Though it is pitched at a general audience, with a chatty tone and informal style, Meta Maths still demands a reasonably robust engagement with mathematics. Early on, for example, Chaitin presents Euler's proof of the infinity of primes using products of infinite series, even if that comes with a warning "this is the most difficult proof in this book. Don't get stuck here". But anyone familiar with Gödel and Turing's key results should find Meta Maths accessible — and a usefully different perspective.
Chaitin talks about himself and his experiences quite a bit in Meta Maths, and makes no pretence of impartiality in his presentation of the history and philosophy. This is sometimes distracting but comes across less as bombastic than as an attempt to communicate his own excitement and his emotional engagement with his subject. It's not clear that anything would be lost by removal of all the exclamation marks, though!
Note: Meta Maths seems to be a popularisation of ideas from Chaitin's book Algorithmic Information Theory (Cambridge University Press 2004).