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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]

#271

Post by perching_aix »

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…

Thanks for the fun facts? Indeed, this is not a math forum. Good morning.

> I can demonstrate this [that literally nobody cares about the CDCC here]

No, you cannot. Mindreading the readers of this site by sifting through people's comments is a barely passable proxy for this at best, especially when that audience has changed dramatically over even just those 14 years, and continues to do so.

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

#273

Post by teravor »

stavros wrote: post #252
noname120 wrote: post #218

Earlier quoted context omitted.

Your comment is not substantiated at all.

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

if you get the same session that wrote the code to review it the poor results are entirely deserved.

and if you get a different instance to review the code then you would know that it works rather well.

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

#274

Post by rando1234 »

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…

It's funny, I found exactly the same thing when I asked about P=NP. The models outright refused to attempt to solve it, claiming it was too hard. I had to really battle to get it to suggest some promising suggestions.

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

#275

Post by Sniffnoy »

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…

People don't talk about the cycle double cover conjecture here because this isn't a math website. Its lack of mention here is therefore poor evidence.

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

#276

Post by kypro »

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…

I thought that too. The prompt is full of metaheuristics.

I remember a couple of years back when people were saying how prompt engineering was a skill, and reading this prompt kinda took me back to that.

Were I to guess, the reason the model couldn't do this itself is because most of the time, for most problems, a lot of this is bad advice.

In search optimisation you're often trading between time and quality. A very broad search will return very bad results for a long time. Where as a more depth oriented search with some heuristic will tend to return a pretty good result (if not optimal or close to optimal) quickly.

I'd assume models naturally want to find some middle ground there because that's the best thing to do most of the time, but for very difficult problems where a decent attempt isn't good enough you want a much broader search that doesn't have the time constraints. Much of the prompt seemed to be in that direction – really encouraging broadness of the search, preventing early convergence, and remove pressure of time constraints.

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

#277

Post by ai_fry_ur_brain »

brokencode wrote: post #268
topaz0 wrote: post #263

Earlier quoted context omitted.

Yeah

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.

Im using silicon valley collequially to represent "tech", not as a google maps pin.

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

#278

Post by aurareturn »

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…

Many white collar jobs are verifiable. Make a robot and suddenly real world tasks are verifiable too.

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

#279

Post by ecshafer »

I am torn by these announcements. On the one hand there is the infinite potential on what we can disover, when AI prompts are solving outstanding problems. On the other, something is lost in an aesthetic sense when it wasnt a man working through this or with a novel insight. If an AI prompt runs on a data center for two weeks and then prints out p=np, it feels a little empty.

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

#280

Post by ceroxylon »

ecshafer wrote: post #279

I am torn by these announcements. On the one hand there is the infinite potential on what we can disover, when AI prompts are solving outstanding problems. On the other, something is lost in an aesthetic sense when it wasnt a man working through this or with a novel insight. If an AI prompt runs on a data center for two weeks and then prints out p=np, it feels a little empty.

I resonate with that feeling, but on the other hand the humans reading the output will receive a pretty big boost in inspiration; new answers usually prompt new questions.
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