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A misalignment of AI in mathematics

mathandai.org

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Re: A misalignment of AI in mathematics

#841

Post by int_19h »

Xelynega wrote: post #322
jimkleiber wrote: post #149

Earlier quoted context omitted.

I wonder if this is a root of the complaints across fields, how AI is ruining the greater picture and process in writing, acting, drawing, filming, coding, and more. That it makes life more ends and less means.

It's also known as "commodification of labour", and AI is just the latest and greatest tool to do it. Luddites complained that the trajectory of technology was to allow less skilled workers to mass produce goods via machines owned by factory owners, as opposed to helping skilled workers build up and use their skills while passing them on. Now we have a lot of money and time focused on LLMs owned by a few companies, m…

> Luddites complained that the trajectory of technology was to allow less skilled workers to mass produce goods via machines owned by factory owners, as opposed to helping skilled workers build up and use their skills while passing them on.

And their complaint was valid from their perspective, but the end result of that process is that now you can have functional and pretty clothing for pennies.

It's true that a lion's share of the gain was pocketed by people who owned the mechanized looms. Now imagine how much more of an advantage it would have been without those people.

Same thing here. We can - and should - get rid of all the megacorp leeches. But the benefits of cheap automation remain regardless, and it's still the same equation - removing the gatekeeping harms those who relied on it to keep the products of their labor priced high, while benefitting everyone else.

Re: A misalignment of AI in mathematics

#842

Post by vitriol83 »

tmhn2 wrote: post #198

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…

But Mochizuki didn't actually prove anything, whereas the labs have already done so.

The pessimistic scenario is the AI labs will continuously hoover up new developments in mathematics and gazump everyone in their respective fields. It's clear they have no desire to participate in any silly academic niceties, like properly assigning credit or expository work for normal humans. What incentive then do humans have to do this work ?

Generally the mood amongst research mathematicians is pretty dire, and I don't really blame them.

To be clear I think AI is super useful for mathematical research, the problem is the methods of the big labs are massively disincentivising mathematicians from engaging in research, and other associated tasks like giving seminar, teaching writing books etc. These arguably have much more value than finding an obscure counter example to Navier-Stokes.

Re: A misalignment of AI in mathematics

#843

Post by omnicognate »

zozbot234 wrote: post #810
freehorse wrote: post #805

Earlier quoted context omitted.

> his prose is directly implying that evil superintelligent AIs are deliberately writing obscure proofs in order to harm the community of human mathematicians That is probably the wildest misinterpretation of sth I have ever read here. Misalignment is used as in the goals and interests of ai COMPANIES are not the same as the ones of the mathematical community. It is very proper use of the word, and if anything imo th…

The point stands whether you attribute agency to AIs themselves or to AI companies. The companies are not deliberately sabotaging human mathematical understanding by writing up purposely inscrutable results, either (which is what the word 'misalignment' would imply in this context): they are merely working with frontier tools that have a very limited capability for human-like understanding. It's left to human mathema…

You seem determined not to understand this, but to spell it out even further: The point is not that the companies are deliberately trying to harm maths but that in pursuing their own goals, which are different to those of mathematicians, they are doing so. Their goals and their methods of achieving them are not aligned with those of mathematicians. This is, incidentally, exactly what alignment means in AI as well: a paperclip maximiser harms humans not because it is intentionally trying to do so but as a side effect of trying to achieve its own objectives, which are not aligned with those of humans (which include not having their entire environment turned into paperclips).

The word is being used entirely correctly, and I'm sure the nod to the AI usage is quite deliberate.

Re: A misalignment of AI in mathematics

#844

Post by voidhorse »

GPerson wrote: post #703
tmhn2 wrote: post #198

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…

It’s frustrating that this comment is at the top because it, along with lots of the replies it inspired, absolutely misrepresents the actual declaration. The declaration is not making any statements about not using any AI in mathematics. The entire point is to push the use of the technology in a direction which is compatible with positive pre-existing features of the math community, and to make it better known what s…

Yes, thank you. The demise of basic reading comprehension skills will be the true end of us all.

Re: A misalignment of AI in mathematics

#845

Post by gjulianm »

ralph84 wrote: post #513
omnicognate wrote: post #199

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…

> primarily as a marketing exercise Like the mathematicians working on famous problems in private until they could claim full credit for something interesting wasn't also a marketing exercise for their own careers. The commercial value (or lack thereof) of a proof doesn't depend on whether it was done by a human or a machine.

> Like the mathematicians working on famous problems in private

This is an extremely rare situation that practically never happens. Most mathematical research is done in the open, with partial results being published, conferences where approaches are discussed, collaborations... The Navier-Stokes solution is a great example: the approach that OpenAI ended up using was something that two mathematicians had proposed previously and was being studied and followed by several others, with different sub-paths within the same approach.

Re: A misalignment of AI in mathematics

#846

Post by int_19h »

jiggawatts wrote: post #679
beambot wrote: post #191

Earlier quoted context omitted.

Humans still have brains (and thus human intellect) even in the presence of AI... Even today, people make varying use of their brains.

But what use will be their brains to others if a machine can do the thinking instead for a fraction of cost?

Whatever they feel like putting them to, instead of whatever they are forced to put them to to earn their living?

Re: A misalignment of AI in mathematics

#847

Post by int_19h »

Forgeties79 wrote: post #416
CuriouslyC wrote: post #282

Earlier quoted context omitted.

Lots of people still make bad music that other people still manage to enjoy (a lot of it has gone multi-platinum!) even though they're not Mozart or Bach.

This would be valid if we didn’t live in under capitalism, which reduces the way we spend our time down to dollars and cents.

Correct. So burn down capitalism, not AI?

Re: A misalignment of AI in mathematics

#848

Post by tim333 »

Animats wrote: post #355

There's an unpopular branch of mathematics which does not have infinities - finiteism.[1] The constructive version of finitism takes the position that there is no such thing as infinity, just arbitrarily large upper bounds. You can have theorems about arbitrarily large numbers, but you never get 1 + 1/2 + 1/4 + 1/8 ... = 2 The benefit of finitism is that it escapes undecidability. The big objection to finiteism is th…

It seems to 'not have infinities' by ignoring them. How many prime numbers are there? How many digits does the square root of two have? I guess you can simplify life by ignoring that stuff and sticking to what is 7x8.

Re: A misalignment of AI in mathematics

#849

Post by gjulianm »

yieldcrv wrote: post #370
Panoramix wrote: post #354

Earlier quoted context omitted.

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…

> I read the article and they are all wrong

I would recommend a bit more humility and trying to better understand why 25 Fields medalists, among them people like Terence Tao (who isn't anti-AI by any means, he's even promoted a registry of AI Lean proofs), are saying this.

> 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.

No. The point is that AI companies are using the models to solve problems in such a way that the useful part of problem-solving, i.e. the theories and tools developed during the process, is not present. And they are doing that because the companies seem to be motivated not by honest advancement of math but by marketing and publicity.

> they synthesize and solve lots of other problems nobody asked for.

No one asked Fourier to solve series representation of functions when he was studying the heat equation, and yet thanks to that we have Fourier analysis.

> 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

The point they are making is that if AI keeps being used as "problem solver" rather than "theory understanding", replicating the proofs and getting the useful parts out of them will be far more difficult.

Re: A misalignment of AI in mathematics

#850

Post by JumpCrisscross »

zozbot234 wrote: post #810
freehorse wrote: post #805

Earlier quoted context omitted.

> his prose is directly implying that evil superintelligent AIs are deliberately writing obscure proofs in order to harm the community of human mathematicians That is probably the wildest misinterpretation of sth I have ever read here. Misalignment is used as in the goals and interests of ai COMPANIES are not the same as the ones of the mathematical community. It is very proper use of the word, and if anything imo th…

The point stands whether you attribute agency to AIs themselves or to AI companies. The companies are not deliberately sabotaging human mathematical understanding by writing up purposely inscrutable results, either (which is what the word 'misalignment' would imply in this context): they are merely working with frontier tools that have a very limited capability for human-like understanding. It's left to human mathema…

> deliberately sabotaging human mathematical understanding...which is what the word 'misalignment' would imply in this context

The entire point of the paperclip maximiser is the AI isn't evil. It isn't trying to hurt humans. It just doesn't care about us.

Nobody claims OpenAI and Anthropic are out to torpedo mathematics. Just that relative to their internal goals of getting publicity ahead of IPOs by winning awards, what happens to mathematics and mathemeticians in the long run isn't a real concern.

The Holocene [1] features relatively few species humans set out to eradicate. We mostly realised something had gone extinct after we accidentally destroyed them. That is what originally misalignment meant in respect of AI.

[1] https://en.wikipedia.org/wiki/Holocene_extinction

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