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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]

#331

Post by dash2 »

Miraste wrote: post #199
in-silico wrote: post #119

Earlier quoted context omitted.

The difference is that artistic sensibility is largely subjective. This means that: 1. It's hard to measure (and people can disagree about it) 2. It can't really be improved using RL without a human in the loop (which is how math is being trained)

At a certain level, yes, but AI is still so bad at writing that its failures are objective and easily measurable

I agree that AI writing is bloody awful, and that it's bad at creativity more generally, but are there actual objective measures of this?

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

#332

Post by geraneum »

mNovak wrote: post #253

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…

Maybe in previous failed attempts that what the model landed on and they’re preemptively stopping it. Did they release the any info on the failed attempts?

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

#333

Post by wyager »

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…

> the very architects of AI are the people whose jobs are most easily automated by AI

Think very hard about what this implies for the future pace of AI R&D

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

#334

Post by achierius »

mapontosevenths wrote: post #313
StefanBatory wrote: post #147

Earlier quoted context omitted.

It's hard for me not to think what's the point. I am a very average, even below average person in times of intelligence. What is even my value or reason to be if I know anything I can do, LLMs can do better? What is even my value both on job market and as a human?

This is a great question. Thanks for asking it. It really got people talking. My $0.02: Your value as a person never had anything to do with your value to the economy. It's time to relearn that fact. Check out some of Tom Hodgkins books for more. Or maybe anxietyculture.com.

Sorry, but most of us need to work to eat. This idea that our "value" is has nothing to do with the economy is an idea rooted in deep privilege, in the ability to say -- if I don't like my job, if I'm not employable, I can just retire, and the only problem will be figuring out how to live life afterwards.

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

#335

Post by pingou »

Retr0id wrote: post #317
StefanBatory wrote: post #147

Earlier quoted context omitted.

It's hard for me not to think what's the point. I am a very average, even below average person in times of intelligence. What is even my value or reason to be if I know anything I can do, LLMs can do better? What is even my value both on job market and as a human?

AI will never be better than me at appreciating a good sunset.

Perhaps it will. And perhaps countless animals are already better than us at appreciating a good sunset, yet we do not seem to value them much.

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

#336

Post by mmoskal »

nilkn wrote: post #28

Since this isn't in Lean and it's extremely easy for something like this to contain a subtle mistake, I think I'd prefer this be announced by a professional mathematician. The proof appears relatively short and elementary (not to be confused with easy -- just not using any advanced or modern machinery) so it shouldn't take long for the mathematics community to do a peer review. Without that, you could easily crank ou…

https://github.com/openai/cdc-lean

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

#337

Post by stevenhuang »

topaz0 wrote: post #318
brokencode wrote: post #268

Earlier quoted context omitted.

There have been multiple posts on here with 800+ upvotes in just the last few weeks for GLM 5.2. The idea that all this enthusiasm is for certain Silicon Valley billionaires and not from genuine interest in AI technology is a baffling take.

To be clear, I am not agreeing that people only upvote their favorite billionaires, just that if this particular thing was done by a Chinese model it would not have gotten the same attention

> a Chinese model it would not have gotten the same attention

Well, you would be wrong.

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

#338

Post by amluto »

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.

No, the comment is right. The prompt had GPT-5.6 reviewing the proof, and the result, unsurprisingly, survives review by GPT-5.6.

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

#339

Post by krona »

riddlemethat wrote: post #310
scarmig wrote: post #298

Earlier quoted context omitted.

LLMs have basic reasoning and a whole lot of memorization. Through that basic reasoning and pruned search, combined with piles of compute, you can prove lots of things. But the memorization of human failure prunes that possibility, and you need to expend effort convincing the LLM not to prematurely prune based on previous human failure.

The current foundational models have basic reasoning with glimpses of brilliant reasoning.

LLMs have almost no fluid intelligence or capacity for abstract inductive reasoning, relying on crystallized intelligence for basically everything.

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

#340

Post by amluto »

Diogenesian wrote: post #99

[deleted - the paragraph immediately following the proof of Lemma 2.1 is crucial and I found it hard to read correctly on my phone with the cramped typography. Having reread it I think the proof is correct.]

I was not a fan of the writing style of the proof. There seem to be some irrelevant details: Is the mention of 8-flow at all relevant? I, at least, found the definition of L on the first line of the proof of Lemma 2.2 to be needlessly inscrutable, and my thesis advisor would have likely stopped reading there and told me to fix it.

Maybe someone should ask the model to make a more clearly written and thus easy to verify proof :)

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