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Ten advances in mathematics and theoretical computer science

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631–640 of 1000 posts

Re: Ten advances in mathematics and theoretical computer science

#631

Earlier quoted context omitted.

> Whilst current models can't 'intuit' and come up with conjectures People keep saying this. Why? Surely the AI can complete the prompt “Generate new research questions based on these observations”? When I read the reasoning traces of coding models they are constantly asking themselves questions and attempting to answer them.

I like the illustration that the models are working on a convex hull of known information. Filling gaps with linear combinations of known facts and results. They can't exit the hull until the "intuition" starts spawning points outside the convex hull.

Is that actually true though? I think it is an analogy, and as an analogy it seems quite risky because “convex hull” and “linear combination” are technical terms that might give the recipient the impression that it is a technical argument.

Re: Ten advances in mathematics and theoretical computer science

#632

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.

Do any of the big AI companies have a model that are good at tasks that require learning? For example, every day people teach teenagers how to drive and with only dozens of hours of practice, they are on the road.

is this not essentially what ARC-AGI-3 is? i agree that in-context/continual learning is somewhere the models are still mostly weak at

Re: Ten advances in mathematics and theoretical computer science

#634

People argue whether we are at y-5, y, or y+5, meanwhile we seem to be on a y=2^x exponential that keeps delivering more and more impressive results. The most interesting question to me is what will be consumed by the exponential like math seems to be undergoing, and what won’t. Writing has been quite stubborn, but I’ve noticed Fable to be quite a big step up there. How about politics? Will we develop new ways to let…

Sigmoidal, not exponential. It would be insane to assume an exponential curve

Re: Ten advances in mathematics and theoretical computer science

#635

Earlier quoted context omitted.

> The most interesting question to me is what will be consumed by the exponential like math seems to be undergoing, and what won’t. Writing has been quite stubborn, isn't it clearly split between verifiable not verifiable ? what is interesting about that question.

I do not think it is so clear. Programming has verifiable and non-verifiable aspects. Competitive programming, passing tests, and performance can all be verified. But translating English requirements into actual software, software architecture, taste, or UI design cannot. And yet over the last couple years we’ve seen huge lifts in all of these areas, not just the verifiable ones. Verifiable areas I think are clearly…

> we’ve seen huge lifts in all of these areas, not just the verifiable ones.

most gains are still coming from data. isnt that supposed to 'run out' though?

Re: Ten advances in mathematics and theoretical computer science

#636

Looking at this thread, I can see that a lot of technical people have ambivalent to negative feelings towards AI, but with each new generation, I become more and more convinced that they're missing out on something interesting. It is indeed true that all models are, at their core, predictors of what occurs next in a sequence. But I think it's worth exploring the implication of what that means. Because when fed tiny p…

> I can see that a lot of technical people have ambivalent to negative feelings towards AI

My negative feelings towards AI are about energy use and inequalities, that kind of stuff. It undeniably works well, but whether or not it is better for society or the planet is a lot less clear.

Re: Ten advances in mathematics and theoretical computer science

#637

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?

gpt4o & associated parasociality is considered an alignment failure and is actively trained out of the model, so that is a terrible example of regression

Re: Ten advances in mathematics and theoretical computer science

#638
post #578

Earlier quoted context omitted.

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

Between a lean proof, and a peer reviewed paper, the former is a lot less likely to be mistaken...

Nothing is perfect.

Re: Ten advances in mathematics and theoretical computer science

#639
post #573

Earlier quoted context omitted.

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.

Would something like "services deflation" even show up in the numbers? That's what I'd expect to happen first

deflation will just be inflated away, always

Re: Ten advances in mathematics and theoretical computer science

#640

People argue whether we are at y-5, y, or y+5, meanwhile we seem to be on a y=2^x exponential that keeps delivering more and more impressive results. The most interesting question to me is what will be consumed by the exponential like math seems to be undergoing, and what won’t. Writing has been quite stubborn, but I’ve noticed Fable to be quite a big step up there. How about politics? Will we develop new ways to let…

> The most interesting question to me is what will be consumed by the exponential like math seems to be undergoing, and what won’t. Writing has been quite stubborn, isn't it clearly split between verifiable not verifiable ? what is interesting about that question.

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