The many well known facts about the lives of Gödel (a friend of Einstein whose most famous result was a shocking demonstration that mathematics is not as powerful as many had believed) and Turing (most famous as a principle inventor of the digital electronic computer and a war hero for his work in breaking the German code during WWII, but also known for mathematical work including a version of Gödel's incompleteness theorem for computers -- the halting problem -- and early work on pattern formation with applications to biology) are intertwined into a story, with fictional details added liberally and the author added as a character to tie it all together.

From an artistic point of view, I was troubled by much that the author chose to do. Including the author as a character in the book is a technique that has been used successfully in the past, e.g. Cervantes appearing in Don Quixote and Kurt Vonnegut in Breakfast of Champions. However, I was not sure what it did here other than to distract from the two main characters. Presumably, adding the author -- who is herself a physicist -- makes the book about three scientists rather than two, a triangle, and she serves to tie them together. But, in fact, the characters of Gödel and Turing are so well contrasted in the story (with sufficient emphasis on both their many similarities and startling differences) that I did not feel this was necessary. Moreover, the frequent mention of apples and "Snow White" (foreshadowing Turing's suicide by poison apple) quickly became tiresome to me.

But, I don't want to dwell on this because I really did like the book and would like to recommend that people read it. What I found most interesting is what the book really seemed to be about! The previous reviews I have read and the blurbs on the jacket did not mention the importance of the questions of the existence of God and the existence of mathematics to the novel. Perhaps this is because these topics were to controversial to advertise, or perhaps it is because I am alone in thinking this...but I really think that what the book did was to contrast the viewpoints of these two mathematicians on these topics.

The book emphasizes (in my opinion, over-emphasizes) the similarities in the "quirkyness" of these two men. Rather than being an introverted man whose paranoid tendencies came into full bloom in his old age, Gödel is presented as being completely paranoid the entire time. And Turing, whose shyness I had always attributed to a reasonable fear of being recognized as a homosexual in a very intollerant society, is presented here as being a highly functional autistic. Certainly, there is no doubting that neither Kurt nor Alan was your typical "party animal", but the book takes this beyond what I think was the case. Reasonable artistic license? Perhaps. It certainly helps in setting up the similarities between the two...right down to the fact that both of their eventual deaths were tied to eating -- well, not eating in the case of Gödel.

But where the book really gets interesting is when it contrasts their world views. It was not just a matter of Turing's view being "mechanical", as the cover suggests. More importantly, it is about the nature of existence. As Goldstein argues in her wonderful (non-fictional) Incompleteness, Gödel interpreted his famous theorem as being proof that mathematics has an existence outside of the human mind...that it is some sort of alternate reality which we can partially perceive but had no role in creating. Similarly, Gödel had a belief in a deity that we could only partiallly perceive and did not create. In contrast, Turing's atheism is clearly (and very well) presented in the story. To him, God is something that humans created. Moreover, I think it is supposed to appear that Turing also believes that mathematics is something that lives in the human mind and not that it is some other universe with an independent existence. However, I am not as certain about this because this viewpoint seems to be less well represented.

Certainly, it is the case that some mathematicians are Platonists, believing that mathematics "exists" independently of human thought and others view it as being a human construction that is beautiful, interesting and extremely useful, but not "real" in the sense that the moon is real and existed before humanity. Often, discussions about this topic can become extremely emotional. (I love the scenes in Levin's novel where Turing and Wittgenstein argue about this in class.) Moreover, it is true and ironic that people with extreme views on this subject (in both directions) often point to Gödel's theorem as evidence that they are correct. (Apparently, this theorem does not help resolve the question after all.)

Janna Levin is a professor of physics at Columbia. Therefore it is not surprising that her knowledge and understanding of mathematics is excellent. I only object to one thing in the book from a mathematical point of view, but it is something that was repeated a few times and so I would like to mention it here. The book states that Gödel's theorem shows that there are true statements of arithmetic that cannot be proven mathematically. I would argue (though I admit some would debate me) that this is not quite accurate. What he actually showed is that it is either true that there are undecidable statements or that mathematics is inconsistent (i.e. that it contains actualy contradictions). That the latter alternative is ignored by some is evidence of their faith in the consistency of mathematics. Gödel had faith in mathematics just as he had faith in God, but such faith does not serve as proof to others.

Well, I've really got to stop writing because it is time for me to go teach a class. Let me just wrap up quickly by saying that I unquestionably recommend this book to anyone who does not already know the stories of these two "characters". But, more surprisingly, I would also recommend it to those who think they've already heard enough about Alan and Kurt. Even jaded readers like me may be able to find a few worthwhile insights in this well-written work of historical fiction.