> I'd argue that the mathematical operations themselves are usually not that complicated. More importantly, the whole book seems to be about ways to derive the (probable) input of a hash function from the output. It is not literally impossible.

I think you're not being pedantic enough here. "Probable" is doing some heavy lifting. And the phrasing is "derive the input," which I think is fair to say. The best you can do with a proper hash is discover one or more possible inputs, but you're not deriving them from the output; the output is just used to check the result. The many-to-one nature of a hash precludes determining the exact input.