A learned idea is equivalent to a new idea. Both have been created and criticized in the mind.

But it’s not exactly the same. Because in certain proofs (e.g., zero-knowledge proofs) the verifier does not have to go though the prover’s thought processes.

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The results from Anthropic study: participants in the AI group finished faster by about two minutes (not statistically significant), yet on average, the AI group also scored significantly worse on the quiz—17% lower, or roughly two letter grades. The high scorers (65%+) did something different: some generated code first, then asked follow-up questions to understand what they’d produced; others requested explanations alongside the code; the fastest group asked only conceptual questions, then coded independently while troubleshooting their own errors.

In short, you have to understand what’s been done.

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