The Wild Numbers

There aren't all that many novels that feature mathematicians as central characters. Furthermore, in the novels that do exist the main character's involvement with mathematics, while important, is often not on center stage, not the main issue. Philibert Schogt's The Wild Numbers, like Apostolos Doxiadis' Uncle Petros and the Goldbach Conjecture, is a novel specifically about mathematics and about how it affects the lives of those who dedicate themselves to it. While Doxiadis focuses on mathematics as an obsession in the life of a brilliant mathematician, Schogt chooses to write his story at a more human level, telling us about a crucial moment in the life of a more typical mathematician.

Right at the start, Isaac Swift describes himself as a "mediocre mathematician." He imagines that description of himself in the mind of a rival, Larry Oberdorfer, whose major crime is having been Isaac's teaching assistant and then turning out to be more brilliant than his elder. While Isaac says that this is what the believes Larry thinks of him, it is clear that Isaac himself thinks much the same. In fact, Isaac's self-image as a weaker and unimaginative mind is a constant presence in the book, casting a pall over the action at every point. Even at his moment of highest confidence, when he is convinced he has just solved a famous open problem, Isaac seems to continually expect the sky to come crashing down upon him... which, of course, it eventually does.

The book opens with Isaac biking down to the University, picking up a copy of a momentous paper he has just written, and receiving confirmation of its value from the elder statesman of the department. Then a small crisis develops, involving a cranky older student who is perpetually presenting the mathematics faculty with proofs of various famous conjectures. This student accuses Isaac of plagiarism, is generally ignored, and sets the stage for Isaac's musing about how we came to this place. What follows is a 100-page flashback describing Isaac's life, his difficulties with women, his stalled mathematical career, his difficulty in dealing with this crank, and his recent victorious attack on the "wild numbers problem," which is supposed to be a famous number-theoretical conjecture.

Will Isaac be able to beat the accusation of plagiarism? Is his proof really correct? What will be the effect of all this on his life? It's a short book, so all of these questions are quickly answered, largely in a satisfying way.

The book reads well overall, but it does have a few flaws. The subplot involving the crank accusation seems to be mostly a concession to the reader for whom the mathematical and personal stories are insufficiently interesting --- in fact, for exactly the kind of person the author takes to task at various points. The whole thing is creaky and contrived, and requires that everyone take this standard-issue crank far more seriously than one would expect.

Equally bothersome is the fact that the novel lacks almost any sense of place. All we know about the town where the story is set is that the local newspaper is called the Chronicle and that there is a (small, it seems, since the Mathematics Department has only eight members) university there. There are offices at the university, and Isaac and his friends have apartments (which suggests a big city rather than a town), but none of it seems to really come together to tell us what kind of places these are. Is all of it set somewhere in Europe? It sometimes seems that way, but then other hints say it's set in the United States, and we are left with confusion.

Finally, there are many annoying little slips that reveal that the author is not a mathematician. Isaac is going to send his paper to a journal called Number, and one of his colleagues calls the editor to arrange for the paper to appear in the next issue. It seems that Number, though it is the most prestigious journal around according to the book, does not engage in peer review!

Similarly, Isaac is teaching "Algebra 101" to, it seems, mostly first-year students, but when we get to see a glimpse of him actually teaching the class, there is talk of "quaternions and octonions" and a confusing bit about being unable to prove a group is commutative because he has not "defined the element of unity." (I presume this means that he has not properly defined or fixed the identity element of the group, but how that might keep one from proving a group is commutative I can't figure out.) Well, perhaps in this mythical city first-year undergraduates are a lot brighter than they are where I come from...

The actors in the various Star Trek movies and TV programs often have to say things that mean nothing to them because they are references to future technology and science. They call this material "technobabble." There is a lot of "math-babble" in this book. The author tries hard to make it sound right, but isn't always successful, though perhaps he succeeds often enough for the main point to get through.

On the other hand, there are many moments when the author gets it just right. For example, at one point Isaac decides not to go to a party because he cannot face "the prospect of yet another woman's smile fade with the word 'mathematician'." The descriptions of Isaac's obsessive behavior when in the grip of a mathematical idea are also convincing, particularly one involving a night out with a girlfriend. And the crucial moment of the book (which to my mind is the one that follows the resolution of the crank's accusation of plagiarism) is also quite well done and affecting.

After the book is finished and put down, one sees that all of Isaac's story is lived under the shadow of what one might call the "Hardy myth," the view of mathematics and mathematicians put forth by G. H. Hardy in his A Mathematician's Apology. The Hardy myth states that only the best mathematicians count, that only young men ever do creative and valuable mathematics, and that proving new and significant theorems is the only valuable thing a mathematician does. This is an influential view, both within the mathematics community and among well-informed outsiders. For most of the book, Isaac lives under this decree, and he has weighed himself and found himself wanting:

As for me, I had given up hope. When you are thirty-five, which is already quite old for a mathematician, and still "numberless" as we call it [meaning not having published a paper in Number], you are well on your way to everlasting anonymity, never to be quoted and always to be seated somewhere at the back at conferences, assuming you manage to scrounge together the funds needed to attend in the first place (page 14).

There are all too many people in the mathematics community who see themselves this way, and it is too bad. It's hard to tell whether Schogt himself believes in the Hardy myth. In any case, one can read this book as an attempt to ask how one can live under such conditions, an attempt to get beyond the Hardy myth to a more humane (and more true) view of what being a mathematician is all about. Schogt's answer may not be completely satisfying, but the fact that he sees the problem and attempts an answer makes his book worthwhile.

For more on fiction related to mathematics, check our Alex Kasman's Mathematical Fiction web page.