Although this description may sound so over-the-top as to have entered the realm of parody, the author apparently intends it to be taken seriously. Not only do I not think readers are supposed to find these fictional excesses funny, his afterword suggests that he expects the reader to take the existence of these giants seriously as well. Perhaps some readers will happily follow where Ochse leads them, but I was not able to suspend disbelief or enjoy this book despite the references to algebraic geometry.

Following the example of The Da Vinci Code, many works in this genre include some obscure references to mathematics that are tied into the conspiracy. Indeed, McCloud is described as being an unemployed math teacher in the very first sentence of the book. However, the mathematical content of the book is in a subplot which essentially only intersects the primary plot through analogies. McCloud's master's thesis concerned the Hodge Conjecture, a real open mathematical problem in algebraic geometry. The fact that we do not know whether the Hodge Conjecture is true or false is explicitly compared in the novel with the fact that the characters also do not know whether Biblical giants actually walked the Earth. Moreover, (spoiler alert), McCloud makes progress on proving the conjecture and even writes to the Clay Institute to claim the million dollar prize.

The Hodge Conjecture is really rather technical and difficult to explain. One first has to have the idea of what an algebraic variety is and what it's subvarieties are. That, I suppose, is not too difficult to state loosely for people since a variety is a sort of geometric object and hence one can picture some surface or solid object and subvarieties are little pieces of it. That doesn't address the algebraic nature of a variety but it is a reasonable approximation. Then, one also has to talk about cohomology, which is an algebraic structure associated to the geometric object that captures information about its topology (e.g. the existence of "holes"). The cohomology is made up of objects called classes. The conjecture itself is even more obscure, as it is the statement that certain specific classes from the cohomology of the whole variety can be made (by linear combination) out of the cohomology classes of the sub-varieties.

Precisely because this conjecture is so difficult to state in an understandable way to the "uninitiated", its inclusion in the book was a strange choice for Ochse to have made. Based on the reviews I have seen, many readers who don't know math were annoyed by the long passages about the Hodge Conjecture that they could not understand. Unfortunately, those who do know math well will not appreciate these passages either since Ochse gets it so wrong. He makes a big deal about the fact that McCloud has the Hodge conjecture tattooed on his body, but the formula shown in the book is not the Hodge conjecture! (The formula that McCloud has on his chest is just a decomposition that is known to be true for Kähler manifolds, not a conjecture and certainly not the Hodge Conjecture. The author presumably spotted it in the Wikipedia entry on the Hodge Conjecture and incorrectly assumed that it was a statement of the conjecture.) His attempt to describe the content of the conjecture in words is terrible:

And, McCloud's method of "proving" the conjecture is particularly unsatisfying as it seems more like a poem than a mathematical proof:

I have some appreciation for the author's attempt to address epistemological questions using the conjecture as a metaphor. To what extent should the characters believe in the giants when they do not yet have conclusive proof of their existence? Indeed, a mathematical conjecture provides a good model for that. However, contrary to the implications of the book, mathematicians do not generally decide to believe that a conjecture is true or false. Perhaps a few do, but for the most part we simply accept the fact that the truth value of a conjecture is unknown. (This runs contrary to the popular stereotype that mathematicians are incapable of dealing with uncertainty or ambiguity. I would argue that we are actually quite good at dealing with those things!) But, the Hodge Conjecture is not the only theoretical object that the book uses in this analogy. It also mentions M-Theory. In my opinion, that analogy serves the desired purpose much better; the use of "M-Theory" in string theory is somewhat like McCloud's pursuit of evidence to support his belief in the race of giants.

Even though this book is not to my taste, there clearly are other people who loved it. If you read this book and can explain why you do like it, especially if your appreciation of it is linked to its mathematical content, then please write to me to let me know and I would be happy to post your comments here.