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Pi in the Sky
One problem with popular mathematics books is that they all tend to deal with the same few subjects - incompleteness, codes, 'Game of life' etc. and to some extent Pi in the Sky follows this path. However, it does have some interesting material on L.E.J. Brouwer, which would be useful for those who want to find out more about intuitionism.
One criticism I have of the book is that Barrow believes in too strong a form of undecidability, for instance his claim that it is never possible to know if a computer program is the shortest one possible for it's task - this just isn't true.