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True, it's an achievement either way. But if an "out of the box LLM" can solve difficult math problems it is an achievement by the LLM vendor. Otherwise it is an achievement by the people doing the vertical integration.

In the context of evolving LLM this is the crucial distinction.

It matters in terms of whether it’s generalizable. We had computers do impressive specific things since decades.

Sure.

But 'purely LLM' also isn't a definition for generalizable.

The distinctions matter since computational proofs have been around for decades.