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Rating: 
Summary: Not a modest man but why should he be?
Review: ...reasons that I rated this a 5 star read.Firstly I agree that Chaitin is not a modest man. I don't think that really matters, because he has made a major contribution to my understanding of this whole area which previously I had found almost impenetrable. The only other criticism I had is the excessive use of the exclamation mark! In all other respects this is a superb book. I found the chapter introducing LISP a little dense (much like me) but I read a book called "The Little Lisper" which is a great book in itself and that helped me. The real beauty of this book for me was working through the various LISP exercises and beginning to understand, to feel almost, the logic and concepts behind the work of people such as Godel and Turing. In other words I felt able to walk for a while in the footsteps of geniuses - and I would count Chaitin among that number. END
Rating:
Summary: Modesty not a strong suit - but then why should it be...
Review: Chaitin is not a modest writer, but then given his personal contribution to the field he discusses here, there's no reason why he should be. This book is not an easy read for the layperson (I know, I am one) but does reward perseverance. The beauty of "The Unknowable" is that it allows the reader to understand the points Chaitin makes by working through the important proofs by famous thinkers such as Godel and Turing (and ,of course, Chaitin). It's a great feeling to walk in the footsteps of giants such as these - and to understand the conlusions rather than accept them as received wisdom. My only reservation is that the chapter introducing the reader to LISP is fairly dense and tough to follow. However I found that reading the first couple of chapters of Friedman and Felleisen's "Little LISPer" made it more comprehensible - and LL is a great book anyway. I'd thoroughly recommend this book to readers with an interest in the Philosophy of Mathematics who do not necessarily have an in-depth mathematical background.
Rating: 
Summary: More annoying than amusing
Review: First the good part about this book. Chaitins first chapter is quite good. Here he outlines the results of Godel, Turing and his own. It is very readable. Without going into the real mathematics he can really make you feel you understand these deep ideas. The later chapters go more deeply in to the ideas presented there and illustrate them with lisp computer programs. Especially the search for lisp programs that evaluate to themselves is amusing. But let's now focus on the parts of the books that I did not like. His exposition is mixed with an account of how he first learned these result. I am charmed the first time when he explains how he read so many books as a kid. But soon I do not want to hear again what he felt as 12 year old. Also he keeps comparing his own work to that of other scientist. We really need to now that he is just as good as Godel and as Turing.
For example he takes pages to explain that Kolmogorov ripped of his ideas. What I also find funny as well is both chapter 1 and chapter 6 give an identical link to "my first major paper". Sigh. He's the best, we get it, ok?, now please move on. Then one more thing. The computer programs that he uses are in lisp. That is fine by me, lisp is a beautiful language. But do you think he uses any of the available dialects? No, of course not, he introduces he own strange version. The programs given do not run in clisp for example. So to sum it up. I learned his own result on incompleness (that one cannot produce the shortes program for a particular function) and that is a nice result. Reading the rest of the book is more annoying than amusing.
Rating: 
Summary: A Complete Waste of Time
Review: I checked out this book from the library with high hope. It turned out to be a complete waste of time. The only purpose of this book is to claim that the author is as great as Godel and Turing. The reason? Unknowable.
Rating:
Summary: Future Classic - Beautiful Ideas
Review: In the 21st century mathematicians will debate the meaning of Chaitin's theorems just as we now debate the meaning of Godel's and Cantor's theorems. We have a rare opportunity here to read the author's interpretation. This book is wonderful. It is, by far, the most polished and most readable of Chaitin's publications. Much of the value of this book comes from the terse LISP proofs, which can be appreciated for their beauty and craftiness. The reader must not only read the proofs but also run the proofs. This can be accomplished by downloading the author's LISP interpreter applet. If you like Hofstadter's GEB you'll love this book but you'll come out of it with a much more optimistic outlook. Hofstadter believes that man is just a machine. I don't think Chaitin shares that view. I know that Godel didn't share that view. Nevertheless, parts of mathematics are beyond our understanding. We have gotten use to the idea that there are true propositions that can't be proved. Chaitin defines numbers, like omega, that can't be known. But this means that there is no end to mathematics. It is optimistic because it means that theorems that have been proved and numbers that are known are all the more interesting. If something is unknowable well then it's just unknowable, but if you can know that it's unknowable then that's really remarkable.
Rating:
Summary: Save your money
Review: This Book is horrible. The only point of the Unknowable is to prove that Chaitin is as smart as Godel and Turing. The entire book can also be retrived off his homepage. If you want to have a good overview of this topic buy Limits of Mathematics by Chaitin.
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