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A misalignment of AI in mathematics

mathandai.org

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Re: A misalignment of AI in mathematics

#561

Post by paulhebert »

ralph84 wrote: post #523
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…

> 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.

These mathematicians dedicated their life to math and were working for a long time to achieve the pinnacle of their careers.

OpenAI just burned millions of dollars over a weekend after hearing that someone else was close to solving the problems. Their interest was in their AI system more than the actual math problems.

Don’t you see how that’s different?

Re: A misalignment of AI in mathematics

#562

Post by chrisjj »

Strilanc wrote: post #236

This letter is complaining that human understanding has been crucial to advancing of mathematics, and AI companies are not bothering with it. But the promise (and horror) of AI mathematics is that, if it succeeds, human understanding becomes irrelevant. That's the goal . So this letter's message will fall on deaf ears. Keep in mind employees at AI companies are publicly stating that they believe they're risking a >10…

> This letter is complaining that human understanding has been crucial to advancing of mathematics, and AI companies are not bothering with it.

Ironic or what. Mr Tao may be remembered as Mathematics' Canute.

Re: A misalignment of AI in mathematics

#564

Post by hollowturtle »

> to the point that they can solve major outstanding problems in many fields of mathematics

I will die on this hill, humans solve math problems not machines, there's no automatic math prover out there. There are humans attempting to solve this problems either by leveraging these tools or not

Re: A misalignment of AI in mathematics

#565

Post by bayindirh »

Ethan_Barry wrote: post #557
bayindirh wrote: post #543

Earlier quoted context omitted.

Didn't some of the recent proofs exploited a couple of blind spots of lean, and they were invalidated? Edit: Yup. A bug report to Lean was disguised as a "Collatz" proof in a humorous way. Links below. - https://x.com/gro_tsen/status/2082483878480977959 - https://infosec.exchange/@0xabad1dea/117002106099986943

There was a hash collision bug in the main Lean kernel that was patched, but AFAIK nothing relied on it. You'd have to know what you were doing to accidentally get there...

The incident in the links I posted exploited several bugs AFAICS, so it's a different story than a single hash collision bug, it seems.

Re: A misalignment of AI in mathematics

#566

Post by scotty79 »

So, if AI solves problems in the open, it's accused of plagiarism and contributing nothing of value. But when it solves the problem behind closed doors it's accused of not contributing enough to the field and even depleting it of fertile problems.

Damned if you do, damned if you don't.

Somehow physicists don't complain.

Re: A misalignment of AI in mathematics

#567

Post by petilon »

RGS1811 wrote: post #484
petilon wrote: post #452

> We are witnessing a general threat to intellectual work, with misalignment between the outcome of the use of AI and its initial purpose. 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…

It's not about job security. It's about the social and intellectual practice of the discipline. The threat to mathematics isn't that suddenly the profitability of their profession (lol) is going to go away, it's that people are thinking of AI as a replacement for the human social and intellectual practices that constitute the discipline.

> The threat to mathematics isn't that suddenly the profitability of their profession (lol) is going to go away, it's that people are thinking of AI as a replacement for the human social and intellectual practices that constitute the discipline.

You could say the same about software development.

Software development is a group effort, so it includes social practices, and certainly includes intellectual practices as well.

For the sake of argument, how is this different from the Luddites? The Luddites feared that machines would displace not only human labor, but also the social knowledge, skilled judgment, and craft traditions embedded in their work.

Re: A misalignment of AI in mathematics

#568

Post by [deleted] »

zahlman wrote: post #517
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…

> Ultimately we think a fatal flaw was found in Mochizuki's proof, so it didn't lead anywhere in particular. But in our hypothetical "AI lean-verified proof of RH" situation, it would presumably generate substantially more of that community activity we saw in the Mochizuki situation. And if it's correct, that community activity would be productive (expository talks, students given problems to flesh out or generalize,…

[deleted]

Re: A misalignment of AI in mathematics

#569

Post by thesmtsolver2 »

vatsachak wrote: post #105
thesmtsolver2 wrote: post #68

Earlier quoted context omitted.

The biggest cope is buying OpenAI's "We can't prove we didn't plagiarize" Apparently, we have AGI that can solve Millennium Prize problems but can't trace simple data flows lol.

How is it plagiarism if no one else had the full proof idea first?

You can steal lemmas, rough proof directions, conceptual ideas etc without stealing the full proof.

Any of that done unattributed is plagiarism.

Either OpenAI is incompetent or evil if they can't publicly prove the allegations wrong. Or even at least state categorically they didn't train on their conversations (even without proof).

Re: A misalignment of AI in mathematics

#570

Post by blharr »

woopsn wrote: post #531

My interpretation is they don't care about scooping mathematicians they were just trying to scoop a competitor. They had a short window in which to complicate Anthropic's priority, when Anthropic announced be able to say "ok nice but we did that too". Upon realizing they'd misunderstood, incredibly they said to this academic (who did not resolve NS) okay well just go ahead and claim the prize, so long as you're not A…

>they weren't trying to scoop a mathematician they were just trying to scoop a competitor

Well. Obviously, yes. But in doing so they still DID scoop out a mathematician in a very unethical way.

In doing so they showed that they basically have a huge gun they can point at X work you care about and develop, and can cut you across the finish line. And take credit for it. Obviously this already _existed_, but is just much more significant because even a rumor can be converted into a complete takeover of a discovery.

> They're not interested, not the kind of entity that can care about theoretical mathematics. These dudes take home 7-8 figure salaries, they solve a Millennium Prize problem then pretty quickly move past it.

I get your point, they don't really care about solving all the maths problems. But they're still going to solve them for clout and profit motives. Up until it stops wow-ing people... at which point they will have likely decimated the frontier of the field.

And this is kind of the root of the entire concern. They will move into the forest and completely steamroll all the problems, then declare victory and move on, leaving only pavement and asphalt behind.

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