Ten advances in mathematics and theoretical computer science • Hacker News Board

Re: Ten advances in mathematics and theoretical computer science

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Post by fckgw » Mon, Aug 03, 2026, 9:53 PM UTC

gste wrote: post #573

Chance-Device wrote: post #105

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.

How do I directly benefit from this supposed "growth"? Seems like its just making things worse for most people.

Re: Ten advances in mathematics and theoretical computer science

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Post by qbit42 » Mon, Aug 03, 2026, 9:54 PM UTC

bamboozled wrote: post #619

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,…

It’s a marketing. They are a sham company. If this article was by Scientific American or something it would be worth a lot more. They are literally trying to keep the hype train on track. Also on HN front page today: AI's debt binge can't last, hidden borrowing reaches $1.65T (fortune.com) https://news.ycombinator.com/item?id=49160699

It is marketing, they are a shady company, and yet, if someone had access to these results before today's modern AI tools, they could get tenure at any university in the world.

Re: Ten advances in mathematics and theoretical computer science

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Post by samatman » Mon, Aug 03, 2026, 9:56 PM UTC

cure_42 wrote: post #25

NitpickLawyer wrote: post #15

Earlier quoted context omitted.

A better analogy would be a manufactured object, say 3d printed for simplicity. The 3d printer is given an input, and an object manifests itself after some time. We say that the creator of the object is the person turning on the machine, sending the data, and collecting the object. Not the machine itself.

I'd say the creator is the one who created the 3d model, not the one who pushed the print button.

True story: I have a moisture issue in my furnace, such that it needs vacuuming out. This involved detaching a length of tubing, but that puts stress on said tubing, sometimes knocks other things out of alignment, and involves completing the seal between the wetvac and the tubing with my hand.

I also have a 3D printer. I also have a ChatGPT subscription, and some OpenSCAD chops. I came up with a part which would go into the top of the down tube to the drainage pump, and mostly-seal the down tube itself, with an opening on the side to vacuum out the moisture. This was purely prooompted, I took some measurements, printed bits of the part, refined the shape, and you know what?

It works! I can stick it down there, turn on the (very loud) wet vac, and go upstairs. On a 1.5Ah battery it sucks for a bit less than ten minutes, which turns out to be plenty of time.

So: who made that?

Don't care. I'm waking up warm at night.

Also: me, obviously. ChatGPT doesn't have a fucking furnace.

Re: Ten advances in mathematics and theoretical computer science

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Post by plaidfuji » Mon, Aug 03, 2026, 9:56 PM UTC

Any computable problem will eventually fall to computers.

LLMs have made math proofs more computable, in the sense that a computer can both generate potential solutions and check the validity of its solutions on its own, with a reasonable chance of converging on something correct. I assume this was already doable to some extent, but it seems like it’s now exponentially easier. That still doesn’t mean that all math is automatically solved.

This is somewhat similar to things like molecular dynamics or protein folding or finite element simulations, etc. Some problems that were previously intractable via computation became tractable. Others - the vast majority of other problems - remain unsolvable by these computational techniques, because the scale of compute required is beyond imagination. These are simple things like simulating the dynamics of a cubic millimeter of water molecules for 1 second. Unfathomably beyond current capabilities (and LLMs aren’t going to change that).

I think LLMs are great, I use them every day and I think they have a ton of value. But if these things were as revolutionary as people promote/fear them to be, you should immediately point them at the highest value math problems and see progress. Like the Millenium Prize problems. Haven’t seen a solution to those.

So there are limits - but we’re about to learn a lot about the new normal of what constitutes a layup math proof vs the truly difficult.

Re: Ten advances in mathematics and theoretical computer science

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Post by throwaway27448 » Mon, Aug 03, 2026, 9:56 PM UTC

bryan0 wrote: post #662

throwaway27448 wrote: post #634

Earlier quoted context omitted.

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

this gets more nuanced because "the sigmoids won't save you": https://www.astralcodexten.com/p/the-sigmoids-wont-save-you

If the sigmoid is incorrect it's certainly more correct than the exponential.

> https://www.astralcodexten.com/p/the-sigmoids-wont-save-you

The conclusion of this article seems to be "you should give ai the benefit of the doubt against all reason". Barf

Re: Ten advances in mathematics and theoretical computer science

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Post by cmdli » Mon, Aug 03, 2026, 9:58 PM UTC

Chance-Device wrote: post #577

fhfncjcc wrote: post #499

Earlier quoted context omitted.

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.

It sounds like they are making a clear argument: models are getting worse for certain domains even while they are getting better at others.

I don't know if I agree with that but it doesn't seem like an irrational claim and does seem credible to me.

Re: Ten advances in mathematics and theoretical computer science

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Post by infinitezest » Mon, Aug 03, 2026, 9:58 PM UTC

sodapopcan wrote: post #664

Chance-Device wrote: post #406

Earlier quoted context omitted.

In the near term handling the transition. Jobs will be lost, careers ended, people won’t be able to reskill quickly enough. At the same time AI is an enormous opportunity to uplift living standards, but nobody has the logistics of this figured out. We need to figure out how to restructure the global economy. How does UBI work internationally, if the AI companies are taking revenue in the US? What’s the tax base for i…

Everything you're saying is oddly simultaneously specific and hand-wavy at the same time. I say this because I'm not sure a lot of these things are solvable or, if they are, it's going to take lifetimes. For example: > How do we replace the work ethic that tells us we are our jobs and idleness is immoral? For many people it has nothing to do with morality, it's hardwired into their instincts. They want to work, and t…

Beautifully put. This exactly summarizes my feelings about this particular tech. I actually find it hugely useful. But I fear we lack the wisdom to use this in a way that won't destroy us.

Re: Ten advances in mathematics and theoretical computer science

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Post by cmdli » Mon, Aug 03, 2026, 10:01 PM UTC

GPerson wrote: post #442

ultimatefan1 wrote: post #118

one of the early premises of how ai takeoff would go was that a system that could solve open problems in advanced mathematics would also discover novel advances in math and computer science that directly unlock drastically better software performance. we are seeing frontier level math breakthroughs (ie performance that would put it in the top 100 or 1000 mathematicians in the world if it were a human, meaning top .00…

I don’t really like AI but let’s stop kidding ourselves, no human mathematician could make progress on a dozen major open problems in a week or two. If you’re measuring it against humans then it is by far the best mathematician to ever live.

I guess it depends on how to measure a single "person"? If you spun up 2000 copies of Terrance Tao, I wouldn't be surprised if you found a few new discoveries at the end of it.

Re: Ten advances in mathematics and theoretical computer science

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Post by kypro » Mon, Aug 03, 2026, 10:02 PM UTC

bigyabai wrote: post #397

kypro wrote: post #381

Earlier quoted context omitted.

[flagged]

> We are now at the point where RSI is feasible What can be asserted without evidence can also be dismissed without evidence. - Hitchen's Razor

Did you read the article?

AI is a math & computer science problem. If AI can do advanced maths and computer science research, then it can begin to suggest useful algorithmic optimisations.

Right now I'm sure the vast majority of these will be junk, but occasionally, even with current limitations, they might occasionally stumble on something.

It's not really whether RSI is or isn't possible, it's really just whether it's the most efficient way for labs to improve their models today given they have limited compute to run AI-generated experiments and access to very intelligent humans who might have a better hit/miss ratio.

Do you disagree with anything I'm saying here? Do you not think current AIs can suggest algorithmic improvements or something?

Re: Ten advances in mathematics and theoretical computer science

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Post by jgord » Mon, Aug 03, 2026, 10:02 PM UTC

titanix88 wrote: post #509

How do we know that these solutions don't exist in the training data? It is open secret that they have used pirated materials for training. Perhaps it plagiarized solutions from works of some obscure Belgian mathematician from the sixties, who did not get mainstream acceptance. I wouldn't be surprised if they also got access to mathematics done in the "defense contractor" setting from various three letter agencies. W…

upvoted for fair point .. its possible an LLM AI could be put to work to search widely for attribution / similar results.

eg. "we spent another 2k on searching for pre-existing proof but found only the weaker result xyz by abc in 1972" would be in the spirit of academics quoting prior work.