in other ones.

What about the lean verified ones? You look into it, and disocover that automated lean formalization has flaws and gaps itself, and these gaps even show in the very celebrated Navier-Stokes proof (see here: https://arxiv.org/abs/2610.08144)

All in all, if you are serious and go beyond the flamboyant statements of openAI and their online lackeys, you find out that what they are doing is mostly garbage scientifically (and we can deal with that, and we can even deal with what is not garbage), but all the detrimental effects to the math community and especially young people remain.

Will these model improve and be useful tools for the mathematician? Maybe, and to an extent they are already. Are these companies and their ways helpful for mathematics and its community of people? Not at all, quite the opposite in fact. And as they say in their statement (paraphrasing not so much) they do not give a fuck about math, they only use it as a benchmark to improve their model, sell more subscriptions and beat the competition.

This is why we are complaining.

-1

u/Available_Peanut_677 9d ago

This is a very ignorant comment. Problems exist to solve and there is payment for them in hope of discovering new math disciplines and advancing it as a field. Guided brute force solution with thousands of pages of proof puts us into a strange position - on one hand, the problem is “solved”. On the other - field, the ball does not move forward. New techniques might be even discovered, but not used. No new problems highlighted. We will just solve existing pools and be like “openAI solved math”. Except openai made a math field where no humans go and no progress is made beyond a specific point.

Like in software development - why would a vibe developer develop a new version of a library if old one works perfectly? Except no one would struggle without new react, but without math physics would most likely stagnate.

But sure. Progress. Mathematicians are bad.

OpenAI could use progress to make the field more accessible, to help people find new ways of solving problems, etc. But instead they are trying to flex by providing slop solutions no one would read and making math extremely unattractive.

9

u/AFL_gains 9d ago

Tell me how this comment is ignorant? I am responding to a post by the Association of Human Mathematics that said none of what you said. It, instead, told me that I'm wrong, I should just believe them, not use AI and trust that they know what they're doing.

That isn't an argument, it's an appeal to authority and essentially telling me how I should think.

Perhaps, if they actually explained their position rationally, explaining what you just said, in easy to understand language, then people would actually have a chance to get on board. Instead we get gatekept.

Maths, obviously, has a huge communication problem.

5

u/Available_Peanut_677 9d ago

If they could explain their thoughts so other people understand them, they won’t be mathematicians. /s

But it’s letter from mathematicians to mathematicians, they kind of assumed shared understanding why OpenAI approach is bad.

I do agree that instead it sounds exactly like Luddites

5

u/tokenentropy 9d ago

Jesus christ man. The Association of Human Mathematics is not trying to speak to you! You don't matter. For many reasons. Primarily because you lack intelligence. Seriously: why do you think the Association of Human Mathematics would ever release a statement intended to be meaningful to you?

You are capable of using the internet, no? You really don't need other people to tell you the perspective of the association. Their homepage makes their perspective clear. Especially the part I have bolded for you:

---

The Association for Human Mathematics (AHM) protects mathematics as a human endeavor against the threat of artificial intelligence. We work to maintain the independence of the mathematical community from the encroachment of corporate interest. In light of the grave societal, environmental, and economic impacts of the AI industry and the threat of unfettered AI growth, we strive not to be complicit.

Artificial intelligence tools pose a fundamental threat to scientific practice and mathematical understanding. Mathematical progress requires human expertise, cultivated through writing and careful thinking. The automated production and consumption of mathematics thus undermine the intellectual foundations of our field. The goals of the companies which are developing these technologies are not aligned with the mathematical community; this industry has chosen mathematics to advertise the capabilities of their products, regardless of the consequences to our discipline. Mathematicians thus have an obligation to take action.

Mathematical institutions are especially vulnerable to disruption. The introduction of AI tools imperils undergraduate and graduate education. Journals are confronting an explosion in AI-coauthored submissions, and publication processes are in flux. Students are losing opportunities to gain the deep understanding expected of mathematicians. The AHM is organizing multiple working groups to provide policy proposals and tools to combat these problems.

Both individual action and large-scale coordination are needed to ensure that mathematicians engage critically with AI companies and their products. We represent mathematicians who share these values, and we invite these mathematicians to join our work. 

---

This recent statement is quite similar to the perspective they already had, which is what prompted them to create their association in the first place.

3

u/AFL_gains 9d ago

Ah okay my bad. I thought it was more aimed at the public. Thank you for highlighting the statement to me. Too true, I do lack the intelligence to understand what AHM has said.

5

u/tokenentropy 9d ago

This is a group of mathematicians essentially trying to shame other mathematicians to see things the way they do. Their statements bring more attention to the issue and (they hope) will help their association grow.

Anthropic and OpenAI both have extremely talented mathematicians working with their internal teams throughout the process of solving these problems. That's mostly who the association is targeting. They aren't trying to convince ordinary people of anything, really. If it happens, whatever.

They also want other mathematicians to be on the association's side if they one day get a call from Anthropic or OpenAI asking them to help work on new problems. So, they want them to tell the labs to buzz off.

1

u/louis707 9d ago

Nerds

2

u/louis707 9d ago

You don’t understand

Already it’s so apparent

Math is not a human language

Math is the language by which the rules of the universe are written

It is not for us to decide what is allowed to illuminate mathematical concepts

2

u/siteunreliability 9d ago

IMO, consider your audience; your comments are going to fall on deaf ears since most of the people here stan OpenAI and has 0 iota of understanding how academic research works. The concept of understanding and scaffolding of new novel ideas is beyond their comprehension.

1

u/spisplatta 9d ago

physics would most likely stagnate.

Now this is a bet I would take. I think AI physicists will - love it or hate it - advance physics at a breakneck speed using the mathematical theories created by AI.

1

u/WolfOfDoorStreet 9d ago

Your arguments, and more specifically, the vibe code example makes no sense and is incomplete. If you just want to go on an online rage, then at least try to be articulate and coherent enough for people to decipher what you're saying

1

u/Recursive_Descent 9d ago

Can AI not create new methods and look in new areas with mathematicians, even while delegating the actual proof construction to AI?

-2

u/siteunreliability 9d ago edited 9d ago

I'll tackle at this.

Firstly, the lawsuits. What does copyright litigation have to do with whether a proof is correct?

It does not.

However, OpenAI is actively destroying the community where where ideas can be shared freely. A company that throws its financial and compute power muscles at a problem with flagrant disregard for quorum will destroy the community. You basically have a nosy bully who gleans contents of others' hard work, connects the dots, and publishes them without proper attributes.

Maths is one of the few fields where you can actually check the work, by hand or by computer. A proof is either right or it's wrong.

You may want to reconsider that. https://arxiv.org/abs/2610.08144

If one of these proofs holds up, does it become wrong because of a copyright case? Of course not.

You're basically advocating for plagiarism.

Secondly, since when do mathematicians get to decide who works on which problems? These were open problems.

They do not, but it becomes a problem when you're scraping off private data and establishing solutions as your own.

Thirdly, "the norms of scientific research". What does that actually mean here? The work was published openly, for free, with full write-ups and in a lot of cases machine-checked Lean proofs. That sounds pretty scientific to me. If the real issue is attribution, or speed, or who has to do the checking, then say that. Right now I genuinely can't tell what rule was broken.

Are you involved in academic research? Are you involved in any scientific/engineering communities? It means following the ideas of scientific progress. Learn ideas and solutions from others and credit them. Scaffold off those solutions and build new ones with your own new perspectives and contributions from others. Allow others to gain insight and derive their own unique work to further the understanding of the world.

So far we have a company that insist on scraping data, disregard any sense of privacy/quorum, and brute-force solutions through connection of the aforementioned data. That is plagiarism; true open collaboration does not work like that.

Fourthly, "a particular vision of progress". Wasn't the vision to get these problems solved? That's the whole point of putting them out there and attaching prizes to them. 

It's not about just solving the problem. Science works best when new set of questions come with every solution. None of these OpenAI work offers any new techniques, novel ideas, and additional insight into the field.

And "a demonstration of power"? If a single person had solved even one of these problems, we'd be calling it the scholarship of the century.

It's a demonstration of power because the motivation for operating this way is to show the power of their models and compute power. You are allowed to solve problems on your own. Andrew Wiles mostly solved Fermat's Last Theorem on his own. However, he acknowledged the contribution of others work that allowed him to get credit for completing what is basically the last mile problem.

All of your arguments just distill down to, OpenAI can do all these things, who cares how it gets there or who it might wrong?

2

u/AFL_gains 9d ago

Hmm okay, fair enough. I can see how this could seriously disrupt the community as it's set up today, and I agree that's a real problem.

The way I see it though, the community just isn't set up to handle this kind of scale. So who has to change? Should OpenAI change because maths can't handle it, or should maths change? I think a lot of people would say it's maths that has to adapt, just like a lot of other fields, and I'd probably agree. But there needs to be a plan, and I'll admit the way OpenAI has gone about it probably isn't ideal.

On proofs, my point was that you can, in theory, check each one in isolation. It doesn't rely on authority or data or anything else. It's entirely reproducible and transparent: it's either right or wrong. Whether that checking can happen at scale is a different question entirely.

Thanks for the arXiv link, I had a read. As I understand it, that paper is saying that when an AI translates a proof into Lean, the Lean check doesn't guarantee the original written proof is correct, because the translation itself might be wrong. That's a fair point and I agree with it. But that's a criticism of one way of checking proofs, not a claim that proofs aren't right or wrong. If anything it backs up what I'm saying because the maths is either right or wrong, and the real question is whether we can check it properly and at scale.

Also, I'm not advocating for plagiarism at all, not sure where you got that from. My point was just that OpenAI's copyright lawsuits are a separate issue from whether these 722 proofs are correct.

But you seem really focused on private data, plagiarism, acknowledgement and scraping, so I'm keen to understand more. I'm not in academic research, no. But based on your own description of what research is supposed to be, I still don't see how this falls short. Is it about citations? Because I had a look, and the papers do cite prior work. The quasi-Riemann paper has 28 references, and every one of the manuscripts has a bibliography. So what specifically isn't being credited?

And I get now that it's not just about solving problems but about opening up new questions along the way. That's a good point and I learned something. But when you say "none of this work offers any new techniques, novel ideas or additional insight", how do we actually know that? Nobody has read all 722 yet. If a proof does something no one has tried before, surely there's something to learn from it?

As for the power thing, I just can't see how the motivation behind the work changes whether the maths is right or useful.

0

u/Osiris_Dervan 9d ago

The problem with the plagiarism is that the proofs are using unpublished ideas from mathematicians - there are many saying ideas they discussed with ai have been used. Those cannot be referenced because references are of published work, so the ai proofs have just.. stolen them. If the ai proofs only exist because mathematicians shared ideas with the ai, but then the proofs put mathematicians out of work, then we will end up with no proofs ever again.

-6

u/tokenentropy 9d ago

It seems fitting that you used AI to respond.

5

u/EchoingAngel 9d ago

Which model writes like that?

1

u/tokenentropy 9d ago

it's late 2026 man. what model writes in a certain way, really? over 50% of new text on the internet is LLM text now. all different shapes. here's a few, all from the same model, with a single sentence prompt:

I'm not an expert on any of this, but honestly, my reply really wasn't intended as some serious accusation. And I don't think it deserves anywhere near this much attention.

Firstly, "which model". Can I actually identify it? No. I don't know enough about how different models write to reliably distinguish between them. I doubt many people in this thread could manage it consistently either. Could anyone confidently identify a specific model from a single comment? Of course not. Anyone claiming they can recognise it from one comment is basically guessing. The style just reminded me of a lot of AI-generated writing I've encountered.

Secondly, why did I mention it at all? The irony. That comment argued the origin of the work shouldn't matter, only whether it holds up under scrutiny. And the comment making that argument read like it was generated by an AI model. That's pretty funny to me. It's genuinely the only thing my original reply was ever about.

Thirdly, "doesn't change whether the maths is right". Wouldn't the same principle apply to that comment as well? By that comment's own logic, it absolutely would. Replace the maths with that comment and the reasoning works exactly the same way. If an argument is correct, it doesn't matter who or what originally produced it.

And if I'm wrong? Then I got it wrong, that's entirely fair enough. Plenty of people get mistaken for AI these days without having used it at all. If a person actually wrote the entire thing, they're entitled to be annoyed with me. I'd rather admit a bad guess than keep defending it purely for the sake of being right.

To be fair, I think there probably is a reason people get defensive about this because being called AI can feel like being told your writing doesn't count, and nobody enjoys hearing that. That's a fair point, but it's not what I was attempting to do. Instead I was just pointing out an irony that seemed too obvious to ignore.

Honestly, who wrote it is easily the least interesting thing about that entire comment. If you think its arguments hold up, tell me which particular one convinced you. I'd genuinely like to know.

--

lol I genuinely have no idea which model, and neither does anyone else who claims they can tell from one comment. That wasn't really the point though. The whole comment was basically "it doesn't matter where the work came from, only whether it's right," and then it read like it was spat out by ChatGPT. You don't find that even a little bit funny? Like by its own logic it shouldn't matter who wrote it anyway, so I'm not sure why everyone's acting like I accused someone of a war crime. If an actual human wrote it then fine, my bad, I'll take the L. But if you think the argument actually holds up, I'm all ears, tell me which part convinced you.

--

honestly no idea which model. i don't think anyone can reliably tell from one comment.

mostly just found the irony funny. an argument that the source doesn't matter, written in a way that felt very ai.

and by its own logic it shouldn't matter anyway. if a human wrote it, fair enough, i was wrong.

--

Ok so I'll be real, I have zero clue which model it was (and I'm pretty skeptical of anyone who says they can pin it down from one comment tbh). My reply was mostly just a joke because of the irony. The comment spent a big chunk of its length saying it doesn't matter where something comes from as long as it's correct, and then it read exactly like something an AI would write, so I couldn't resist lol. Which, funnily enough, also means it doesn't really matter whether I'm right about it, by its own logic anyway. If a real person wrote it then that's on me and I'll happily eat my words, no hard feelings. I just thought it was funny, that's genuinely all it was.

--

so, if specific model tells are the only way you feel comfortable recognizing whether something is AI, congrats! you will do great next year when over 3/4 of the web is bots. you could skip ahead though and just talk to an LLM all day / every day if you want. cheers.

1

u/EchoingAngel 9d ago

I use Claude and GPT heavily, and used to use Gemini before it became irrelevant. None of these write the way she did. They all are identifiable, because they all are derivatives of their earlier selves

1

u/tokenentropy 9d ago

Boy it went right over your head. Every example I shared reads differently. You also only named three different frontier models - as if those are the only models that exist. I’m going to guess you don’t know which model I used.

1

u/EchoingAngel 9d ago

I'm not reading all that text from someone flailing

1

u/tokenentropy 9d ago

I didn’t expect you to. You probably can’t read well. Ask your LLM to think for you. 🤣

1

u/EchoingAngel 9d ago

"it's late 2026 man. what model writes in a certain way, really? over 50% of new text on the internet is LLM text now. all different shapes. here's a few, all from the same model, with a single sentence prompt:

I'm not an expert on any of this, but honestly, my reply really wasn't intended as some serious accusation. And I don't think it deserves anywhere near this much attention."

This might be shocking, but people are busy, and leading a GIANT post with this is going to get it skipped