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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]

#311

Post by onecomment1 »

perching_aix wrote: post #301
onecomment1 wrote: post #283

Earlier quoted context omitted.

[flagged]

> If people cared they would [have mentioned it before]. What are YOU on about? I explained why and how I think this is both wrong (especially in the ridiculously absolute form it was posted in), and a weird point of contention. This is a tech (startup) forum, with an increasing pull towards more general audiences. Math and sciences have strong ties to tech, but you won't see people discussing specific math conjectur…

Thank you for taking the time to respond thoroughly. You made me reflect upon my frustrations and anger. I take back my flagrant comment.

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

#312

Post by linzhangrun »

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 models also need a specially tuned version for mathematical research, just like "gpt-5.3-codex".

Looking forward to "gpt-5.6-mathx".

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

#313

Post by mapontosevenths »

StefanBatory wrote: post #147
WhitneyLand wrote: post #75

If all checks out this is a huge milestone. AI has now solved one of the most famous open problems in graph theory, using an off the shelf model, in one hour. It might be a better mathematician than most humans at this point. Kind of like when chess software started beating everyone except grandmasters. What’s left? Proposing and building out entirely new theories and frameworks? Then better than any human? Then alie…

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.

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

#314

Post by stevenhuang »

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…

This was one of the most famous open graph theory problems lol. I am not a mathematician and even I ran into this when doing generative map design for game dev.

The only thing you've demonstrated here is some very funny confidently incorrect coping behavior.

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

#315

Post by drpixie »

> GPT-5.6 Sol Ultra produces proof of the Cycle Double Cover Conjecture

Very misleading article title.

Title should be "Un-named humans produce unverified proof of CDC Conjecture using GPT-5.6" ... but I expect only advertising copy when it comes from the AI industry.

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

#316

Post by mapontosevenths »

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.

Every generation has felt some version of this.

"Keyboards are soulless. Handwriting is personal – as unique as fingerprints." - Joyce Carol Oates on typewriters

"This discovery of yours will create forgetfulness in the learners' souls, because they will not use their memories; they will trust to the external written characters and not remember of themselves. The specific which you have discovered is an aid not to memory, but to reminiscence, and you give your disciples not truth, but only the semblance of truth." - Socrates on writing

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

#317

Post by Retr0id »

StefanBatory wrote: post #147
WhitneyLand wrote: post #75

If all checks out this is a huge milestone. AI has now solved one of the most famous open problems in graph theory, using an off the shelf model, in one hour. It might be a better mathematician than most humans at this point. Kind of like when chess software started beating everyone except grandmasters. What’s left? Proposing and building out entirely new theories and frameworks? Then better than any human? Then alie…

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.

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

#318

Post by topaz0 »

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.

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

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

#319

Post by vessenes »

ak_111 wrote: post #26

Unlike the unit distance problem, the impressive thing here is that it is a proof rather than a counter-example. However, it seems the proof is extremely concise so it seems that it is exploiting a clever trick that somehow all the experts missed. So not to dunk on this amazing result (or move the goal post), but it seems now the only achievement that AI hasn't managed in mathematics is presenting an autonomous "theo…

Grant Sanderson recently distinguished mathematicians that create syntax (he might use the word ontologies in some circles) from those who manipulate it on the Dwarkesh podcast. I liked this delineation a lot. We seem to be at ‘manipulating syntax’.

Creating useful ontologies still seems a ways off here. Not to complain about this awesome result, just to think about where some future goalposts might be laid (and of course complained about / discussed at length when reached)

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

#320

Post by Davidzheng »

zerobees wrote: post #22

This is not a remark about AI, but there's something funny about mathematics in that every novel result is broadly perceived as a big deal. We attach basically zero value to writing a new program that hasn't existed before, or a piece of text that hasn't existed before. It's boring, or even a net negative, unless you can show that the result benefits the world in some way. We'd find it weird if OpenAI put out a relea…

Sorry but I completely disagree with your statement that "every novel result is broadly perceived as a big deal". Most results certainly are not consider this way (even though the average result has difficulties that are much higher than novel computer program you may have in mind -- no offense)
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