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I have taken the survey. Thank you Yvain for running it.
False. Criticism and optimization overlap highly in the nature of the reasoning but it is possible to construct an optimizer that is not capable of criticism. If you really want one. I'm not sure what exactly Harry's intended human-level practical point is---some applications apply even though the claim is technically false but some may not.
I believe his human-level point is that if you are unable to find a problem with a current system, you will believe optimising it is impossible.
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What examples can you give of books that contain discussions of advanced (graduate or research-level) mathematics, similar to what Greg Egan does in his novels (I suppose the majority of such books are hard sci-fi, though I'm not betting on it)? I'm trying to find out what has already been done in the area.
There's this in mathematics. Also, this website might be a good place to look, though most of its examples seem less advanced than what you are looking for.