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The book turned out slightly different than expected: From the title, I had assumed to find a list of things that "we can never know", and -- being a follower of Hilbert -- I was more than sceptical.
Instead, the author delivers what in another genre would have been a collection of anecdotes: more or less disjointed facts, all in some way connected to limitations of understanding. There are classic paradoxes, Gödel's incompleteness theorem, NP-hardness, and the halting problem. There are some metaphysical questions as well as the more counterintuitive aspects of quantum mechanics. In the end, all of this is stuff that an educated person should know about, there's very little that,'s truly unknowable: the paradoxes conjure up situations that are actually impossible; quantum mechanics is, for the most part, well understood (it just doesn't agree with common sense): and undecidability and infeasibility in computer science pertains to general problems only -- deciding the halting problem for a given program can actually be quite doable. And even Gödel might be circumvented with extra axioms.