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An OpenAI model has disproved a central conjecture in discrete geometry

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Re: An OpenAI model has disproved a central conjecture in discrete geometry

#891

Post by RedCinnabar »

libraryofbabel wrote: post #448

This HN thread depressed me. I’m still thinking about why. Look past the press-releasey gushing from OpenAI and there are all sorts of interesting and subtle questions here about the role for LLMs in mathematical research. I urge folks to click through to the accompanying comments from mathematicians published alongside the result. There is a really interesting discussion going on. I particularly recommend Tim Gowers…

What I don’t understand is why people dismiss this kind of progress with false claims. Especially when discussing programming, people start to act irrational using arguments from back in 2022.

I think that you can easily address your concerns about this new technology (since we all are concerned about the future) but at the same time acknowledge how revolutionary it is.

Re: An OpenAI model has disproved a central conjecture in discrete geometry

#892

Post by julianozen »

trostaft wrote: post #232

Speaking as a postdoc in math, I must say that this is rather exciting. This is outside of my field, but the companion remarks document is quite digestible. It appears as though the proof here fairly inspired by results in literature, but the tweaks are non-trivial. Or, at least to me, they appear to be substantial to where I would consider the entire publication novel and exciting. Many of my colleagues and I have b…

Nice response to read

Re: An OpenAI model has disproved a central conjecture in discrete geometry

#893

Post by golol »

yreg wrote: post #769
golol wrote: post #696

Earlier quoted context omitted.

No it is not Leibniz/Euler/Galois. More like writing good papers that contribute to the broader understanding of a theory. I think if one evaluated a mathematicians research output and it consisted of mostly the kinds of problems AI has solved so far, it would give the impression that this person is somehow very good at picking accessible problems to target, but has not made a larger impact on the field.

The goalposts are Euler level not the current model capabilities.

Yes what I was saying is what I believe about the goalposts.

Re: An OpenAI model has disproved a central conjecture in discrete geometry

#894

Post by noobermin »

devttyeu wrote: post #228
zozbot234 wrote: post #38

The summarized chain of thought for this task (linked in the blogpost) is 125 pages. That's an insane scale of reasoning, quite akin to what Anthropic has been teasing with Mythos.

That's here for anyone wondering - https://cdn.openai.com/pdf/1625eff6-5ac1-40d8-b1db-5d5cf925d...

So, I'm not really a mathematician, but the first 3-8 pages reads like nonsense and a bunch of unrelated facts. A bit surreal may be, but if this the norm for this kind of thing, I'm amazed it arrives at any useful result at all.

Re: An OpenAI model has disproved a central conjecture in discrete geometry

#895

Post by InsideOutSanta »

raincole wrote: post #280

I like how everyone laughed when OpenAI said their models will have "PhD-Level Intelligence" and now the goalpost has been moved to if AI can create new math (i.e., not PhD-Level, but Leibniz/Euler/Galois level.)

What were you imagining when OpenAI said that their models would have "PhD-Level Intelligence"? Were you imagining that there were specific tasks they could do that were on par with what a human with a PhD could do? Because by that definition, many computer tools have "PhD-Level Intelligence". By that definition, Wolfram Alpha has "PhD-Level Intelligence".

What I assumed they were saying is that their LLMs would be as intelligent as a human with a PhD across all, or at least most, knowledge tasks, and they clearly are not.

Re: An OpenAI model has disproved a central conjecture in discrete geometry

#896

Post by gpderetta »

noslenwerdna wrote: post #543
precision1k wrote: post #541

I see mixed emotions here. I understand both. On one hand it's exciting and fascinating. On the other it's concerning. One concern I haven't seen mentioned is the possibility that, as these models become larger and more powerful, their capability to solve frontier math problems will also grow. Does there become a point where humans are no longer the driver of innovation and research in this world, and instead are rel…

For those of us who care about the answers to these questions, rather than who gets credit for doing it, we will welcome any faster means of solving these problems.

what if at some point we will no longer be able to understand the answers?

Re: An OpenAI model has disproved a central conjecture in discrete geometry

#897

Post by turzmo »

cma wrote: post #833
turzmo wrote: post #785

Earlier quoted context omitted.

Not denying that these advances are impressive, but it is important to consider that this is a cherry-picked result. This doesn’t mean that AI can now be expected to do problems of similar or lower difficulty, but that it happened to work well on one problem. What you won’t see is how many others they had to try to get this result.

Earlier of their systems have solve other Erdos problems that people had worked on, this one was more monumental and had had a lot more prior effort that didn't solve, but this isn't a one-off.

This is true, but I still think the relevant question is, how many did they try before they found one that yielded to LLMs? The conclusion is very different if they tried 100 open problems and succeeded at one.

Re: An OpenAI model has disproved a central conjecture in discrete geometry

#898

Post by CosmicHazard »

teiferer wrote: post #727
trostaft wrote: post #232

Speaking as a postdoc in math, I must say that this is rather exciting. This is outside of my field, but the companion remarks document is quite digestible. It appears as though the proof here fairly inspired by results in literature, but the tweaks are non-trivial. Or, at least to me, they appear to be substantial to where I would consider the entire publication novel and exciting. Many of my colleagues and I have b…

> Every day, it grows harder and harder to contain a mental map of recent relevant progress by simple virtue of the amount being produced. And by opening the door to LLM-generated results, you'll see greater and greater amounts without any hope of ever navigating this field again without machine help. It's a little like a software project which more and more gets extended by a AI agents with less and less review by h…

and the longer that this goes on, then the decision making and critical thinking will be offloaded to the LLM's as well.

Re: An OpenAI model has disproved a central conjecture in discrete geometry

#899

Post by Schlagbohrer »

sigmoid10 wrote: post #846
RealityVoid wrote: post #805

Earlier quoted context omitted.

I find AI a great scaffolding for improving understanding and mental models. BUT! It's all in how you use it.

The real question is: Do you need to understand it fully for it to improve your life? For example, if you're in fundamental science (or generally a fan of reductionism), it for sure would be nice to understand the universe instead of just having access to an AI that can comprehend it. But to the majority of the population it only matters that someone (or something) understands it enough to make it useful to others.

Reminds me of a Carl Sagan quote, that our society is built on science and technology yet few understand it.

Re: An OpenAI model has disproved a central conjecture in discrete geometry

#900

Post by justanotherjoe »

recitedropper wrote: post #881
fergie wrote: post #746

Earlier quoted context omitted.

> The entire AI industry has been (not so secretly) paying a lot of experts in many fields to generate large amounts of novel training data. Novel training data that isn't found anywhere else--they hoard it--and which could actually contain original ideas. Really? Any references to read more?

- https://www.theverge.com/cs/features/831818/ai-mercor-handshake-scale-surge-staffing-companies - https://outlier.ai/math/en-us - https://www.opentrain.ai/ - https://www.pin.com/blog/ai-labs-hiring-train-models/ Much of this is data annotation, reasoning trace evaluation, and problem set curation. But there is no way they haven't atleast paid some mathematicians to work on research grade problems in tandem with thei…

At one point you just have to look at a mirror and ask, what would impress you.

Also why pay anyone, when they can keep up with all the papers that not one man can read them all? That seems to me like wasted money.

Another point is that that's not how AI training works anyway. It's much easier to put it in context rather than re-train them with every bit of random maths you find out. Things at the tail-end of the power law doesn't stick. At least, last I checked...

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