[krackers]

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?

[tyre]

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...

[krackers]

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]

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"

[ajkjk]

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.

[sawjet]

Neither of those links work for me

[lostmsu]

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

[charlieyu1]

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

[nullsanity]

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.

[h-jones]

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.

[pfdietz]

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.

[muldvarp]

> 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?

[pfdietz]

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.

[muldvarp]

> 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.

[HappyPanacea]

This is slow?