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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fn-mote a day ago | parent | next [-]

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.

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hgoel a day ago | parent [-]

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.

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YeGoblynQueenne 13 hours ago | parent [-]

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?

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hgoel 8 hours ago | parent [-]

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.

	▲	YeGoblynQueenne 5 hours ago \| parent [-]
		Right, that's what I'm trying to understand, the extent to which models need expert guidance. I don't doubt an LLM was used, I just want to know- how.

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Izkata 19 hours ago | parent | prev [-]

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