The surprising thing is that the counterexample seems relatively "simple" in that it's low degree, with coefficients that aren't too large.

Does anyone more familiar with this know why this _wasn't_ found earlier, when it seems like you could brute-force through some low-order polynomials?

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tyre a day ago | parent | next [-]

Reading the chain of thought for Fable, it is incredulous as well. It keeps thinking that it must be missing something or that this is a trick, because it can't have just found a counterexample to a famous conjecture. It's just like us!

https://cdn.xcancel.com/pic/orig/EA1E99C3DAE99/media%2FHNpQX...

https://cdn.xcancel.com/pic/orig/3B5C0B867A7C3/media%2FHNpQU...

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krackers a day ago | parent | next [-]

Which tweet has the chain of thought? I was curious how it discovered this, did it use some symbolic brute force or some clever trick? Also is that the raw or summarized COT, it seems to have the hallmarks of raw COT (the frequent interjections) but I thought Anthropic always used summarizers in between

	▲	SonOfLilit a day ago \| parent [-]
		By the CoT content, this is a screenshot of someone giving Fable the result and asking if it's true, not the CoT of discovery. e.g. "maybe the user's example is DESIGNED to be "correct in the stated facts" &c"

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ajkjk a day ago | parent | prev | next [-]

It's funny how similar this is to a human reaction to the same thing. It's the right level of incredulity, to be sure, and the first thing you do is you start re-reading the conjecture to makes sure you didn't misunderstand the requirements.

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sawjet a day ago | parent | prev | next [-]

Neither of those links work for me

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lostmsu a day ago | parent | prev [-]

No surprise given half HN still does not consider it general intelligence. Models are being toxic shamed into it.

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charlieyu1 a day ago | parent | prev | next [-]

There are still many degree 5 polynomials, up to 35 terms for a single function, then you need to find three of them as well

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nullsanity a day ago | parent | prev [-]

Same awnser as much of the LLM Proofs - people cared about other things. There isn't a lot of money in academic math, and the ones that love it don't look for low value findings. Proofs like these are, funnily enough, usually the domain of hobbyists - but over the last few years, the "Monetize everything" mentality and struggling first world economy has pushed people away from interesting academic pursuits on their free time.

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h-jones a day ago | parent [-]

My understanding is that this is in a different league (Smale problem) than a lot of the other results that have been coming out (Erdos), though I could be wrong.

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pfdietz a day ago | parent [-]

The Erdos problem solutions have been accelerating, including a $250 problem and a $100 problem.

It's been fun watching the cope collapse from day to day. No one told me a slow takeoff Singularity would have so much schadenfreude.

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muldvarp 20 hours ago | parent | next [-]

> It's been fun watching the cope collapse from day to day. No one told me a slow takeoff Singularity would have so much schadenfreude.

I'm constantly surprised at how much schadenfreude there is on hacker news about LLMs. Like, do you guys (and girls) not have to work for a living?

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pfdietz 20 hours ago | parent [-]

I don't. I'm retired.

I'm also not going to live all that much longer, most likely, so it's kind of annoying I'm not really going to see any upsides to an AI world either. I'm discounting the possibility of our AI overlords figuring out a miracle like reversing aging.

But it is really f-ing cool that automated math is now a thing and we are seeing it. Eat your heart out, past me.

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muldvarp 19 hours ago | parent [-]

> so it's kind of annoying I'm not really going to see any upsides to an AI world either

I don't think the "permanent underclass" will see many upsides either. They certainly won't have the money to pay for it. I'm excluding myself in that statement because luckily I have access to large amounts of barbiturates.

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pfdietz 19 hours ago | parent [-]

The math community was not a global underclass. World wealth is increasing, the actual global underclass is seeing rapidly improving lives.

You may be seeing a loss of privilege due at least in part to the inevitable reversion to the mean of US economic dominance. But on a global scale, things are going well. AI will lead to a much larger pie.

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muldvarp 19 hours ago | parent [-]

> The math community was not a global underclass.

I never claimed they were. The term "permanent underclass" refers to the preferred world order of AI techbro billionaires[1] where human labour is worthless and in consequence normal people no longer have any leverage. Societies where most of the value is dug out of the ground and where human labour is comparatively worthless already exist and living there is not necessarily fun[2].

> World wealth is increasing, the actual global underclass is seeing rapidly improving lives.

The global underclass has been seeing improving lives well before LLMs were a thing. The question is whether they will _continue_ to see their lives improve if their labour is no longer required.

> You may be seeing a loss of privilege due at least in part to the inevitable reversion to the mean of US economic dominance.

I'm not from the US, I don't live in the US, and in fact I've never been to the US.

> AI will lead to a much larger pie.

Which will only benefit people if their piece of the pie doesn't shrink because they don't have any leverage. There is also more than one pie. The real estate pie for example won't grow, instead every piece of the pie will become even more expensive. Most people only own pieces of the pie that will decrease in value (human labour) not pieces of pies that will increase in value.

[1]: https://www.nytimes.com/2026/04/30/opinion/ai-labor-work-for...

[2]: https://en.wikipedia.org/wiki/Resource_curse

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pfdietz 17 hours ago | parent [-]

Why do you think tech bro billions aren't also subject to replacement by AI? They compete with each other, and if AI does their jobs better than they can themselves they are strongly incented to use AI.

Absent a world dictatorship there's always competition here. And fully superhuman AI eliminates the main objection to socialism, that you need markets with smart people to make an economy function. Full automated luxury communism (like Ian Banks) is a possible outcome.

	▲	muldvarp 16 hours ago \| parent [-]
		> Why do you think tech bro billions aren't also subject to replacement by AI? Because they're billionaires. They don't actually work for a living. They own stuff for a living. > And fully superhuman AI eliminates the main objection to socialism, that you need markets with smart people to make an economy function. Full automated luxury communism (like Ian Banks) is a possible outcome. Luxury communism is also a possible outcome in countries with large oil reserves (Venezuela for example), it's just not a likely outcome because common people have no leverage and billionaires didn't become billionaires by giving stuff away. Even if "fully automated luxury communism" were a likely outcome, the transition there would be very rough and would take years. If software engineering is automated away in 2028 it could still take years or decades before the first general purpose robot can take over plumbing. (Former) software engineers will have a rough transition.

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HappyPanacea 21 hours ago | parent | prev [-]

This is slow?