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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

#191

Post by skinner_ »

don_esteban wrote: post #93
mathisfun123 wrote: post #66

Earlier quoted context omitted.

I don't disagree with you but there's no need for exaggeration; ain't no high school student writing this: > In particular, proofs for special graph classes, constructions of cycle covers with some edges covered other than twice, bounded-length or prescribed-cycle variants, reductions to another unproved conjecture, computational verification through any fixed graph size, and candidate counterexamples without a compl…

the fact that such things have to be explicitly in the prompt points to the fact that the underlying system is still far from where it needs to be (basically, lacks basic understanding what a proof is)

No, that's not what this is. This is a warning to the LLM that coming back with partial results is not good enough.

Take a grad student with a perfectly good understanding of what a proof is. Their supervisor gives them a major problem to work on. Almost always, the problem is too hard, the student comes back with partial results, and student and the supervisor iterate from there. Now imagine that they have an unusually cruel and unreasonable advisor who tells them, do not dare to talk to me until you've fully solved the problem. This paragraph is exactly that. It's there exactly because the underlying system is smart enough to know that real mathematicians do not work like that.

Re: Ten advances in mathematics and theoretical computer science

#192

Post by danparsonson »

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.

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.

Re: Ten advances in mathematics and theoretical computer science

#193

Post by Delk »

woeirua wrote: post #146
Delk wrote: post #77

Earlier quoted context omitted.

I honestly don't think a language model is enough for self-awareness, regardless of the exact model of awareness. A language model (or an image model or whatever) cannot even be sentient, and I think sentience is a prerequisite for awareness. Even if we express a lot of our subjective experience with words, the language is just a symbolic representation of those experiences. The qualia themselves, even those that are…

So… your model is 100% vibes based. Got it.

I wasn't trying to give a model. The point was that I don't think it's necessary to give one.

You didn't address any of what I wrote, let alone provide any counterarguments. Which part of what I wrote do you think was wrong?

Re: Ten advances in mathematics and theoretical computer science

#195

Post by drdrey »

macleginn wrote: post #194

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?

> The results were achieved by an internal version of Astra, our next major model.

Re: Ten advances in mathematics and theoretical computer science

#196

Post by jryle70 »

0x5FC3 wrote: post #23
traes wrote: post #16

Earlier quoted context omitted.

This isn't really a productive way to think about these things, IMO. It's quite possible it would take hundreds of years for any specific group of PhDs to solve them. Or one individual PhD could have the correct flash of insight and solve it in a month. There's absolutely no way to predict this, besides trying to gauge the apparent simplicity of the proof or counterexample (which is likely to be misleading). Until so…

I understand and I am not trying to deny the impressiveness or the velocity of AI in general. But at some point we have to ask how much do we trust the labs at face value without much transparency of how they got to the results when there is trillions of dollars on the line.

Do you think OpenAI investors are more cavaliers than yourself who doesn't have any stake in it?

Re: Ten advances in mathematics and theoretical computer science

#197

Post by wbl »

dist-epoch wrote: post #95
aabhay wrote: post #6

My main gripe here is the lack of transparency around the total experiment and construction. I doubt that they simply pointed their model at these ten specific problems alone and gave the model one shot; therefore the $2000 number could be completely misleading, similar to P-value hacking by not disclosing the total experimental setup. I want to know: 1. How many total problems were given to the model, and what perce…

I don't think you want to bring cost into this argument. Even if the cost was $1 mil for these 10 problems, that's maybe 10-20 math researchers for a year. Do you really think that if you paid that to humans, they will deliver the same results?

If you told them this was the problem and they would still have a job if they failed probably. The reasons people don't go head on these problems is career incentives and psychology.

Re: Ten advances in mathematics and theoretical computer science

#198

Post by NitpickLawyer »

danparsonson wrote: post #192
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.

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 again. That's what "moving the goalposts" means.

It's also very much not a new phenomenon. It's been happening since the 1980s. As you can see from this quote from GEB by Hofstadter:

> There is a related "Theorem" about progress in AI: once some mental function is programmed, people soon cease to consider it as an essential ingredient of "real thinking". The ineluctable core of intelligence is always in that next thing which hasn't yet been programmed. This "Theorem" was first proposed to me by Larry Tesler, so I call it Tesler's Theorem: "AI is whatever hasn't been done yet."

Re: Ten advances in mathematics and theoretical computer science

#199

Post by unknownian »

sashank_1509 wrote: post #180

[flagged]

You shouldn't be getting downvoted for something that a majority of pure math and art enthusiasts believe to be true. The truth is many of these entrepreneurs and VCs are obsessed with AI not for money or human progress, but because it makes them feel closer to being a "god" rather than a mere mortal. Much of it (especially AI art) is out of spite for human creativity, which is done by mortals with limitations.

Re: Ten advances in mathematics and theoretical computer science

#200

Post by ifwinterco »

uh_uh wrote: post #119
dist-epoch wrote: post #95

Earlier quoted context omitted.

I don't think you want to bring cost into this argument. Even if the cost was $1 mil for these 10 problems, that's maybe 10-20 math researchers for a year. Do you really think that if you paid that to humans, they will deliver the same results?

It is comical at this point. Some people just can not stand the thought of AI actually delivering and are trying to find whatever ways to discredit it.

Yes, but if their machine god really is as good as they say it is, why are they constantly resorting to statistical sleight of hand at best and outright lies at worst with every public statement?

That's not normally how people act when they're confident in their product

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