Hacker News Board Hacker News, browsed like a classic message board
Live data from Hacker News

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

cdn.openai.com

Post reply on HN
Print view View original

261–270 of 467 posts

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

#261

Post by vmg12 »

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?

You have inherent value by virtue of being human. Unfortunately it seems like people have forgotten humanism.

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

#262

Post by WhitneyLand »

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?

Your value is intrinsic as a human being. We’re capable of love and shared experiences that a machine will never know.

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

#264

Post by edflsafoiewq »

bgirard wrote: post #9

It's really neat that the prompt was released! I'm curious how many unsolved problems are tried against frontier models when they come out. Are we trying every problems against every release? What is the solve success rate? Is there a sub-community within Mathematics that is coordinating this effort? How much untapped opportunity is there here?

I find it kind of interesting the whole output wasn't released. A common criticism of mathematical writing is results are "pulled out of a hat"; you only write up a polished, final proof, but hide everything that went into developing it. It's kind of ironic the practice is even carried on when an LLM writes the proof.

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

#265

Post by nsz65 »

ianm218 wrote: post #240
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…

> Ironically it couldn’t be further from the truth… and likewise the predictions of widespread labor obsolescence Could you explain what you mean here? It feels like there is one bucket of verifiable work - programming, math etc that AI will clearly excel at. There is another large bucket of like law/ accounting/ financial analysis where I don’t have any reason to think AI won’t be super human at, but the work is mor…

Anything where unpredictability is a daily part of the job.

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

#266

Post by kristopolous »

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…

The point of this is if AI is solving things that nobody cares about, that's the utility here. It's doing something nobody else wants to bother with

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

#267

Post by bottlepalm »

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…

We absolutely care about the implications of AI solving hard problems. I'm sure you can find thousands of posts on HN deriding AI progress the entire time, trivializing it as nothing more than a 'stochastic parrot'

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

#268

Post by brokencode »

topaz0 wrote: post #263
phoghed wrote: post #259

Earlier quoted context omitted.

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

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.

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

#269

Post by nomel »

0x457 wrote: post #171
a_e_k wrote: post #115

Earlier quoted context omitted.

Once on a late-night session, I had Cline!Claude spontaneously point out the time to me and suggest that I get to bed and come back fresh the next day. I don't think it's in the system prompt, but that the harnesses time-stamp each turn in the context. And from what I've seen, they also include the current and max context, so that the model can decide whether to continue work, suggest compaction, or prefer actions th…

> Once on a late-night session, I had Cline!Claude spontaneously point out the time to me and suggest that I get to bed and come back fresh the next day. I had Claude say something "It's getting late, let's pick this up tomorrow" at like 11am. As for context, in my experience Claude starts trying either to do maximum work with minimum tokens when it's approaching limit, or it starts deferring useful work while doing…

It's in the training data! Long conversations between humans result in humans getting tired and going to bed.

I have this reality baked into my workflow:

1. Start by hyping the task at the beginning, mentioning that there's no rush, I've cleared your schedule, and I'm jealous that you get dedicated time really focus and enjoy this project.

2. Periodically say "Great work, let's finish this next week. Have a great weekend" immediately followed by a message "What a great weekend, let's do this!" sort of hype, for it to continue. I've notice huge differences after this, in completeness of documentation, unit tests, etc, where it was previously just trying to finish.

3. Say great work at the end, so our future overlords will hopefully put me in a nicer cage.

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

#270

Post by koe123 »

famouswaffles wrote: post #221
drdexebtjl wrote: post #180

Earlier quoted context omitted.

Is this something humans have been unable to do? There’s only so many people with the necessary skills to solve this. And you need these humans to choose to spend their time solving this, and not something else.

>Is this something humans have been unable to do? It's a famous open problem so yeah >There’s only so many people with the necessary skills to solve this. And you need these humans to choose to spend their time solving this, and not something else. Sure, but that doesn't mean a lot of very skilled people hadn't attempted and failed to solve this.

And you’ve known about this problem for how many minutes?
Post reply on HN