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Ten advances in mathematics and theoretical computer science

openai.com

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Re: Ten advances in mathematics and theoretical computer science

#311

Post by MinimalAction »

dash2 wrote: post #207
piker wrote: post #2

I don’t feel the existential dread of mathematicians is correct. It seems to me in fact these results are bringing math mainstream. I now personally look forward to the interpretations and discussions of the significance of such results by human mathematicians. Now I understand that it’s mostly the super stars benefitting from the increased attention. Folks who are less established don’t share in that glory. But on t…

I find this whole way of looking at things weird. Did maths exist just to entertain and employ mathematicians? Surely maths is, like, useful? Not immediately, not predictably, but in the long run? In which case, whether mathematicians feel bad about it is mostly irrelevant - it's like complaining about the railway because it may put coaching inns out of business.

Absolutely not the same! People need jobs to bring in income. I don't believe those who profit off of this will share it with the world. The power is all concentrated in the few hands that decide whether or not the rest get any semblance of income in the long run. I don't believe UBS until it happens.

Re: Ten advances in mathematics and theoretical computer science

#312

Post by kcexn »

QuesnayJr wrote: post #210
kcexn wrote: post #158

Not being an expert in any of the fields OpenAI has "advanced" I don't want to prematurely downplay the significance of this contribution. However, I am worried that the language they are using in this blog post is exaggerating for the sake of marketing. It is true there hasn't been a reliable computational approach to solving these problems before. But do these proofs contribute new ideas to the mathematical corpus,…

The ones I'm familiar with are big breakthroughs, but they are both counterexamples. Examples have an advantage in that once you have the example in hand and a sketch of the proof (which they have provided), then an expert can probably work out the details themselves. The sofic groups question was the outstanding question about sofic groups. Almost everyone thought that non-sofic groups existed, and there were plausi…

Interesting. Do you have any more specific insights into where you feel AI was a big value-add to these problems? I don't want to be overly dismissive of AI, but I also feel that the AI hype engine frequently positions claims as being 'ground-breaking' when they are really just interesting incremental results.

The general consensus of developers is that AI can only do the work of a strong 'junior'. Yet as soon as we are presented with pure mathematical results, people seem incredibly ready to accept that AI can do more than what a strong student could achieve.

Re: Ten advances in mathematics and theoretical computer science

#314

Post by silver_sun »

xyzsparetimexyz wrote: post #103
melagonster wrote: post #94

Wow, so this is the end of science :(

It's just another tool that can help solve problems. It doesn't know _what_ problems to solve. It turns out that a lot of old problems are now low hanging fruit for these new models. In terms of 'expanding the frontier', we've just discovered dynamite and can now blast our way through mountains. The bottom of the ocean or space are still as hard to reach as ever.

It's not even predictable like dynamite. Sometimes it can blast through a mountain, impressively, the problem is you can't predict which mountain it works on. And other times it can't even make a dent in a molehill, which is perplexing given what it was capable of earlier. Can we even call it dynamite?

Re: Ten advances in mathematics and theoretical computer science

#315

Post by simianwords »

mathisfun123 wrote: post #287
simianwords wrote: post #279

Earlier quoted context omitted.

do you think you are clever for being skeptical about LLMs if OpenAI comes up with a correct proof of Reimann's hypothesis? "but you shouldn't trust OpenAI because something something marketing" i would classify you as a flat-earther if that happens.

> do you think you are clever for being skeptical about LLMs brother like 3 people have pointed out what they're skeptcal of is cost not LLMs - at this point you're willfully misconstruing what people are saying to you just to get a kick out of repeating your same tired strawman.

Brother I already conceded that money is somewhat important but it is missing forest for the trees.

If OpenAI solved Reimanns hypothesis and the first comment is says something about lack of transparency and marketing, i would say it’s ignorant.

Re: Ten advances in mathematics and theoretical computer science

#316

Post by simianwords »

SpicyLemonZest wrote: post #225
simianwords wrote: post #141

Earlier quoted context omitted.

Would this be your reaction if OpenAI also solved millennium problems? The point we are trying to make is that the significance of this news is much larger than the skepticism you are providing.

If OpenAI resolved the Riemann hypothesis by finding a nontrivial zero at 0.50000003 + 3531696584231.17843174i, that would be very cool and probably very impactful. But it might not necessarily demonstrate model capabilities beyond those which have already been demonstrated, especially if the session that found it was one of a thousand launched to explore different areas of the problem space. More generally, do you e…

Ok are you one of those people whose first reaction to such a news is “this is just marketing for OpenAI and we need transparency”? In that case you are just interested in culture wars and not results.

Re: Ten advances in mathematics and theoretical computer science

#317

Post by defrost »

simianwords wrote: post #315
mathisfun123 wrote: post #287

Earlier quoted context omitted.

> do you think you are clever for being skeptical about LLMs brother like 3 people have pointed out what they're skeptcal of is cost not LLMs - at this point you're willfully misconstruing what people are saying to you just to get a kick out of repeating your same tired strawman.

Brother I already conceded that money is somewhat important but it is missing forest for the trees. If OpenAI solved Reimanns hypothesis and the first comment is says something about lack of transparency and marketing, i would say it’s ignorant.

To "solve it" would require either a single counter example disproving the claim, or a proof that the conjecture about the Riemann zeta function is true.

If OpenAI claimed the conjecture to be true but provided no details about the proof then the first comment should absolutely be about lack of transparency.

Re: Ten advances in mathematics and theoretical computer science

#319

Post by qnleigh »

qnleigh wrote: post #299

Can anyone comment on the significance of any of these results for their respective fields? Or what impact they might have? Presumably none are quite at the level of the Jacobian conjecture, but some of the results on group theory and sphere packing sound pretty important at first glance.

Found some discussion here [1] from someone who actually worked on a few of these problems.

[1] https://x.com/henryquantum/status/2083623695436623915?s=20

Re: Ten advances in mathematics and theoretical computer science

#320

Post by simianwords »

defrost wrote: post #317
simianwords wrote: post #315

Earlier quoted context omitted.

Brother I already conceded that money is somewhat important but it is missing forest for the trees. If OpenAI solved Reimanns hypothesis and the first comment is says something about lack of transparency and marketing, i would say it’s ignorant.

To "solve it" would require either a single counter example disproving the claim, or a proof that the conjecture about the Riemann zeta function is true. If OpenAI claimed the conjecture to be true but provided no details about the proof then the first comment should absolutely be about lack of transparency.

> no details about the proof

do you really imagine a scenario where OpenAI would claim to solve it and not give details about the proof? how is this even possible? why would anyone believe them?

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