|With parents and a younger brother who are all "mathematical geniuses", Livey Ell (who is in danger of getting kicked out of cheerleading unless she improves her algebra grades) is a bit too normal. Things get out of control when her brother's computations brings Bob, a mathematical creature from Hilbert space, to life.
This science fiction novel aimed at a young adult audience includes brief discussions of the Riemann Hypothesis (perpetuating the myth that it would somehow be upsetting if zeroes of the zeta function were to be discovered off the critical line), Hilbert space, Pythagorean cults and fractals (in the form of a "fractal sword"). Additionally, there are religious overtones to the story which develop when some of the characters are discovered to be angels and/or demons.
The author knows quite a bit about mathematics (he insists that the highpoint of his mathematical education was truly understanding the definition of the limit in calculus, but has clearly read a lot of popular mathematics since then), and so much of this rings true. He includes some famous mathematical jokes and anecdotes and presents characters that (while stereotypical) reflect some knowledge of the mathematical community. I don't think he knows what a Hilbert space is (besides that it is a cool sounding name), and suspect his notion of "the Hilbert space of all Hilbert spaces" does not even make mathematical sense. (What would be the inner product of two Hilbert spaces? I seriously doubt it would be complete under any reasonable definition.) But, that doesn't prevent the book from being fun and worth reading.