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A misalignment of AI in mathematics

mathandai.org

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Re: A misalignment of AI in mathematics

#371

Post by vector_spaces »

adastra22 wrote: post #309
omnicognate wrote: post #201

Earlier quoted context omitted.

The statement is not about AI but about the behaviour of AI companies. OpenAI have put vast resource into solving open maths problems: many millions of dollars of compute just on the Navier-Stokes result, plus whatever they spent on the broader Millenium Prize problems initiative and the other results they have published. Anthropic are doing the same. The statement is asking them to stop doing this. AI companies are…

Humanity is better off for knowing these proofs. This strikes me as academic NIMBYism.

Do you "know", in any meaningful sense, any of OpenAI's recently publicized proofs? Do you suppose that there is any large community of non-academics that does?

One of the points the parent makes, along with the TFA, is that academia -- or more specifically, the "mathematical community"-- is a setting primarily for creating and ingesting mathematical knowledge, and disseminating it to the next generation and to other fields. Humans absorb this material slowly, through lots of discussion and collaboration -- it is necessarily a slow process. Facilitating this is one of the important functions of academia. Your usage of academic as a slur here is a bit silly for this exact reason.

I don't claim it is perfect, and we can argue about pedagogy in elementary courses till the cows come home. That's not really material. But this is one of the only settings in which such knowledge is broadly valued for its own sake, and in which there is a semblance of incentive to help others "know" this stuff as well, be they future generations of mathematicians, science and math educators and communicators, practitioners in other fields, or genuinely curious amateurs.

Re: A misalignment of AI in mathematics

#372

Post by jeremysalwen »

tmhn2 wrote: post #130
jeremysalwen wrote: post #20

To me it doesn't seem like what AI has destroyed is the ability for mathematicians to develop understanding and share it with each other, but rather it's destroyed the yardstick (solving open problems) that has traditionally been used to measure how much they have contributed to that understanding. I do see how this is a problem in terms of assigning credit, but I think the cat is already out of the bag in terms of t…

The issue of credit is a relatively minor point in the declaration. It's more about bypassing the culture and processes mathematicians have developed that lead to human understanding, generating new ideas, and bringing up new generations of mathematicians. (See also his article about "non-renewable mining" of good problems.) Reducing mathematics to "let's just generate results through an isolated and automated system…

I agree that the declaration doesn't focus on credit, but I think it's still at the root of the problem. Because ask yourself: if the AI generated proofs are not creating any new ideas or insight, just brute forcing a boolean true/false result, then why can't mathematicians simply ignore their results? Why does it matter if OpenAI or even amateurs with AI are "solving" these problems, without contributing to any deeper understanding?

I don't think "intellectual poisoning" is really the mechanism that harms the mathematics community.

The harm is if you have a community of mathematicians who are focused on expanding human understanding, then having instant access to a bunch of AI proved results muddies the water about who has contributed what. If someone could scoop any significant theorem at any time by pointing an AI at it, how do you really demonstrate that you have created new understanding? Or that your new understanding is about something important? How do you prove that the AI needed your new concepts to be able to solve it?

Re: A misalignment of AI in mathematics

#373

Post by yieldcrv »

Panoramix wrote: post #357
adastra22 wrote: post #309

Earlier quoted context omitted.

Humanity is better off for knowing these proofs. This strikes me as academic NIMBYism.

Your point is largely addressed in the article, did you try reading it? "In many fields and activities, years of training have traditionally served not only to produce a final answer or product, but also to develop understanding and the ability to formulate new questions and ideas. However, building on a vast body of previous human work, AI systems are becoming increasingly capable of producing the results of such wo…

Different person here, I read the article and they are all wrong. Hope that helps.

Okay, to elaborate, substantively, their point is that the people using these AI models are not doing it for the love of the game, but for marketing. And instead of them - and nobody - spending millions of dollars to solve the problem, successfully, they want every problem of their academic industry to persist because even though they never solve the problem, they synthesize and solve lots of other problems nobody asked for. And get to boost their egos?

Yeah, stop that. Actual alignment is on the humans themselves, if they want to remain relevant as academics and mathematicians, they need to learn how to replicate the proofs and the steps that alluded humans for decades and don't worry about the narcissistic elements that slow their industry down.

Re: A misalignment of AI in mathematics

#374

Post by ex-aws-dude »

The thing is no one is stopping anyone from getting the same knowledge/understanding/insight

If those things are disincentivized because the original problem is “solved” and there is less prestige to motivate people doesn’t that say more about issues with the community of mathematicians than the AI

Re: A misalignment of AI in mathematics

#375

Post by pizzly »

tmhn2 wrote: post #280
ksoped wrote: post #252

Earlier quoted context omitted.

It's not just the isolated dumping, it's the fast, isolated, possibly untraceable dumping, without long term support. It'll basically become slop fatigue if OpenAI starts dumping out proofs faster than the community can keep up, and some turn out to be wrong, never formalize it, don't stay to support it, etc.

I wonder if they will continue to dump proofs, though? Their point has been made, the novelty will wear off, and it maybe won't be a priority use of their resources to spend however many millions on another big proof--they will move on to the next thing to show off I'm sure. At that point, the ones generating proofs will be, I hope, mathematicians (professional and otherwise) that are more interested in the results a…

I think AI companies making a point is not the only thing at play. Discovering new maths ultimately leads to new technologies and applications. It may start theoretically but end up being of practical use in the future. Even if humans do not understand it (lose interest, too complex, or just way too many new proofs to go though) AI can use this AI derived math corpus which will help it in other fields.

Re: A misalignment of AI in mathematics

#376

Post by mypalmike »

omnicognate wrote: post #201
jeremysalwen wrote: post #20

To me it doesn't seem like what AI has destroyed is the ability for mathematicians to develop understanding and share it with each other, but rather it's destroyed the yardstick (solving open problems) that has traditionally been used to measure how much they have contributed to that understanding. I do see how this is a problem in terms of assigning credit, but I think the cat is already out of the bag in terms of t…

The statement is not about AI but about the behaviour of AI companies. OpenAI have put vast resource into solving open maths problems: many millions of dollars of compute just on the Navier-Stokes result, plus whatever they spent on the broader Millenium Prize problems initiative and the other results they have published. Anthropic are doing the same. The statement is asking them to stop doing this. AI companies are…

I suspect that beyond just marketing, these pursuits yield plenty of useful information about model design that will likely lead to model improvements and optimizations for both mathematics and general reasoning going forward.

Re: A misalignment of AI in mathematics

#377

Post by youoy »

causalmodels wrote: post #269
omnicognate wrote: post #201

Earlier quoted context omitted.

The statement is not about AI but about the behaviour of AI companies. OpenAI have put vast resource into solving open maths problems: many millions of dollars of compute just on the Navier-Stokes result, plus whatever they spent on the broader Millenium Prize problems initiative and the other results they have published. Anthropic are doing the same. The statement is asking them to stop doing this. AI companies are…

What do we do about the problems that don't require many millions of dollars in resources? Last weekend I spun up a small agent swarm and pointed it at a field of math I have some affinity towards. Within four hours I had settled three conjectures, one of which is rather famous (for the field, not in general). It cost me about four hundred dollars. I am at a loss about what to do with these results. On one hand I fee…

It depends.

If you are trying to understand better the field, then do a good write up of the proofs so that people can learn from it.

If you want to earn the respect of people because you found interesting proofs. Then do a good write up of the proofs so thst people can learn from it.

If you want to plant flags and pollute peoples minds. Then please publish it anonimously, no one wants to correct LLM slop for you.

Probably we should build a repository of AI slop proofs that are only allowed to be publish anonimously. That way people may be more inclined to work on it because they would feel like they are cleaning your house for free.

Re: A misalignment of AI in mathematics

#378

Post by zozbot234 »

deanCommie wrote: post #360
tmhn2 wrote: post #200

As a mathematician maybe I am a little more optimistic than this declaration. I am thinking of Mochizuki's abc conjecture: He worked in relative isolation, and dumped a huge incomprehensible proof on the community (to oversimplify a bit). That's not totally unlike what might happen if AI generates a huge, incomprehensible proof of let's say RH. Well, what is the result? In the Mochizuki case, it was a lot of skeptici…

Even before AI we used to say if you write code that you only barely understand, then it will be to complicated to debug. (and/or maintain) Mochizuki was still one human and it required legions of other humans to unpack and untangle to confirm that it didn't lead to anywhere in particular. AI is now capable of constructions so complex that no human or human team can unpack. And its ability to increase that complexity…

> AI is now capable of constructions so complex that no human or human team can unpack.

How can we possibly know this when we haven't even seriously started on the endeavor of actively reverse engineering these AI-generated proofs? That's a proper job for human mathematicians, because the AIs themselves are demonstrably clueless about what steps in a proof are genuinely interesting and load-bearing from a human POV. This is evidence of a limitation in AIs' capabilities, not of any kind of misaligned behavior. The fact that Tao actually uses that term in his complaint is deeply disappointing.

Re: A misalignment of AI in mathematics

#379

Post by kzrdude »

nonsensical_ wrote: post #256
azan_ wrote: post #238

Earlier quoted context omitted.

Care to elaborate?

Mostly that he really should have seen this coming. These people absolutely do not care what happens to mathematics (or any other field). They compulsively lie and steal and they played Tao and others like a fiddle. He danced to their tune and now that the music has stopped, now do they complain. He was the poster boy of the mathematician yielding these tools for his own benefit. But he forgot who the owners are. Too…

You should read his comment from wednesday here: https://terrytao.wordpress.com/2026/09/07/finite-time-blowup...

And yes, at one point it gives you right about them taking advantage of him. He sat down for an interview and found later that they just used the "best clips" out of it for an OpenAI ad.

Re: A misalignment of AI in mathematics

#380

Post by magicalist »

pfdietz wrote: post #291
dominotw wrote: post #216

Earlier quoted context omitted.

yeah beacuse no one trust any of their benchmark results now they are scrambling to find a signal thats undeniable

I expected this. They prove a millenium result, but it doesn't count because they are bad people. It's this sort of thing that motivates people to burn down the institution you might be trying to defend.

> It's this sort of thing that motivates people to burn down the institution you might be trying to defend.

lol, yes, this sort of thing is what many people who voted for Trump were saying, and things are going great for them.

> They prove a millenium result, but it doesn't count because they are bad people.

OpenAI has only themselves to blame for this, and they know it. They could have handled this so much better. I'd bet there's more meeting time right now going into how to unveil future math results than on meeting about the actual math research.

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