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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

#491

Post by bonoboTP »

bluerooibos wrote: post #476
overgard wrote: post #457

Earlier quoted context omitted.

https://garymarcus.substack.com/p/openais-amazing-but-vastly... https://garymarcus.substack.com/p/two-critical-updates-re-as... As always, PR hype. Goalposts have not moved. Guys, please use critical thinking. The haters don't hate by default, we hate because we're gaslit about this stuff every day and it's annoying. Extraordinary claims require proof, and they're not giving us information that would be essential to…

Gary Marcus has been moving the goalposts since day 1. The guy is a psychologist. Why would anyone care what a psychologist has to say about AI? He's likely made good money from constantly moving the goalposts and being a denier, due to the publicity he gets.

He's simply a good phone number to have for journalists under time pressure who need to add the contrarian voice to their upcoming story. He delivers it reliably, then never reflects on how he was wrong in the past, just blasts forward as if nothing happened and just makes the next bonkers claims to the journalists who are very thankful for the prompt delivery of how AI is a nothingburger, and fake and won't ever do XYZ that it then proceeds to do in N months.

I remember the time when he insisted that diffusion-based image generators trained on Internet scale data will never be able to make an image of a horse riding an astronaut. Today you can generate 4K video of that.

Re: Ten advances in mathematics and theoretical computer science

#492

Post by robotpepi »

WarmWash wrote: post #409
DrBazza wrote: post #96

Replace philosophers for mathematicians and Douglas Adams was spot on again. Whilst current models can't 'intuit' and come up with conjectures, they can certainly disprove some of them very quickly through the kind of grind that humans can't do. I suppose there really are some mathematicians out there today, whose last few years of study, have just been up-ended by this. -- "Yes we are," insisted Majikthise. "We are…

>Whilst current models can't 'intuit That's how they are finding these solutions though, unless we are just going to label intuition as something only humans can do. Like a submarine being unable to swim or whatever that example is.

it could also be that they try every possible approach that has been proposed by humans. it seems that was the case for the non sofic group example. humans are not able to do the same at that scale. it's unfortunate that we don't know what's happening behind the hood with these models, and that's a huge danger also for the rest of us without access to them.

Re: Ten advances in mathematics and theoretical computer science

#493

Post by applicative »

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.

It is a fact of experience, and indeed effectively a theorem, that the better they get at coding and math, the dumber they are. These are the wages of RLVR etc

Re: Ten advances in mathematics and theoretical computer science

#494

Post by s4i »

fooker wrote: post #329
Alifatisk wrote: post #324

Earlier quoted context omitted.

Care to elaborate? Curious about this. Is this because LLMs have been geared towards understanding user user intent behind a prompt rather than following the instructions exactly?

There's a full fledged 'reasoning' step that basically expands your prompt. As long as you are not missing important information, how you word the prompt does not have any effect.

Isn’t that a huge simplification? Of course the way you phrase the prompt can carry semantic meaning, maybe subtly, but still. And sometimes that matters a little and sometimes a lot. I’ve stopped numerous agent sessions over the last few weeks to reword my initial prompt to get the agent off an unintended track.

Re: Ten advances in mathematics and theoretical computer science

#495

Post by ausbah »

dash2 wrote: post #467
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.

If it doesn't help average people, why do millions of them pay for it?

addiction? get lured in with the promises of enhanced productivity and knowledge asking, leave with half your brain rotted and a $200/month subscription

Re: Ten advances in mathematics and theoretical computer science

#496

Post by tuvix »

evenhash wrote: post #408
DrBazza wrote: post #96

Replace philosophers for mathematicians and Douglas Adams was spot on again. Whilst current models can't 'intuit' and come up with conjectures, they can certainly disprove some of them very quickly through the kind of grind that humans can't do. I suppose there really are some mathematicians out there today, whose last few years of study, have just been up-ended by this. -- "Yes we are," insisted Majikthise. "We are…

> 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.

All arguments like this boil down to semantics at a certain point, but yes large language models can “intuit” because they can generalize between examples. The issue then becomes how you pack new examples into context.

Humans can “intuit” based on a much larger, if not unlimited, context. Also I just want to say that human cognition is something so insanely complex and deep that we will not understand it at all in my lifetime. To attribute all, or really any, aspects of human cognition to a machine at this point is silly to me.

Re: Ten advances in mathematics and theoretical computer science

#497

Post by sdenton4 »

WarmWash wrote: post #409
DrBazza wrote: post #96

Replace philosophers for mathematicians and Douglas Adams was spot on again. Whilst current models can't 'intuit' and come up with conjectures, they can certainly disprove some of them very quickly through the kind of grind that humans can't do. I suppose there really are some mathematicians out there today, whose last few years of study, have just been up-ended by this. -- "Yes we are," insisted Majikthise. "We are…

>Whilst current models can't 'intuit That's how they are finding these solutions though, unless we are just going to label intuition as something only humans can do. Like a submarine being unable to swim or whatever that example is.

Some of them...

The two places were seeing lots of movement are:

* Updates to lower/upper bounds. In many cases, these kinds of problems are the deep-math equivalent of calculating more digits of pi. Yes, if you throw time at it you'll break the record, but it may not be terribly worthwhile.

* Finding counter examples which disprove conjectures. This is really useful, and helps offset some positivity bias on the human side, often bringing together known tools from distant silos.

If you read the list of ten results, almost all fall into one of these buckets.

Re: Ten advances in mathematics and theoretical computer science

#498

Post by robotpepi »

QuesnayJr wrote: post #210
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,…

The ones I'm familiar with are big breakthroughs, but they are both counterexamples. Examples have an advantage in that once you have the example in hand and a sketch of the proof (which they have provided), then an expert can probably work out the details themselves. The sofic groups question was the outstanding question about sofic groups. Almost everyone thought that non-sofic groups existed, and there were plausi…

> but proving a group was non-sofic was out of reach

a colleague was telling me that the base idea for proving that something is not sofic already appeared in the literature around 2019 or so (this is the "expanders graphs" that are mentioned in OpenAI s paper. no one had managed to find a concrete example though. this doesn't make the result less impressive in any case.

Re: Ten advances in mathematics and theoretical computer science

#499

Post by fhfncjcc »

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.

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 styles of prose than their equivalent from two years ago. (Models of increased scale are a mixed bag.)

Maybe you’re the one who needs breaking out of your cached beliefs.

Re: Ten advances in mathematics and theoretical computer science

#500

Post by dwaltrip »

overgard wrote: post #457
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.

https://garymarcus.substack.com/p/openais-amazing-but-vastly... https://garymarcus.substack.com/p/two-critical-updates-re-as... As always, PR hype. Goalposts have not moved. Guys, please use critical thinking. The haters don't hate by default, we hate because we're gaslit about this stuff every day and it's annoying. Extraordinary claims require proof, and they're not giving us information that would be essential to…

I use these strange machines all the time. They have gotten notably smarter. That’s my personal experience.

They still do things that I find incredibly annoying and “dumb”. And I still have to clean up messes they make quite often.

But on the whole they are clearly smarter than before. No extraordinary claims needed. I just try to learn how the tool works and how to use it effectively.

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