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Ten advances in mathematics and theoretical computer science

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Re: Ten advances in mathematics and theoretical computer science

#741

Post by gerdesj »

gerdesj wrote: post #723
plaidfuji wrote: post #673

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…

"Any computable problem will eventually fall to computers." By definition. Its those pesky NP jobbies that get in the way.

Just to re-iterate the point:

Whenever the handwaving starts around a discussion relating to a NP hard problem, I find it useful to imagine a Canadian bloke (MHRIP) in a red top, with a ... Scottish accent ... saying:

"Ye cannae break the laws o' physics, Jim". (maffs not fisics, obvs!)

If that is a bit tiresome for the gung-ho AI evangelist, there is also the rather knotty snag that that blasted Austrian geezer Gödel fiddled up: incompleteness.

Its almost as though these bloody clever scientific and that types keep on putting artificial blocks in the way of LLMs laying golden eggs!

I'm quite happy with the "marginal gains" I get with a DGX Spark. It will pay for itself within three months doing stuff on prem and us not sending data to someone else. It will scale.

Re: Ten advances in mathematics and theoretical computer science

#742

Post by nilkn »

rencrisa wrote: post #603
simonw wrote: 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It also links to a paper written by an LLM where the model "reconstructs how the proof came together" based on the unpublished reasoning traces: https://cdn.openai.com/pdf/reasoning-walkthroughs.pdf I wish they'd publish the prompts though!

It seems that a lot of folks misunderstand the guarantees that lean provides. I just want to state that having "lean proofs" that build (checks) does not mean the actual real theorems we care about hold. Ignoring lean kernel bugs, ultimately a human (not an agent) has to verify the lean encoded theorem statements (specs/specifications) that the lean proofs are checked against. For non-trivial theorems such as these,…

This is the Lean proof that a nonsofic group exists (34,440 lines): https://github.com/openai/ten-proofs/blob/main/NonSoficGroup...

This is an extraction from that of the actual theorem statement (39 lines): https://github.com/openai/ten-proofs/blob/94bc0feb6a9ff12c7d...

Re: Ten advances in mathematics and theoretical computer science

#743

Post by tyre »

hnlmorg wrote: post #719
plif wrote: post #697

Earlier quoted context omitted.

Not new about LLMs. Targeted ads / big data is this. Another degree of capability, yes. But we have been trending here for a long time.

It’s unfortunate that you’re being downvoted because this comment is true. And it just goes to show how far we’ve sunk that people have forgotten the problems of ad tech in the age of LLMs.

You’re making a weird number of assumptions about people’s voting and extrapolating to assertions about Society.

Ads are not really the same. They can’t be as tightly targeted to what resonates with someone. Programmatic ads are certainly much better and closer than, say, television advertising, but users can’t _engage_ with them. Like actually chat with them.

That’s where this is headed and people are not ready. I don’t think we could prepare them, anyway.

Re: Ten advances in mathematics and theoretical computer science

#744

Post by tyre »

attila-lendvai wrote: post #732
tyre wrote: post #547

Earlier quoted context omitted.

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…

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.

Re: Ten advances in mathematics and theoretical computer science

#745

Post by [deleted] »

energy123 wrote: post #50
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…

The old way of establishing career credibility is being destroyed, for better or worse. Accomplishments that used to be career-defining are hard to distinguish from AI, and correlate more with access to compute. Think about Bill Gates's math paper he wrote in college. That kind of thing is gone now as a path to credibility. There's still competitions and grades, but the diversity of paths is going away. Maybe new one…

[deleted]

Re: Ten advances in mathematics and theoretical computer science

#746

Post by 0xWTF »

galleywest200 wrote: post #740
kortilla wrote: post #702

Earlier quoted context omitted.

That presupposes that the left in the US wants to do the right thing. Something like government run grocery stores is not clearly correct and there is very little evidence supporting that it will work well yet it is a very popular leftist policy in New York.

City run grocery stores are certainly not evil.

... not overtly, intentionally evil.

FTFY

Re: Ten advances in mathematics and theoretical computer science

#747

Post by nilkn »

roncesvalles wrote: post #681
amazingamazing wrote: post #137

Can’t wait for this stuff to have quality of life increases for the average person. So far all I see is that AI has made owning a computer more expensive, made some jobs redundant, increased spam and distrust with questionable authenticity of content and of course made some Americans very rich.

It has had significant quality of life increases for me. I use LLMs for everything from: - travel and restaurant recommendations. my last few outings have been entirely LLM-advised and they turned out excellent. LLMs seem to have ingested every single Google review, photo, and menu of every business on Earth and can answer very nuanced questions like "is the garlic chicken at garnished with coriander?" - fitness, nut…

I'm just barely old enough to have experienced a couple waves of technology being introduced and creating these sorts of life optimizations. It almost never actually improves quality of life. It just makes life more optimized, and since everyone else is doing the exact same optimization as you, that optimization goes from novel and fun to table stakes to a basic necessity to compete and function in society professionally, at which point it's really nothing but pure efficiency, not genuine improvement in relative happiness.

Re: Ten advances in mathematics and theoretical computer science

#748

Post by tyre »

lettergram wrote: post #552
tyre wrote: post #547

Earlier quoted context omitted.

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…

> My guess is that, in the US, the right will cynically adopt manipulation to great effect and the left will take a moral stand against shady practices and lose elections. I think that statement may itself highlight how prevalent manipulation is. I fully anticipate all groups to continue maximal manipulation they can. One thing with LLMs is that it'll be a far less unified view, so a "divide and conquer" strategy is…

In US politics, the right is far, far better at winning elections than the left. This isn’t about personal preference. It’s objective political science.

Look at the most contentious issues in the US: abortion, climate change, taxing the wealthy, gun control, Affordable Healthcare Act.

The Democratic Party platform is aligned with national polling on every one. Every one of those issues has >60% support with voters and the Republican Party has blocked them all.

They play the game to win. And they do.

Re: Ten advances in mathematics and theoretical computer science

#750

Post by totetsu »

sothatsit wrote: post #534

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…

I think you’re making a category error in your definition of politics here. Certainly technologies can favour winners and losers, but the struggle is an inherently human one.
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