In a recent post, Cole Wyeth makes a bold claim:

. . . there is one crucial test (yes this is a crux) that LLMs have not passed. They have never done anything important.
They haven't proven any theorems that anyone cares about. They haven't written anything that anyone will want to read in ten years (or even one year). Despite apparently memorizing more information than any human could ever dream of, they have made precisely zero novel connections or insights in any area of science^[3].

I commented:

An anecdote I heard through the grapevine: some chemist was trying to synthesize some chemical. He couldn't get some step to work, and tried for a while to find solutions on the internet. He eventually asked an LLM. The LLM gave a very plausible causal story about what was going wrong and suggested a modified setup which, in fact, fixed the problem. The idea seemed so hum-drum that the chemist thought, surely, the idea was actually out there in the world and the LLM had scraped it from the internet. However, the chemist continued searching and, even with the details in hand, could not find anyone talking about this anywhere. Weak conclusion: the LLM actually came up with this idea due to correctly learning a good-enough causal model generalizing not-very-closely-related chemistry ideas in its training set.

Weak conclusion: there are more than precisely zero novel scientific insights in LLMs.

My question is: can anyone confirm the above rumor, or cite any other positive examples of LLMs generating insights which help with a scientific or mathematical project, with those insights not being available anywhere else (ie seemingly absent from the training data)?

Cole Wyeth predicts "no"; though LLMs are able to solve problems which they have not seen by standard methods, they are not capable of performing novel research. I (Abram Demski) find it plausible (but not certain) that the answer is "yes". This touches on AI timeline questions.

I find it plausible that LLMs can generate such insights, because I think the predictive ground layer of LLMs contains a significant "world-model" triangulated from diffuse information. This "world-model" can contain some insights not present in the training data. I think this paper has some evidence for such a conclusion:

In one experiment we finetune an LLM on a corpus consisting only of distances between an unknown city and other k

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