Of course, I had heard about this science fiction novel which is as famous for its controversial connections to the Church of Scientology which its author founded as for its literary content. (See, for example, this Wikipedia entry.) However, until I received an e-mail from Julie Willis at Galaxy Press, I was unaware that it was also an example of mathematical fiction. They kindly sent me a free copy of the book, which I have finally finished reading. So, let me run through some of the ways that math appears:

Near the beginning of the book, Jonnie is being educated by directly downloading information from disks into his brain. At first he is learning only how to read, but he picks a random disk just to see what is on it and learns that if all three sides of a triangle were equal then so were the angles. The funny thing is, because he had skipped ahead he knew this fact about triangles and angles even though he did not yet know what triangles and angles were or even what it meant for things to be equal.

There is quite a bit said about the fact that Psychlos (who have five claws on one paw and six on the other) use a base 11 numerical system. I'm not sure what would give Hubbard the idea that there's something particularly wonderful about base 10 or particularly bad about base 11, but it says things like:

In my opinion, that's nonsense, but it also isn't terribly important to the plot.

Another mathematically interesting (but not terribly important) passage concerns the evolution of the Psychlo digits from pictographs, many related to mining:

But the important mathematical aspect of the book concerns the bizarre form of teleportation on which the whole Psychlo empire was based:

It was precisely to protect this secret method that Psychlos carefully guarded all of their mathematical knowledge. Their mathematics had quite a reputation for being impossible to understand. As a non-Psychlo alien explains to Jonnie:

On page 971 of this tome, Jonnie finally learns (from a Psychlo who had been exiled for the crime of believing in souls) that all Psychlo equations are encrypted. The encryption scheme is based on the association of an integer to each letter of the Psychlo alphabet and the names of the eleven gates at the Imperial Palace of Psychlo (“Betrayer's Gate”, “Devil's Gate,” “God's Gate”, “Infernal Gate”, etc.):

A few thoughts about this:

• What a weird coincidence that the letters B, E, and T in the Psychlo alphabet are associated to the numbers 2, 5 and 20, their positions in the English alphabet (not to mention the fact that "Betrayer's" is an English word.)
• If any intelligent alien ever found some Psychlo equations for things that they already knew (like the Pythagorean theorem or Schrödinger's equation), they would serve as a sort of Rosetta Stone and it probably would be pretty easy to figure out this code in less than 302,000 years.
• As explained, the letter "B" can never be used in a Psychlo equation for anything other than "Betrayer's". Presumably, this is not true only for B but for all of their letters. Then, I wonder what they use for variables or named constants...

Keep in mind that there is a lot more to this book than math. (For example, there is some chemistry, lots of warfare, and Jonnie's clever plan to overthrow the Psychlos. And, if you read between the lines then it also expresses some of Hubbard's opinions about psychologists and governments.) As for the writing itself, it seems like very old-fashioned science fiction to me. Even though it was written in 1980, it reads like a cross between the pulp “sci-fi” of the early 20th century and the "space opera" SF from the 1950s and 1960s. If you are someone who loves that old stuff, that would be a great endorsement. But, not everyone does. So, based on your own tastes and the math-focused excerpts above, you can decide for yourself whether you'd like to read L. Ron Hubbard's “Battlefield Earth”.