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

Post by laichzeit0 » Sat, Jul 11, 2026, 1:00 PM UTC

adamtaylor_13 wrote: post #241

munksbeer wrote: post #216

Earlier quoted context omitted.

Sorry to be nihilist, but you never had any objective value if you're thinking in these terms. As far as we know, the universe "just is". There is no universal objective value of human beings, at all, any one of us. You have to make or find your own value in the universe. I try not to think too hard about the nihilist side and try to appreciate that for some unfathomable reason, I seem to have what I call consciousne…

> As far as we know, the universe "just is". I don't know this. In fact, billions of people around the world don't know this. In fact, all evidence points to the contrary. You have objective value being made in the image of a personal God. Denying that leads to a lot of pain, namely nihilistic suffering because it's on you to "pull yourself up by the bootstraps" in any endeavor involving your own self-worth.

Post by HarHarVeryFunny » Sat, Jul 11, 2026, 1:04 PM UTC

DiscourseFan wrote: post #378

futureshock wrote: post #302

Earlier quoted context omitted.

I think a lot of this has to do with the post-training these models normally get. They are designed to answer basic questions with straightforward and short summary answers. They have the capacity to reason deeply, but they are not biased towards that unless prompted. I think it's because LLMs as they are in 2026 are both highly capable but also parlor tricks. They are not sentient, you just set them up with the cont…

Even Fable hallucinates. I had it tracking down some very obscure Ancient Greek inscriptions and the response just made up a translation/context for one inscription after "looking it up." Now, it was still a very particular thing and I really had to get into the weeds to push it to that point, but who knows how many other gaps, near or far, it will happily skip over just for the sake of coherence. I think this is an…

Post by emil-lp » Sat, Jul 11, 2026, 1:30 PM UTC

turzmo wrote: post #412

Both impressive and terrifying. But as always, the methodology is buried: how many open problems were tried until they found a success? If they tried this on 1000 problems and this is the one that succeeded, it still means that there are 999 open problems that an LLM cannot one-shot. It seems likely that this would remain the situation until the next model. If this is the first one they tried, maybe we’re totally hos…

Post by dannyw » Sat, Jul 11, 2026, 1:58 PM UTC

lubujackson wrote: post #104

jvanderbot wrote: post #55

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It is very concise, and reads precisely as you suggest: to exploit properties already discovered and therefore combined in a novel way. I'm just delighted by the prose. It reads like an old paper. The ones that were just straightforward theorems with proofs that do exactly what they say.

In my (very) limited use of GPT-5.6, I have noticed it is quite concise in general, and significantly better at abstract thinking. Doing a PR review of a large change it was interesting to see Fable and 5.6 mention a few similar points with Fable much more long-winded and less readable, while 5.6 caught more "second-level" concerns and Fable more "in the code" concerns, so they both are quite useful in concert. In ge…

Post by cbm-vic-20 » Sat, Jul 11, 2026, 2:06 PM UTC

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…