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Ten advances in mathematics and theoretical computer science

openai.com

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Re: Ten advances in mathematics and theoretical computer science

#411

Post by hollowcelery »

kcexn wrote: post #308
simianwords wrote: post #162

Earlier quoted context omitted.

> However, I am worried that the language they are using in this blog post is exaggerating for the sake of marketing Your worry.... is because they used the word advanced? For marketing? The word is used very appropriately here. There were PhD's who spent a big part of their career tackling these problems.

I have no idea how many PhD's have spent how much time of their careers tackling these very specific problems, and I doubt you do either. I'm trying to understand if these specific problems were the kinds of problems that would have justified an expert investing weeks or months to solve. Or if they were the kinds of problems that would normally have been given to students to investigate.

They are significant problems which experts have spent months or years studying. I heard a mathematician say that resolving non-sofic groups and Connes's rigidity would be career-defining for a mathematician.

Re: Ten advances in mathematics and theoretical computer science

#412

Post by bryan0 »

I think there's another interesting story here about how this was apparently moderately flagged and triggered the flame-war detector which kept the story off the front page of HN 2 days ago[0]. I think people are having a hard time processing this information rationally(?)

What can we do to make conversations around these incredibly exciting and important topics more constructive? HN is where I expect to read expert comments on these topics, has this style of conversation moved elsewhere?

[0]: https://news.ycombinator.com/item?id=49157930#49132926

Re: Ten advances in mathematics and theoretical computer science

#413

Post by variadix »

kypro wrote: post #371

I want to iterate the most important thing about this is that it's yet more evidence of AI's accelerating competency in solving math and comp sci problems, and suggests we're now getting close to the point where you could throw AI at AI research challenges (which are largely just math and comp sci problems) and potentially find very real algorithm improvements. AI development is likely to be more compute bottlenecked…

I’m starting to think the probability of RSI within 12 months is more like 99%

I’m not sure it will be FOOM, maybe it will require AIs to iterate on hardware to get orders of magnitude more compute/storage/energy which would more likely require months/years, but algorithmic progress would likely saturate quickly. I guess it depends on how much you think further AI progress depends on hardware vs. software.

Re: Ten advances in mathematics and theoretical computer science

#414

Post by scarmig »

8note wrote: post #385
enraged_camel wrote: post #369

Earlier quoted context omitted.

>> The motte is "AI useful". The bailey is "Singularity is nigh". But there are people like Ed Zitron, frequently posted and cited here, who disagree even with the former.

to an extent zitron is saying its not useful, but as a more nuanced opinion, "ai is not cost effective, nor is it improving profits or revenue"

From a random article I grabbed of his (https://www.wheresyoured.at/subprimeai/):

"it isn't clear whether generative AI actually provides much business value at all"

"cannot seem to find a product that people will pay for, in part because the results are so mediocre"

"Last week, we got our first real, definitive glimpse of what’s around that corner that future. And boy, was it underwhelming."

"OpenAI claims that o1 “performs similarly to PhD students on challenging benchmark tasks in physics, chemistry, and biology.” Just not in geography, it seems. Or basic elementary-level English language tests. Or math. Or programming. "

"Worse still, it's kind of hard to explain why anybody should give a shit about o1."

"o1 shows that OpenAI is both desperate and out of ideas."

"the software is not becoming more useful"

Honestly, every other line is quotable in this context.

Re: Ten advances in mathematics and theoretical computer science

#415

Post by Ar-Curunir »

kcexn wrote: post #307
Ar-Curunir wrote: post #177

Earlier quoted context omitted.

The problems from CS (CVP and circuit complexity) are very important problems that have been worked on by top researchers for 30-40 years. Some of these researchers include Turing Award winners. A solution to them would be a best-paper award at many top CS conferences.

I assume you're talking about No. 5, the arithmetic circuit complexity bound? The existence of a lower bound than state-of-the-art is certainly a significant result and worth publishing. But the wording of the result makes it sound like we don't know what the lowest possible complexity bound might be. So, prior to this result did we think there couldn't be a lower possible bound? Or did the arithmetic circuit communi…

Circuit complexity lower bounds (and lower bounds in general) are notoriously difficult to come across.

For example, despite our best efforts, the state of the art lower bounds on time complexity of algorithms for solving 3SAT is O(n). In contrast, our best algorithms for the task run in time roughly O(2^n). That’s an exponential gap. This is despite decades of trying to find lower bounds.

Re: Ten advances in mathematics and theoretical computer science

#416

Post by pavpanchekha »

skybrian wrote: post #405
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…

This will depend on the problem; I expect big algorithmic performance improvements in AI since the algorithms are still new, inefficent, and constantly being improved. But maybe not for sorting, fast fourier transforms, or other well-studied basic algorithms?

A lot of algorithmic improvement in AI is ultimately bottlenecked by compute. It is very easy to come up with ideas that could improve models! But to prove that they do, especially at scale, is expensive and takes a long time.

Re: Ten advances in mathematics and theoretical computer science

#417

Post by treis »

claytongulick wrote: post #410
evenhash wrote: post #406

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.

> People keep saying this. Why? For the same reason that you can't draw a 15 of Diamonds from a regular card deck.

Of course you can. Tape a 7 and 8 of diamonds together and boom 15 of diamonds

Re: Ten advances in mathematics and theoretical computer science

#418

Post by GolfPopper »

Chance-Device wrote: post #404
c7b wrote: post #372

Earlier quoted context omitted.

And what does taking it seriously entail?

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…

[flagged]

Re: Ten advances in mathematics and theoretical computer science

#419

Post by fixedpointsnake »

ck2 wrote: post #358
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.

"AI" has limits in that it cannot invent knowledge, it can only distill and search for patterns in existing knowledge not sure how many will get this reference but "AI" for science and math is like super-shoes for runners at first we are blown away by the impossible improvements including sub-2-hour realworld marathon and every other PR/CR/WR is dialed down but then the improvements slow and reach a stall point becau…

I agree. The most likely scenario is that this is just a "new normal" lift that is percolating through human endeavors and will saturate at some point. For example, the whole cyber-security bruhaha should ultimately resolve into higher standards for code published -- we can now cheaply find and fix a whole slew of minor bugs that weren't worth our time before.

The fact we see a lift is not the same as evidence that the lift is unbounded.

The lift being finite is supported by the fact improvements have come at the edges: improvements from human feedback, improvements in harnesses, improvements on model compatibility with harnesses, improvements in inference efficiency with new architectures, etc. If we were just training better models from scratch that would be one thing, but we are just making better use of a tool we've developed.

Re: Ten advances in mathematics and theoretical computer science

#420

Post by scotty79 »

enraged_camel wrote: post #369
gowld wrote: post #354

Earlier quoted context omitted.

What you are doing is "motte and bailey". The motte is "AI useful". The bailey is "Singularity is nigh".

>> The motte is "AI useful". The bailey is "Singularity is nigh". But there are people like Ed Zitron, frequently posted and cited here, who disagree even with the former.

I think Ed Zitron is mentioned just because his name is Zitron. He just repeats ad nauseam opinions concentrated around one simple, very boring pole on a wild and interesting landscape of emerging reality. Anybody could be doing that. A lot of people do that. Yet no other is named Zitron. And that's why I heard name Ed Zitron hundred times. That's how you become a voice of (a part of) the generation. Just have a memorable name and repeat the same opinion over and over that people can flock around comfortably. Content is irrelevant.

Personally I prefer to follow explorers rather than swamp-sitters.

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