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GPT-5.6 Sol Ultra produces proof of the Cycle Double Cover Conjecture [pdf]

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Re: GPT-5.6 Sol Ultra produces proof of the Cycle Double Cover Conjecture [pdf]

#251

Post by coldtea »

Garlef wrote: post #227
qarl2 wrote: post #201

Earlier quoted context omitted.

Hmmm... seems to me that if you can find a solution without creating the desired explanation - then that's a problem with the original question - not the solution itself. And discovering a bad question leads to the correct question. No?

> then that's a problem with the original question - not the solution itself I think there's a good counterexample to this: Atiyah/MacDonald proove the Nullstellensatz ultimately by using some trick involving determinants. They give a very nice theoretical treatment of the content and context of the theorem. But the proof at one crucial point uses techniques that live conceptually outside of this context: While its p…

>(You could of course argue that they did not give enough context ... but that's exactly my point: the trick makes the proof work but hides the explanation)

Can't one see it in another way: that the trick illuminates a deeper explanation, connection the theorem's context and the stuff that's conceptually outside of that context. And that the problem is we don't know why the two domains (the context and the conceptually outside of it one) are related and cooperating in this way.

Re: GPT-5.6 Sol Ultra produces proof of the Cycle Double Cover Conjecture [pdf]

#252

Post by stavros »

noname120 wrote: post #218
stavros wrote: post #215

Earlier quoted context omitted.

Of course it believes the proof is sound, it wrote it. If you want to check an LLM's output, you should use a different LLM.

Your comment is not substantiated at all.

If you'd ever tried to get an LLM to review its own code, you'd know.

Re: GPT-5.6 Sol Ultra produces proof of the Cycle Double Cover Conjecture [pdf]

#253

Post by mNovak »

Unrelated to the accomplishment or proof itself, but it's interesting how much of the prompt, even in this latest-and-greatest model, is spent essentially telling the model to actually solve the problem. Things like "Reject status reports, vague optimism, and claims that an unproved global compatibility statement is 'routine'."

Also a lot prompt spent feeding it strategies, which feel like they should/will eventually be deduced by the model itself, not explicitly stated. That's not to take away from the outcome in any way; rather, it feels sort of like when you would prompt GPT 4, "think through your answer step by step," as a sort of proto-chain of thought.

Re: GPT-5.6 Sol Ultra produces proof of the Cycle Double Cover Conjecture [pdf]

#254

Post by ai_fry_ur_brain »

itsthecourier wrote: post #246
romaniv wrote: post #244

No one here actually cares about Cycle Double Cover Conjecture. I can demonstrate this by pointing out that the only time this conjecture was ever mentioned on the website was 14 years ago in a submission[1] that linked to a (now retracted) proof paper. That story received exactly zero upvotes. No one cared enough to upvote it and no one cared enough to ever mention this conjecture again. [1] https://news.ycombinator…

yeah, I think what makes this post different was that AI did it. hopefully science will advance faster in the next decades with AI researchers helping

[flagged]

Re: GPT-5.6 Sol Ultra produces proof of the Cycle Double Cover Conjecture [pdf]

#255

Post by qarl2 »

Garlef wrote: post #227
qarl2 wrote: post #201

Earlier quoted context omitted.

Hmmm... seems to me that if you can find a solution without creating the desired explanation - then that's a problem with the original question - not the solution itself. And discovering a bad question leads to the correct question. No?

> then that's a problem with the original question - not the solution itself I think there's a good counterexample to this: Atiyah/MacDonald proove the Nullstellensatz ultimately by using some trick involving determinants. They give a very nice theoretical treatment of the content and context of the theorem. But the proof at one crucial point uses techniques that live conceptually outside of this context: While its p…

Ah... is this just the difference between a constructive and non-constructive proof? Is that the distinction you're making?

Re: GPT-5.6 Sol Ultra produces proof of the Cycle Double Cover Conjecture [pdf]

#256

Post by semiquaver »

pianopatrick wrote: post #249
plaidfuji wrote: post #230

It seems like a solid set of criteria for how easily a task can be automated by AI agents is: - extent to which correctness of solution be easily specified and checked - extent to which new potential solutions can be implemented as text - extent to which prior art exists online This basically maps to software engineering and math. I think a fair bit of AI hype comes from the fact that the very architects of AI are th…

Let's assume AI is only good at software and math. If we can use AI to write lots of good software for cheap, that software can automate away a lot of jobs. So AI does not have to take the jobs directly, software written by AI can. Especially if that works for software for robots.

Yup. There’s infinite latent demand for software, we just don’t know yet.

Re: GPT-5.6 Sol Ultra produces proof of the Cycle Double Cover Conjecture [pdf]

#257

Post by Chu4eeno »

adamtaylor_13 wrote: post #241
munksbeer wrote: post #216

Earlier quoted context omitted.

Sorry to be nihilist, but you never had any objective value if you're thinking in these terms. As far as we know, the universe "just is". There is no universal objective value of human beings, at all, any one of us. You have to make or find your own value in the universe. I try not to think too hard about the nihilist side and try to appreciate that for some unfathomable reason, I seem to have what I call consciousne…

> As far as we know, the universe "just is". I don't know this. In fact, billions of people around the world don't know this. In fact, all evidence points to the contrary. You have objective value being made in the image of a personal God. Denying that leads to a lot of pain, namely nihilistic suffering because it's on you to "pull yourself up by the bootstraps" in any endeavor involving your own self-worth.

To cite the famed Russian philosopher Norm Macdonald; "Scripture. Faith. Grace. Christ, Glory of God. Smart man says nothing is a miracle. I say everything is."

Re: GPT-5.6 Sol Ultra produces proof of the Cycle Double Cover Conjecture [pdf]

#258

Post by judge2020 »

Anuiran wrote: post #234
throw1234567891 wrote: post #225

Earlier quoted context omitted.

But Sol is running on Cerebras. That’s the whole point of this. That’s how they get 750 tokens per second. There is no other way.

Regular Sol does not run on Cerebra’s. I don’t think anyone public has access to that. https://x.com/thsottiaux/status/2075596669958472146?s=46&t=Z...

Yeah they posted an update below it

> apparently that is just Sol being Sol on fast mode, not 750 tps. :x O.o

> This is real and it is not 750 TPS. Anyone with 5.6 Sol Ultra on fast mode can reproduce this! It’s all GUI interactions with CUA. No MCP or bpy needed.

https://x.com/kimmonismus/status/2075493505011482922?s=20

Re: GPT-5.6 Sol Ultra produces proof of the Cycle Double Cover Conjecture [pdf]

#259

Post by phoghed »

ai_fry_ur_brain wrote: post #254
itsthecourier wrote: post #246

Earlier quoted context omitted.

yeah, I think what makes this post different was that AI did it. hopefully science will advance faster in the next decades with AI researchers helping

[flagged]

You honestly think this wouldn’t be upvoted equally or more if a Chinese model did it?

Re: GPT-5.6 Sol Ultra produces proof of the Cycle Double Cover Conjecture [pdf]

#260

Post by calf »

Garlef wrote: post #196
qarl2 wrote: post #193

Earlier quoted context omitted.

> However, it seems the proof is extremely concise so it seems that it is exploiting a clever trick that somehow all the experts missed. Why is that a "however"? My reading is that it found a genuinely new solution that is both elegant and previously missed. Seems like exactly the kind of result a human mathematician would aspire to.

> a human mathematician would aspire to Some do. But there's also the notion that a clever trick is a bad explanation.

Is this what the prompt means by proof strength gap, or is that something else entirely? (Sorry not a mathematician.)
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