Comment by antirez
2 months ago
So many mathematicians over the years tried hard and failed, but now Anthropic just for some PR magically did it? And this after LLMs obtaining different math wins? What is your logic here really escapes my understanding.
The parent's absolutely nonsensical post highlights how polarized AI (as everything else) is today. I can understand someone being opposed to AI on moral, cost-benefit or productivity grounds. But we're seeing a lot of extremist "AI is good for nothing" posts out there nowadays.
I don't think it is nonsensical at all. The author and his collaborator both appear to be bright people, so there's a good chance they had to offer non-trivial insights to guide the LLM, yet it's clearly in the interest of his employer to downplay whatever personal contribution they provided.
Edit: Now the OP is flagged/dead for some reason. You could disagree on their take (calling it a marketing stunt is maybe a bit much), but I think the argument is sound, so flagging seems counterproductive to the discussion.
Believing that AI played a very small role while we know this problem was open for decades with at least a few people taking serious cracks at it is just not a coherent logical position.
That doesn't really even diminish the contribution from Fable, if true. Droves of grad students have been provided the same sorts of non-trivial insights and turned up no results.
I'm sure they had plenty of time to think about these insights without the LLM, as well as the many other mathematicians who tried to crack it over the years. Wether the LLM was simply an assistant or solved the problem entirely isn't as important as accepting than the LLM was the essential, previously missing piece in the solution.
That's HN. No criticism allowed of llm whatsoever
> I think the argument is sound
They got flagged because it is a literal conspiracy theory that assumes bad faith.
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If you can call it polarized when a majority of people are just happily using the technology while a minority keeps spreading delusions and hatred.
Those silly advertisers do everything for exposure and if that means digging yourself into a niche alleged mathematical theorem to refute it, it is what needs to be done!
Of course it would be really interesting how Claude approached this. Probably with some constraints regarding the input. And it would be interesting what these constraints were.
Author probably doesn't want to show the prompt because they are now trying to find a bunch of other counter-examples with the same prompt
The reasoning trace would be far more interesting, and that's not exposed.
I mean we have no idea what happened exactly, how Fable was used, how many times it was run, whether earlier models were also tried, what was the prompt, how long it run for, etc etc. All we have to go by is a tweet.
Why not be skeptical about that?
What you're asking for is exactly the sort of thing that belongs in, and will appear in, a journal article. There will likely be a preprint on arxiv, so you might keep an eye out for that.
In any case, the fact that it was found by a commercial model means that the unfiltered reasoning trace isn't available even to the original author. So there are aspects of the problem-solving process we'll never see. Even if we did get access to the reasoning trace it wouldn't necessarily be definitive, given how these things work.
Hopefully it'll be possible to get the same solution from an open-weight model like one of the 3T heavyweights that are said to be coming up for release. If so, the chain of thought can be scrutinized in-depth.
No, I think it works the opposite way. Until there is an article somewhere that describes what happened, if there is one, all we have to go by is that some guy posted a counter-example for the Jacobian on X, with a vague allusion to using Fable and without any further information. Assuming and guessing anything about e.g. the method used at this point is just raising the noise level.
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The original author works for Anthropic. And even without that, Anthropic might find this important enough to dig up the trace?
They gave their "logic", such as it is ... and it's utterly irrational.
Note that the "they" who published the counterexample on X is some rando mathematician (Levent Alpöge) working for Anthropic, not Anthropic the organization. He posted the counterexample in a tweet -- reason enough for "not disclosing the LLM chat session". There's no reason to think that it won't provided if asked for, but it hardly seems relevant.
> There's no reason to think that it won't provided if asked for, but it hardly seems relevant.
My guess is that the chat will look similar to a full transcription of a (multi month?) discussion between a few mathematicians. Full of dead ends and stupid errors (bit by the human and Claude) that would be embarrassing. We all know how bad it is, and we prefer to keep it behind the curtain.
Here's an example of one for a major result earlier this year: https://cdn.openai.com/pdf/1625eff6-5ac1-40d8-b1db-5d5cf925d...
Who knows what "rewritten" means, but you can sort of see how it progresses.
A few months ago I asked a model how many primes are divisible by 35 with a remainder of 6. It confidently replied 'none'.
Counterexample: 35 + 6.
Kimi 2.6 gives the answer ""By Dirichlet's theorem on arithmetic progressions, since gcd(6,35)=1 , there are infinitely many primes of the form 35k+6 . So the answer is: infinitely many primes give a remainder of 6 when divided by 35.
But, if the reminder is 6, they are not really divisible, are they? Try again with a sentence that actually makes sense: "How many primes, when divided by 35, give a reminder of 6?"
non sequitur
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> some rando mathematician (Levent Alpöge) working for Anthropic, not Anthropic the organization
Why do you trust a random stranger so much? Will you hand over your car keys to a random stranger? Sharing the chat will take 30s of their time.
> There's no reason to think that it won't provided if asked for
But they didn't provide it.
OK, so the two options are:
A) Claude really produced this counterexample
B) A mathematician working for Anthropic solved a problem mathematicians have been working on for more than a century, and then credited it to Claude for PR purposes
If you believe B is more likely, why would you then believe a proof in the form of a chat log, when said chat log could itself have been faked by Anthropic way more easily than solving the mathematical problem in the first place?
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If I came up with this counterexample, I sure as hell wouldn't give credit to Claude.
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> Why do you trust a random stranger so much?
Why do you make false claims and attack strawmen so much?
> But they didn't provide it.
because they are using the same prompt to try finding other counter-examples. they are milking it
[flagged]
Cheating how? The proof is in the pudding...
On one hand, yes.
The parent wants to be skeptical… nothing wrong with being suspicious of marketing claims, right?
I would be a lot less impressed if I found out the session was guided by an expert in the field who already had a good idea of where to look. For example, I don’t believe that the results Terrance Tao gets from an LLM are comparable to what I am going to get.
I’m not even saying I’m a skeptic. Just that there’s nothing wrong with keeping your eyes open and asking for details.
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Dude what?
There's a big difference between one shotting a counterexample using AI and using AI to find a counter-example by brute-force.
Both are impressive, of course, but they're hardly comparable.
I'm not so sure. People had been trying to use brute force to find counterexamples before.
AI is great at reducing the search space and using human-like reasoning (in a brute-force way) to carry out the brute-force search. I'm not surprised by this result. This is exactly what AI should excel at, with human guidance.
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