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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]

#81

Post by hnisfulomrons »

throw310822 wrote: post #57
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…

> We attach basically zero value to writing a new program What does it mean "new"? And, was it a difficult or trivial accomplishment? A solution to a well known open math problem is both new and non-trivial- you know that many, very smart, very well trained human experts have dedicated time to the problem and haven't been able to solve it, despite good incentives.

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

#83

Post by therobots927 »

Jweb_Guru wrote: post #77
therobots927 wrote: post #68

Is there anyone more knowledgeable than me about proof checking software who could tell me how off the mark I am here? Assuming you have decent proof checking software, is it possible that this solution was achieved by throwing GPT at the problem a couple hundred thousand times until it passed the proof checker?

As someone who's used proof checkers a fair amount, if you don't have some high level idea about the proof, it's an open problem, and the hard part isn't some extremely tedious finite case analysis, it's extremely unlikely you'll get anywhere by trying to mechanize by throwing stuff against the wall to get it to typecheck. When people talk about mathematics being a closed formal system as though this trivializes any…

Well the key thing here is I’m not saying the LLM has no idea what it’s doing. But LLMs are prone to hallucinations which can really impact a string of interdependent logic like a proof. So I’m assuming it would respond with something that’s not complete nonsense to this proof most of the time. Where I’m skeptical is if this was a true one shot, or if they had to iterate and try multiple different prompts, or even the same prompt over and over again to reach a working solution.

So I’m just asking if the proof checking software is capable of evaluating this proof. Because if it is, that makes the brute force approach a lot more feasible as you reduce human review overhead significantly.

If it is, that would imply you could run the prompt through the LLM as many times as you want until you “strike gold” so to speak.

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

#85

Post by npinsker »

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…

You say those things like they're a short step away, but that might not be how it works out.

For example, AI has made zero progress in the last few years in surpassing professionals at art or writing. Its prompt-following skill is much better, and sure, it can render hands and text now, but its artistic sensibility is completely stagnant.

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

#86

Post by hnisfulomrons »

Frost1x wrote: post #39
not-a-llm wrote: post #25

Earlier quoted context omitted.

pretty sure already millions of dollars (in inference costs) were already thrown at the Riehmann hypothesis as the models get stronger, larger amounts will be thrown at it imagine paying "just $1 bil" to go down in history as the company who's model solved the hardest/most famous open problem in mathematics. imagine the worldwide press headlines. as they say, the Riehmann Hypothesis is the hardest way to earn a milli…

I’m all for it since it’s value directly returned to humanity.

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

#87

Post by simianwords »

scrlk wrote: post #82
simianwords wrote: post #54

what's the difference between Sol Ultra and Sol pro? is pro a thing of the past now

Ultra = parallel subagents with max reasoning Pro = test-time compute (best of N responses)

why would you use one over the other?

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

#88

Post by Gtex555 »

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…

A lot of mathematics often takes 100+ years to find a practical use because we have developed it so much that we have use all the easy maths. Things like CS or SWE are so new that you can still find stuff today that can be used tomorrow. Things like computation and cryptography was all discovered like 100 years before we had a practical use for it. Its an example of late stage scientific discipline. Things like physics, chemistry and biology will get here as well eventually.

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

#89

Post by dnautics »

andai wrote: post #38
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…

>mathematics is basically the only scientific discipline that rejected any notion of utility I think this might depend on the department, but I was at a pure math department last year, and struggling with my Linear Algebra textbook (written by the professor, incidentally, who was not a great communicator). I consulted the machines, and learned, to my great delight, that linear algebra is used in like 20 different fie…

despite being theoretical i would have greatly benefitted in learning linear algebra if i had seen even one or two not-obvious applications, like galois fields for reid solomon erasure coding.

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

#90

Post by Jweb_Guru »

CamperBob2 wrote: post #73
amazingamazing wrote: post #40

Earlier quoted context omitted.

You believe this based off what?

Based on these people not being idiots or charlatans? Why wouldn't they verify it, knowing that any shenanigans would certainly come to light?

Frontier labs have had multiple major announcements in the past about supposedly novel LLM generated theorems that turned out to be vastly overstating what actually happened. That's part of why they were so (appropriately) cautious with the unit distance proof.
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