Is this the first LLM-solved problem famous enough to have been on https://en.wikipedia.org/wiki/List_of_unsolved_problems_in_m...
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]
#12Announcement: https://x.com/__eknight__/status/2075643450196971805 Prompt: https://cdn.openai.com/pdf/04d1d1e4-bc75-476a-97cf-49055cd98...
> Spend at least 8 hours on this before even thinking of returning or giving up. Do current model harnesses have concepts of amount of time spent? Sometimes the model notices if a subprocess takes too long/hangs and kills it, but I've never seen it time itself.
they can call CLI tools to notice the passage of time. the harness can include timestamps too
Re: GPT-5.6 Sol Ultra produces proof of the Cycle Double Cover Conjecture [pdf]
#13Statement of AI use. The proof in this note is entirely due to GPT 5.6 Sol Ultra and the writeup with Codex (with GPT 5.6 Sol).
Clearly that sentence isn't AI generated ...
Re: GPT-5.6 Sol Ultra produces proof of the Cycle Double Cover Conjecture [pdf]
#14Is this the first LLM-solved problem famous enough to have been on https://en.wikipedia.org/wiki/List_of_unsolved_problems_in_m...
No there was the planar unit distance problem
(Erdős problem 90)
Re: GPT-5.6 Sol Ultra produces proof of the Cycle Double Cover Conjecture [pdf]
#15It'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?
The prompt was released, but not the cost of the result.
Re: GPT-5.6 Sol Ultra produces proof of the Cycle Double Cover Conjecture [pdf]
#16Announcement: https://x.com/__eknight__/status/2075643450196971805 Prompt: https://cdn.openai.com/pdf/04d1d1e4-bc75-476a-97cf-49055cd98...
> Spend at least 8 hours on this before even thinking of returning or giving up. Do current model harnesses have concepts of amount of time spent? Sometimes the model notices if a subprocess takes too long/hangs and kills it, but I've never seen it time itself.
of you ask it, surely it can run a "time" in its sandbox from time to time and see how long it worked for
Re: GPT-5.6 Sol Ultra produces proof of the Cycle Double Cover Conjecture [pdf]
#17But is the proof accepted to be correct? That is what distinguishes this from being notable compared to any other AI slop proof.
Yeah it's a very very short proof that uses no mathematics developed within the last 30 years. Which doesn't necessarily make it wrong, but in the absence of mechanization in Lean or proper peer review I think this it is premature to post this. Notably the unit distance proof did not fall into this category.
Re: GPT-5.6 Sol Ultra produces proof of the Cycle Double Cover Conjecture [pdf]
#18"Assume for purposes of this task that a complete affirmative proof exists"
everybody knew the problem was impossible to solve
then one day somebody new arrived and they forgot to tell him/her, so he/she solved the problem
Re: GPT-5.6 Sol Ultra produces proof of the Cycle Double Cover Conjecture [pdf]
#19It did not use Lean or other proof assistant?
Re: GPT-5.6 Sol Ultra produces proof of the Cycle Double Cover Conjecture [pdf]
#20Good post, it perfectly captures the problem with AI. Here we have a claim that the double cover conjecture has a proof. Verified by… no one per the link.
Now imagine this proof is wrong. How would you know? Ok, think about the process in which you determine the correctness - why not do that initially?
And there it is. The problem laid bare. Ironically it reduces to the P and NP one.