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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

#281

Earlier quoted context omitted.

They are political problems, a computer could never solve them.

A computer could solve them by creating the right technological ,social, rhetorical and economical solutions but that would lots of money anyway

We already know the solutions

Re: Ten advances in mathematics and theoretical computer science

#282

Earlier quoted context omitted.

Dunno about the parent commenter, but I personally interpret the concept as having a hidden representation of self that is continually tended to, and influences future choices. This implies statefulness, which models are intentionally not at inference time (*). (*) Even if we hack around this and just do the usual trick of simply laundering statefulness to a higher level, in this case the context window being fed in,…

> Dunno about the parent commenter, but I personally interpret the concept as having a hidden representation of self that is continually tended to I don't see why an LLM could not have a sense of identity or personality while it's evaluating a specific prompt, or even change self awareness while evaluating a prompt since many outputs model a back and forth conversation. My point is that without a mechanistic model of…

Sure, but then such a model is not going to make itself. People pitting their vague intuitions is how such models eventually form. I'd also push back regarding that my comment would have been handwavey or without mechanistic elements, even if it was on the whole informal.

This is kind of also the reason e.g. the HN site guidelines are worded the way they are. Regrettably, forums naturally yield themselves to tit for tat type exchanges, but there's really no reason one could not bounce such vague intuitions off of another. I do not have to be right or wrong, and you don't either. Admittedly difficult when its some intensely contentious topic.

If a mechanistic model existed, there would also be no reason to talk about this in the first place. There'd be nothing to discuss, you'd be simply told how a given model characterizes from this perspective on the model cards.

Re: Ten advances in mathematics and theoretical computer science

#283

Earlier quoted context omitted.

Never understood all this talk about moving goalposts - you understand that's how science works, right? We improve, we learn, we recalibrate our expectations based on what we've learned. If we never "moved the goalposts", we'd be stuck scoring the same goals over and over.

> We improve, we learn, we recalibrate our expectations based on what we've learned. That's not what people mean when they say "moving the goalposts". It means that people are adamant that something wasn't important/hard/impressive once the "AI" solves it. And then they come up with another thing that needs to be solved in order to prove it is important/hard/impressive. And once that happens, they do it again. And ag…

If it seems like I don't understand the meaning of that very well-known phrase, then clearly I have failed to make my point. I'll try again. And please note that I will use some generalizations to make my point more clearly, rather than because I don't understand nuance; kindly grant me a charitable reading.

In recent years, I have commonly seen the phrase "you're moving the goalposts" deployed by the "it might be sentient" crowd to shoot down the "it's a stochastic parrot" crowd when the latter respond to a new development with "OK but...". In a well-understood field of inquiry, that would be a clear case of goalpost-moving, in the commonly-understood meaning of the phrase where requirements are retroactively changed in response to them having been met. Thank you OP. 'Artificial Intelligence', and indeed intelligence in general, is very much not a well-understood field of inquiry - in fact we don't even have a common agreement about what 'intelligence' is. We are therefore learning as we go (even after all this time!) but making rapid progress in recent years. When rapid progress is made in a poorly-understood field, then how can our definitions and requirements for success not change? This is arguably one of the most pathological development projects ever - what are the requirements? 'It thinks like a human'? What does that mean? And the answer is we don't know what that means, and we're working it out as we go - moving the goalposts. If we didn't move the goalposts, then by definition we already knew exactly where we were headed at the beginning, and we very clearly did not.

Side note that, in case it's not obvious, none of this detracts from how impressive LLMs are. They're a marvel of the modern age, all the problems notwithstanding. However I reserve the right to stay sceptical about their capabilities.

Re: Ten advances in mathematics and theoretical computer science

#284

Earlier quoted context omitted.

> We improve, we learn, we recalibrate our expectations based on what we've learned. That's not what people mean when they say "moving the goalposts". It means that people are adamant that something wasn't important/hard/impressive once the "AI" solves it. And then they come up with another thing that needs to be solved in order to prove it is important/hard/impressive. And once that happens, they do it again. And ag…

Yes, this is exactly what is meant by “moving the goalposts”. And it’s a fairly well known expression applying wherever people retroactively change their requirements in reaction to those requirements having been met.

It's almost like I disagree with your use of the phrase in this context, rather than that I don't know the meaning of it.

Re: Ten advances in mathematics and theoretical computer science

#285
post #45

Earlier quoted context omitted.

[flagged]

It's a very important clarification if it took $2000/problem on 20 problem attempts or on 1,000 problem attempts for each successful one. That may be the deciding factor on whether or not it's economically viable to replace a mathematician with a ChatGPT subscription.

There is no universe where it is economically visble to replace a mathematician with a ChatGPT subscription, because no one else understands math. It makes no sense. The data are still interesting, but not for that capability.

Re: Ten advances in mathematics and theoretical computer science

#286
post #211

Earlier quoted context omitted.

I believe we're seeing a new kind of mathematics that will require completely new formats for publication, a bit similar to those used in experimental sciences. AI-powered mathematics should be fully reproducible, so it's the authors' responsibility to disclose the exact model type, inference settings/seeds and the full prompt history leading to the result. Of course that would ideally require open weights models. It…

If the proofs are formally verified by a proof assistant (Agda, Roq, Lean, ⋯), I see no reason we would need to know how these came about. All the information needed is in the proof.

Unfortunately, we seem to already have an example of an LLM producing a proof in a week known open problem (the Collatz conjecture) in which it looks like it was sneaking a flawed proof through bugs in the proof checker. https://infosec.exchange/@0xabad1dea/117002106099986943

Re: Ten advances in mathematics and theoretical computer science

#287

Earlier quoted context omitted.

> If OpenAI solves the millenial problems, my skepticism will only be restricted to the correctness of proof. Not that it was "marketing" haha Company X does not make money from proving theorems but does make money from selling you a service which supposedly proves theorems. Company X then proves some theorems and explicitly calls out they were very cheap to prove using its service. And you think you're actually clev…

do you think you are clever for being skeptical about LLMs if OpenAI comes up with a correct proof of Reimann's hypothesis? "but you shouldn't trust OpenAI because something something marketing" i would classify you as a flat-earther if that happens.

> do you think you are clever for being skeptical about LLMs

brother like 3 people have pointed out what they're skeptcal of is cost not LLMs - at this point you're willfully misconstruing what people are saying to you just to get a kick out of repeating your same tired strawman.

Re: Ten advances in mathematics and theoretical computer science

#288

I am duly impressed by the powerl of the nameless internal AI, but not a single human contributor's name listed anywhere? Did someone at least make this model a coffee?

surely some human regularly typed "think deeper, make no mistakes".

Re: Ten advances in mathematics and theoretical computer science

#289

Earlier quoted context omitted.

They very often have been in the past. Why do you think this time is different?

“Often” is load bearing. I don’t think markets are more likely than not to be musical chair shaped. To make this conversation more concrete, give me a falsifiable prediction on there existing a bubble. And then I’ll tell you if I believe in it or not.

The price of inference is going to go so low that OpenAI and Anthropic will not be able to turn a profit, thus cannot afford the investment into more data centers, thus crash due to investment in the space having been overdone

Re: Ten advances in mathematics and theoretical computer science

#290

In a way the most remarkable thing about this is that it isn't even at the top of the HN homepage. Even if this is a step up from what we've seen before, we're no longer astonished by the idea that AI can make significant advances in mathematics and computer science.

This is not at the top as it is actively flagged by people that can't psychologically cope with the advances of AI. Hacker News is no longer a web site of an elite.

So condescending. “Can’t psychologically cope”? Can you hear yourself? There’s some advances, but we’re losing a lot too. Don’t get dazzled by the hype.
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