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I would think this type of behavior (ugh, or dare I say default mindset) by consumer-facing LLMs will always be desirable for ‘hard’ problems (things previously unsolved) because it’s a bit like having saftey mechanisms in place to prevent hallucinations for users incapable of verifying correctness of the output. You’ve got to do a little work to prove you understand that it’s hard but it’s still something the LLM might be able to accomplish.

I think this is also a healthy mindset for a person to have in many cases. If my boss asks me "go solve P = NP", as extreme example, I would also give some pushback.

I spent about a month walking through proving something with Claude a few months ago and it _constantly_ told me that it was impossible and I should stop working on it, right up until it proved it.

It will likely burn a lot of tokens, take a long time, and might not work, so hopefully they'll still ask if you really want to spend the money on the attempt.