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

Re: Ten advances in mathematics and theoretical computer science

#871

Post by verisimi » Tue, Aug 04, 2026, 9:01 AM UTC

tyre wrote: post #548

sothatsit wrote: post #535

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…

We will get much better at manipulation and better at people “writing” things to justify their own feelings. What’s new about LLMs is that you can scalably manipulate people individually. It used to be that you could either have scale (speeches, tweets, interviews, website, etc.) or individual engagement (replying to mail/tweets/town hall questions.) Now you can pull the history and preferences of an individual, then…

> We will get much better at manipulation and better at people “writing” things to justify their own feelings.

Yes, ai has strong narcissistic traits. And so do the people that own them. And pay for them.

In response, people in general will become fat more capable of recognising the manipulation. And will become more paranoid.

Re: Ten advances in mathematics and theoretical computer science

#872

Post by miguelnegrao » Tue, Aug 04, 2026, 9:02 AM UTC

plaidfuji wrote: post #674

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…

If by solution you mean a proof and by testing you mean encoding it in lean and compiling it, the space of possible syntactically correct proofs which you can encode probably explodes in a way that is well beyond what any computer could try to brute-force. LLMs don't brute-force proofs, i believe their approach is quite similar to humans. I believe the same is essentially true for counter-examples of the type that have been found latelly, they are not found by search, but by using theory.

On the other hand even if the compute allocated by openai is esquivalent to day 10 human mathematicians, the machines can work 24h per day, that is already a lot more productive.

Re: Ten advances in mathematics and theoretical computer science

#873

Post by frabcus » Tue, Aug 04, 2026, 9:05 AM UTC

sodapopcan wrote: post #666

azinman2 wrote: post #479

Earlier quoted context omitted.

I also don’t understand why UBI is desirable. Putting everyone on welfare means everyone is poor. This won’t end well, and it’s certainly not the case that 99% of the population will let a tiny number of people remove their income in favor of pennies for all. Political violence will come first, easily.

No idea why anyone would downvote this, it's true. As someone else pointed out "b = basic." And does anyone think it will adjust with inflation?

Because the implied alternative of the comment is that people will carry on having jobs, which breaks the entire premise that there is AI that replaces all human labour. The comment is missing the point - UBI is the only suggestion anyone has so far that meets this fundamental question about the technology. We will be less poor than without UBI, unless we come up with a better plan.

Re: Ten advances in mathematics and theoretical computer science

#874

Post by oblio » Tue, Aug 04, 2026, 9:05 AM UTC

chrisjj wrote: post #863

oblio wrote: post #710

Earlier quoted context omitted.

1. Do frontier lab LLMs make your rent cheaper? Groceries? Healthcare? 2. Do LLMs reduce the loneliness epidemic? 3. Do they reduce population aging in almost all counties around the world? 4. Do they reduce political polarization? 5. Do they bolster democracies? 6. Do they decelerate climate change and general environmental destruction? 7. Do they accelerate sustainability and the circular economy (not circular fina…

> 8. Do they reduce the workweek Sure. Often to zero.

I'm talking statistically, not what happens for a lucky few.

Keynes was hoping that our workweek would be 20h/week by now, through technological advancement. Instead places like the US are thinking about adopting 9/9/6 and some US states are legalizing child labor again.

Re: Ten advances in mathematics and theoretical computer science

#875

Post by frabcus » Tue, Aug 04, 2026, 9:08 AM UTC

cautiouscat wrote: post #569

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…

I’ll be the first to call myself cynical. > 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 takin…

I guess we'll have to fall back on the plan of hoping one of the 7 Anthropic co-founders has secure power in this world, and decides to use EA principles to give us all a bit of their share of the future light cone ;) (The wink because I'm kinda not really joking that this seems the best plan, if we actually get superintelligence from a US AI company)

Re: Ten advances in mathematics and theoretical computer science

#876

Post by ed_elliott_asc » Tue, Aug 04, 2026, 9:08 AM UTC

thisisnotauser wrote: post #722

sothatsit wrote: post #535

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…

My wife is working on her PhD in microbiology now, using OpenAI to implement her research ideas. Genetics is just too much data, and she eats through tokens like nobody's business. I thought I was careless with them, but she barely lasts a full day before exhausting her quota. There's definitely a lot of value there, but dealing with the data problem is a big obstacle in biology. I can only imagine what she could get…

This absolutely terrifies me, surely one misread piece of data or a hallucination here or there and a little “oh sorry about that, I guessed at this portion of the data to save time” and the data used is useless?

Re: Ten advances in mathematics and theoretical computer science

#877

Post by MichaelMoser123 » Tue, Aug 04, 2026, 9:21 AM UTC

Valakas_ wrote: post #831

5555watch wrote: post #501

Earlier quoted context omitted.

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.

I have news for you. All humans do is also filling gaps with combinations of known facts and results - in new ways. "Everything is a Remix" is a good watch on youtube that explains this. Picasso might look like he has an invented personal style, but his style is a combination of different little details he took from others and mixed in a new way. Mozart the same. No music artist could ever create music in a vacuum. E…

> "Everything is a Remix" is a good watch on youtube that explains this

Not completely. Novelty used to be a major thing, when Humans did it. Another important criteria used to be if that new thing makes sense at all. Here the language model has a problem, as it doesn't have the means to evaluate this criteria.

Re: Ten advances in mathematics and theoretical computer science

#878

Post by cultofmetatron » Tue, Aug 04, 2026, 9:31 AM UTC

tyre wrote: post #745

attila-lendvai wrote: post #733

Earlier quoted context omitted.

the fact that the useless left/right divide is still so widely used shows that manipulation is working well even pre LLMs... when it comes to the important question, then both "sides" are the same team. or if you want it with a pinch of humor: when a boot is on your face, it makes precious little difference whether it's the left or the right boot. (i lived the first 10 years of my life in communism)

If you think that the American Left is anything like communism, I’m sorry, but, respectfully, I can’t take your comments seriously. The left in the US would be center-right in Europe, who are certainly not communist (they have separate parties that are communists!) Even the socialist strain of the US has nothing to do with socialism scaremongering about Venezuela, etc.

both democrats and republicans take their money from the same donors. its all a show.

Re: Ten advances in mathematics and theoretical computer science

#879

Post by ur-whale » Tue, Aug 04, 2026, 9:41 AM UTC

andai wrote: post #807

MostlyStable wrote: post #644

Earlier quoted context omitted.

From a mathematician who was intimately familiar with some of these problems [0] >I don’t understand it yet. Maybe it’ll take me an afternoon to check all the calculations, but what would still be missing is why this was an approach that would’ve made sense in the first place. Is there some broader context or theory within which this would’ve been the obvious thing to do? What other results can be proven using these…

I think it might be like waveform collapse, but very high dimensional.

> I think it might be like waveform collapse, but very high dimensional.

The waveform collapse is natively "very high dimensional", not sure why the "but" part of the sentence belongs here.

Re: Ten advances in mathematics and theoretical computer science

#880

Post by synarchefriend » Tue, Aug 04, 2026, 9:42 AM UTC

annzabelle wrote: post #782

mitthrowaway2 wrote: post #757

Earlier quoted context omitted.

So are they right or wrong about the sigmoids?

I dunno. They've been saying this for decades, including in a very well read Harry Potter fanfic, and I'd always dismissed them as kooks, but maybe they're right in the end.

You are confusing Scott Alexander with Eliezer Yudkowsky.