There are many good things to say about this book. Its literary quality is very high. It is an emotional and thought provoking work of art. I'm sure you can find reviews elsewhere that discuss this aspect of it, and I will not deny it. However, it is the purpose of this website to focus on the mathematical aspects of works of fiction, and in that regard this book falls short. So, although I'm sure that I will later receive angry e-mail messages from people who loved the book and do not want to allow me to criticize this one failing, that is what I will do below.

The author has a very strange idea of what mathematics is and what mathematicians do. Although I suspect it stems more out of ignorance than malice, I would go so far as to say that this book slanders mathematics.

Professor Giacopo Tigor's idea of a snowflake constant seems to be something which he came up with arbitrarily, and rather than attempting to mathematically prove anything, he simply collects snowflakes as they fall and makes measurements, hoping to confirm his theory. Since he is a "Euclidean geometer" he hopes that proving his theory correct (experimentally) will restore Euclid to a place of importance in mathematics which he sees as having been undone by the new fractal geometry. In fact, mathematics is not so much of an experimental science, and it is not one in which we generally end up trying to defend our theories against opponents at conferences (as the character in the book attempts to do, unsuccessfully, prompting his flight). Two of the nice things about mathematics are that we prove our results in our heads rather than in laboratories and that there is generally agreement about whether something is proved or not. Moreover, it is not true that Euclidean geometry and fractal geometry are somehow competing theories of geometry and that the proponents of one are enemies of the proponents of the other.

Tigor's graduate student, back at U Penn, is upset by his disappearance and speaks to him a few times on the phone. If this was a website about African-Americans in fiction rather than mathematics in fiction, I would probably be writing about how the representation of this black student (who talks to his PhD thesis advisor in the most unbelievable, and rather offensive, slang) is racist, but I will leave that to others. Instead, I will bemoan the author's idea of a thesis project for a geometry student: computing the average tidal variations in the Delaware Bay for the next 25 years. The student determines that this is too difficult to do, and so Tigor attempts the problem himself, using (for no apparent reason) the formula for the Hausdorff Dimension (incorrectly referred to as "Mandelbrot's fractal equation") and factoring in "the butterfly effect".

Simple mathematical terms are used incorrectly (e.g. "isomorphism" is defined in the book as "what we call formations that are composed of structures similar to themselves"), but the general misconception of the field of mathematics is more disturbing. Especially when Tigor reviews the general state of the field as:

It is when the book says things like that, none of which I can agree with and all of which seems like an outrageous insult from someone who doesn't even know what he's talking about, that I have trouble appreciating the book as the magnificent work of fiction that it otherwise is.

Not all of the mathematical references are wrong or offensive. I like the brief discussion of Goldbach's Conjecture which occurs as Tigor unexpectedly collapses and has the hallucination that eventually leads him to look for Noah's Ark. And the discussion of Hilbert and Cantor when he and the mathematician Igor improbably meet Cantor's grandson is alright, too. However, Jungk's attempt at describing the significance of transfinite cardinals is disappointing:

It is disappointing in part because it is possible to explain this much more clearly (by bringing in Cantor's diagonalization argument), and because I do not think it is quite right as stated anyway. What he wants to say is that although there are infinitely many points corresponding to whole numbers on the number line, and infinitely many points on the line in general, the two infinities are not the same. In fact, the latter set is much larger. It is possible to explain this -- even to a non-expert -- just by introducing the idea of trying to pair up the elements of two infinite sets and I wish Jungk had tried to do that. In any case, I think it is not correct to say that the cardinality of the continuum is "infinity times infinity times larger" than the size of the set of whole numbers. Rather, if I'm remembering my transfinite arithmetic correctly, some exponentiation is required.

One thing I often wonder about while reading mathematical fiction is why the author chose to include mathematics and mathematicians in his/her writing. Sometimes it is clearly because of the author's own love of the subject, or because they have a particular mathematical idea they wish to convey. Sometimes it is because they want to immediately convince the reader that a certain character is smart, and making it a mathematician seems to do that. However, sometimes it seems to be only because the author wants to write about a character who is mentally unstable or insane. In this case, I am again left with the feeling that the reason the author wrote about a mathematician here rather than a biologist or sociologist or political scientist is the (false) stereotype which makes readers believe in a crazy mathematician more than a crazy person of some other profession.

I must admit to not having read this novel in the original German; I read the British version (called "The Snowflake Constant") translated by Michael Hofman. At a couple of non-mathematical points, the text degrades into incomprehensible nonsense, and I'm not sure whether this is a reflection of the original German or merely a mistake on the part of the translator (or typesetter, I suppose.) I'm curious to know whether any of these mathematical difficulties I've discussed above were actually introduced by the translator.