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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]

#381

Post by srdjanr »

virgildotcodes wrote: post #330
richardbarosky wrote: post #237

Earlier quoted context omitted.

Interesting take! I feel like 2 of them are maybe overstated: > - extent to which correctness of solution be easily specified and checked I don't think most software is like solving a math problem or series of math problems. Algorithmic problems are very narrow and might be more like this though, where an oracle that verifies answers as either correct or incorrect exists beforehand. The correctness function of most s…

> how much users want to use/pay for it, which is a pretty fuzzy problem Isn’t this quantifiable by revenue?

It's a very lagging metric, and also influenced by sales, market conditions for your customers etc.

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

#382

Post by frankohn »

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 are a human being, one of the most wonderful thing the nature has ever created, besides all the other living beings and the wonderful earth we live in. Do not tell yourself you have a value just because some company may want to hire you or not.

Companies and industries already use tools and machinery for tasks were once done by human beings. AI is just another tool they will use and it will probably replace human beings from some intelligence related tasks.

However that may bring more disruption to the society if the government in your country do not protect and help people and leave free rein to capitalistic greed.

I'm my opinion that already happened in the US, not by using AI, but merely by using H1B visa to get intelligence worker from abroad. What happened is that the companies are doing great and getting the best smart people in the world but American people and society have been disrupted.

Live your life fully, be good to yourself and to others. Don't worry about the market.

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

#383

Post by ai_fry_ur_brain »

brokencode wrote: post #281
ai_fry_ur_brain wrote: post #277

Earlier quoted context omitted.

Im using silicon valley collequially to represent "tech", not as a google maps pin.

So what billionaire are people rooting for when a new GLM comes out? How many people do you honestly think even know who owns or leads Z.ai? I certainly don’t.

[dead]

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

#385

Post by krona »

singularity2001 wrote: post #369
krona wrote: post #339

Earlier quoted context omitted.

LLMs have almost no fluid intelligence or capacity for abstract inductive reasoning, relying on crystallized intelligence for basically everything.

If anything their capability of abstract inductive reasoning is way beyond the average human given how much better LLMs are at solving math problems, it's the paradox that they can do complicated reasoning before they can do intuitive peep-pe-boo.

abstract inductive reasoning requires dynamic learning in unfamiliar contexts. All the benchmarks which measure this specifically (in particular, task composition) see LLMs fail catastrophically. There is quite a lot of research published on these limitations now.

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

#386

Post by arational »

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?

Well, you provide training data to the savior and our Lord AI. /s

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

#387

Post by munksbeer »

honeycrispy wrote: post #326
adamtaylor_13 wrote: post #241

Earlier quoted context omitted.

> 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.

This is one reason why I can't stand hn. Edgelord nihilistic comments that say nothing matters and take everything for granted get up-voted while credible and rational statements about God get down-voted.

That is an incredibly insulting comment. I am married, two children, have lead a fantastic fulfilling life. Just because I don't believe the Flying Spaghetti Monster created the universe doesn't mean I am an "Edgelord".

Remember the phrase, you also don't believe in God. There are hundreds of gods you don't believe in.

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

#388

Post by kzrdude »

ankit219 wrote: post #323
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…

llms are good at greedy depth first search[1]. so prompt / human needs to tell the model the breadth parts to take. and human writing the prompt here did a lot more than that. asking to include parallel-edge 2-cycles, admitting disconnected graphs, specifying the emptyset cover, multiset counting, it all likely came from previous fake proofs. [1]: see: ankitmaloo.com/fable - its the way most llms are trained, and is…

I guess "depth first" is just an expression of so called chain of thought, which is just a linear sequence. I don't know if GPT has any search-like (tree search) algorithms in their reasoning, it would be quite interesting if they did (they probably have researched this area, at least).

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

#389

Post by throw1234567891 »

judge2020 wrote: post #258
Anuiran wrote: post #234

Earlier quoted context omitted.

Regular Sol does not run on Cerebra’s. I don’t think anyone public has access to that. https://x.com/thsottiaux/status/2075596669958472146?s=46&t=Z...

Yeah they posted an update below it > apparently that is just Sol being Sol on fast mode, not 750 tps. :x O.o > This is real and it is not 750 TPS. Anyone with 5.6 Sol Ultra on fast mode can reproduce this! It’s all GUI interactions with CUA. No MCP or bpy needed. https://x.com/kimmonismus/status/2075493505011482922?s=20

Who’s they, who’s chubby, why would I care.

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

#390

Post by nextaccountic »

richardbarosky wrote: post #237
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…

Interesting take! I feel like 2 of them are maybe overstated: > - extent to which correctness of solution be easily specified and checked I don't think most software is like solving a math problem or series of math problems. Algorithmic problems are very narrow and might be more like this though, where an oracle that verifies answers as either correct or incorrect exists beforehand. The correctness function of most s…

> The correctness function of most software is how much users want to use/pay for it, which is a pretty fuzzy problem.

This is indeed a problem, but we (well we humans, but also agents) correct this by introducing partial verifiers like tests, running lints, type checkers, etc that both verify that at least some requirements are met, and also verify that the software is internally self-consistent. And more importantly, breaking down the software into small modules that are more clearly defined

The task to get user requirements and decide the right architecture requires more creativity and is fuzzier than implementing each module. Perhaps over time there will be models specialized for each task.

And actually this approach mirrors math, if agents ever develop new math on the fly to solve a problem. Developing new math is analogous to deciding how to break up the software in modules (and also analogous to designing a language, if we subscribe to the SICP notion that libraries actually are mini-languages on their own)

That is, LLMs for math is still in the phase where they are used to prove stuff (which by Curry-Howard, is like writing code), rather than deciding what to prove (which is like deciding the signatures of each function, again by Curry-Howard)

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