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Comment by lg5689

LLMs are indeed very special compared to past efforts at automated theorem proving. The search tree for proofs is enormous, even short textbook exercises (i.e. a few dozen lines of Lean) were difficult with GOFAI techniques. Adding a few orders of magnitude to your compute budget barely moves the needle, since the search space increases exponentially for every line of the proof.

Now LLMs have produced multi-thousand line Lean proofs. This is impossible by simply "try everything and see what sticks". LLMs are able to target their efforts to only promising proof strategies. Yes it helps that they work at superhuman speed, so they can try thousands of strategies where a human might try a dozen. But their results cannot be explained only by compute increases; they need genuine mathematical insight.

parent lg5689 2 months ago

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