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I have read it, now. Not all... but its quite... superficial. As it turns out, its explains Gödel just to the Hilbert Programm.
I guess, otherwise the author has to explain Cantors proof first (The diagonalization (its right in English? Diagonalisierung)) and the entire concept of meta-mathematics and Gödelization.
While the relationsship between the Girls and the MC is funny, the constellation is a bit too common. I mean, 3 Girls are into the same dude.
I think, between the Miruka and him its the most interesting, since Miruka appears to have deeper feelings but she isn't able to show it. So, she orginized a math class.
Miruka is kind of the social unfit science nerd... what is in a way hot, even if outlandish in real life.