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Ten advances in mathematics and theoretical computer science

openai.com

571–580 of 1001 posts

Re: Ten advances in mathematics and theoretical computer science

#571

Earlier quoted context omitted.

I understand your sentiment, but I think this really is something different. This isn’t a craft going away, or even an industry being replaced, it’s potentially everything we do. It’s the ground being pulled away beneath people’s feet, everyone, everywhere all at once. I think the vacuum it leaves in people’s lives needs to be filled with something, and I haven’t heard any good ideas about this or how the transition…

There is a glaring fallacy in your “AI will change everything as it is super intelligent” hypothesis. If it is so great thinker which can do everything why not just solve this social impact thingie? Or maybe it is not so capable?

I don’t think it’s magic. Things need to actually be made to happen regardless of intelligence, and that’s a social issue. Also if AI were powerful enough to fix everything by itself effortlessly it would already be far too powerful for us to control, and we probably shouldn’t allow that to happen on general principle.

Re: Ten advances in mathematics and theoretical computer science

#572

Earlier quoted context omitted.

I’m personally hoping for the next big AI gangbanger to be theoretical physics. Boy does that field need a good reshuffle. I think when any novel mathematical theory can be done by AI you’ll see simultaneously theoretical physics getting wrecked as hard as pure math is. At that point we might see new physics or paradigm shifting technology emerging.

What? No. Frontier physics is experiment driven.

There have been times it was theory driven.

Re: Ten advances in mathematics and theoretical computer science

#573

Pretty cool. The impact of AI is getting undeniable, there aren’t many positions left to move the goalposts to at this stage, next they’ll have to be outside the stadium entirely. The sooner people can be broken out of their denial about all this the better, and we can start actually taking it seriously.

People will be broken out of their denial by actual economic growth. That's what this is all meant to be for... I think we might start seeing some surprising numbers.

Re: Ten advances in mathematics and theoretical computer science

#574

In a way the most remarkable thing about this is that it isn't even at the top of the HN homepage. Even if this is a step up from what we've seen before, we're no longer astonished by the idea that AI can make significant advances in mathematics and computer science.

This is not at the top as it is actively flagged by people that can't psychologically cope with the advances of AI. Hacker News is no longer a web site of an elite.

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Re: Ten advances in mathematics and theoretical computer science

#575

I am duly impressed by the powerl of the nameless internal AI, but not a single human contributor's name listed anywhere? Did someone at least make this model a coffee?

surely some human regularly typed "think deeper, make no mistakes".

My grandmother is very sick and the doctors need this proof to help her.

Re: Ten advances in mathematics and theoretical computer science

#576
post #274

The GitHub repo with the Lean formalizations just came out a couple of hours ago: https://github.com/openai/ten-proofs It also links to a paper written by an LLM where the model "reconstructs how the proof came together" based on the unpublished reasoning traces: https://cdn.openai.com/pdf/reasoning-walkthroughs.pdf I wish they'd publish the prompts though!

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Re: Ten advances in mathematics and theoretical computer science

#577

Pretty cool. The impact of AI is getting undeniable, there aren’t many positions left to move the goalposts to at this stage, next they’ll have to be outside the stadium entirely. The sooner people can be broken out of their denial about all this the better, and we can start actually taking it seriously.

The models are frequently getting worse at items that they aren’t being benchmarked for — and that’s happening more and more over time! Other people in other fields aren’t idiots, they are accurately perceiving the fact that these models are being hyper optimized for our industry, and are becoming less capable in other domains over time. Models of the same scale are massively worse at writing a broad variety of style…

So your answer is: ignore the progress, it’s not really happening, actually it’s getting worse.

That’s not a credible position, but there isn’t anything that I or anyone else can say to someone who simply doesn’t want to believe something.

Re: Ten advances in mathematics and theoretical computer science

#578

Earlier quoted context omitted.

It sounds like he hasn't verified the results of a problem that he has personally worked on, so how many of these problems have actually been verified?

From what I understand all of them have Lean proofs/certificates thus are basically 100% proven without a doubt.

We recently saw that lean itself isnt proven correct. Its not likely but i wouldnt call it verified if its only verified in lean

https://x.com/gro_tsen/status/2082483878480977959

Re: Ten advances in mathematics and theoretical computer science

#579

Earlier quoted context omitted.

Proof? In my experience modern models are better at all tasks than models from two years ago, especially complex multi-step tasks.

you are working on coding. they are working on things like "creative writing" remember that gpt 4o was popular among those who had ai as a romantic partnet?

> remember that gpt 4o was popular among those who had ai as a romantic partner

I suspect GPT 5.6 would be even better at it, if given the same sycophantic system prompt and lack of guardrails.

Re: Ten advances in mathematics and theoretical computer science

#580
post #327

Henry Yuen's (whose work problem 6 builds on) comments on this are worth reading IMO: https://bsky.app/profile/henryyuen.bsky.social/post/3ms2jpch...

This starts to feel like chess engines. It’s obvious their play is superior but it’s impossible for humans to understand the moves.
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