The Claude C Compiler illustrates the other side: it optimizes for passing tests, not for correctness. It hard-codes values to satisfy the test suite. It will not generalize. Property-based testing would likely catch this particular case, but the general problem remains: for any fixed testing strategy, a sufficiently adversarial system can overfit to it. A proof cannot be gamed. It covers all inputs by construction.
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On the last day, we were scheduled to give a final report, and wanted to walk our point of contact around. What we did was not magic, but we did place business cards in places where we broke in: The boss’ office, the archive, and several other places. They were not our business cards, but those of our colleague, so it would be an awkward conversation to have.