The four vertices of an unlikely love "rectangle" are (a) a dying, maverick cryptographer, (b) a pregnant Internet wiz, (c) a romantic middleaged Greek archaeologist and (d) Turing, an artificially intelligent computer program with the personality and memories of mathematician Alan Turing. The primary mathematical content comes in the form of lectures on the history and philosophy of computation that Turing gives to the archaeologist. Though I will offer a few minor complaints below, I must admit that these lectures are excellent and that they are included in a very clever way in an emotionally powerful work of art. As an anonymous site visitor has said, this is...
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Anonymous
A true masterpiece!

I am embarrassed to admit that I have not gotten around to actually reading and reviewing it here until six years after its release!
Authors love to bring Alan Turing back from the dead, and though the computer version of him in this story is too miraculous to believe, it is such a wonderful fantasy that I found myself able to suspend all disbelief in regards to this aspect of the story. Some other technological aspects, such as the virtual affair between the vertices (a) and (b) and the farfetched idea for the original purpose of the ancient Greek computing device, were harder for me to accept.
The inclusion of an appendix made up of email messages exchanged by readers of an early version of the book may have seemed very "Web 2.0" at the time, but I think it is not as useful as a true set of author's endnotes would have been.
The author, being a computer science professor at UCBerkeley, knows his math well. Unlike many other books of this type, this one does not contain any mathematical errors that I can warn the reader about. However, I was a bit disturbed by his claim that the mathematics of calculus was not justified by proof until the development of nonstandard analysis. (If he is right about this, then I wonder what I have missed in the "Advanced Calculus" class I just taught in which we seem to have rigorously derived all of the main theorems from a set of standard axioms for the real numbers!) Also, some of Turing's lectures, while technically correct, are a bit too clever for their own good and may confuse readers who are really learning the material for the first time. (For instance, his attempt to avoid Cantor's diagonalization proof and instead discuss the more general idea of paradox does not strike me as didactically wise, as the discussion in the appendix seems to confirm.)
But, despite these minor complaints, the book is generally right on target, and when it is it is great! In particular, the lectures on the origins of "proof" (from a Greek perspective), of computability/provability (from a computer science perspective), of price equilibria, and on the deeper implications of Euler's work on the Bridges of Koningsburg are all fantastic. And, they are woven into a story involving love, death and birth that literally gave me the chills. Highly recommended! 