[jibal]

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.

[gus_massa]

> 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.

[viccis]

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.

[8bitsrule]

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.

[buzzin__]

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.

[buzzin__]

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?"

[jibal]

non sequitur

[8bitsrule]

Perhaps ... but the lesson in trusting AI math was worth it.

[jibal]

You're missing the point. The counterexample to the Jacobian conjecture is valid regardless of how it was discovered ... elsewhere on this page people are even suggesting that the Anthropic mathematician may not have actually used Claude and came up with the counterexample himself.

Trusting AI math is not an issue here. It's as if you had asserted that no primes when divided by 35 produce a remainder of 6 and the model said that 41 is a counterexample and then you complained about not being able to trust AI math.

P.S. As someone else noted, your AI query was malformed ... no prime is divisible by 35, nor is any integer divisible by an integer with a remainder of 6 -- divisibility implies a remainder of 0. So perhaps the AI simply took what you wrote literally.

[0x1ceb00da]

> 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.

[Liquid_Fire]

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?

[fn-mote]

The concern is that there could have been expert knowledge input, whose importance/worth we are unable to evaluate.

I don’t believe a mathematician produced the counter example secretly, but how much did they contribute to the result?

AI isn’t magic, so to evaluate the value delta, you need to know the value of the input.

[hgoel]

While I agree that we need the inputs to properly evaluate what this means for LLM capabilities, I don't really believe that the amount of knowledge input matters much for the overall significance of the result.

These kinds of results are interesting for LLMs because mathematicians have been working on them for decades. If the result doesn't already exist, there's no way it's in the training data, and if mathematicians have been unsuccessfully tackling the problem for decades, it is believable that the use of a new tool made the result possible, even if guided by a great mathematician.

[YeGoblynQueenne]

Yes, but the question is the extent to which the new tool was guided by the mathematician.

Are we talking a bicycle, powered by a human stepping on the pedals; or a rocket that will fly to the moon on its own with people inside?

Don't you want to know? I mean, doesn't everyone want to know?

[hgoel]

Yes, of course, that would be interesting info to have. I just mean that from what we have already we can reasonably infer that the LLM played a role in the result being obtained.

If I am not mistaken, all of the flurry of novel results has come from existing mathematicians. This makes me suspect that the models aren't at the level where just any layman can get results. They require a skilled human in the loop to keep them on the rails and to properly explore the solution space.

[Izkata]

Weirder has happened: https://mathsci.fandom.com/wiki/The_Haruhi_Problem

[InsideOutSanta]

If I came up with this counterexample, I sure as hell wouldn't give credit to Claude.

[david-gpu]

Indeed, the incentive is the opposite: hiding the fact that they used an AI would boost their own personal brand.

[dooglius]

He worked for Anthropic, so such a claim would be very unconvincing

[david-gpu]

Because only people who work for Anthropic use AI tools? What is the reasoning here? The guy is a mathematician, after all.

[dooglius]

You have it backwards. Only people not working for Anthropic do not use AI tools.

[jibal]

> Why do you trust a random stranger so much?

Why do you make false claims and attack strawmen so much?

[dist-epoch]

> But they didn't provide it.

because they are using the same prompt to try finding other counter-examples. they are milking it