a list compiled by Alex Kasman (College of Charleston)
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The introduction to this novel is a work of pseudoscholarship, explaining how the chapters to follow were decoded by an NSA cryptographer with the help of the author. The intro contains references to a few real mathematicians, but also a beautiful piece of "fictional mathematics" in its description of the apparent impossibility of the initial encryption and the possible interpretations. (Contrary to what it says in the liner notes, Mason is not really a professor of paleomathematics...at least not yet. However, he is the winner of a Starcherone Prize for having written this clever work of fiction.)
Note added Dec 2010: It turns out that the Introduction and Appendix which contain the mathematical fiction components appeared in the first edition of the book, printed by Starcherone Books, but not in the second edition, printed by Farrar Straus Giroux. So, depending on which version of the book you obtain, you may or may not be able to see any fictional mathematics in it (although the author claims the entire story itself has mathematical structure). If you are not able to get the right version in print, note that these wonderful pieces of pseudoscholarship can still be found online at http://replay.waybackmachine.org/20080704030502/http://thelostbooks.com/chapters.htm. We're told in the appendix that the Lost Books are quite old:
Nevertheless, Mason's NSA connection was able to determine by applying his modern techniques that the book appeared to have been encoded using fractal compression techniques. Using a clue from Raymond Lully, they are then able to "break the code" and most of the book consists of the decoded chapters themselves. The chapters of the "Lost Books" themselves are beautifully written and full of intentional confusion and anachronism. Most mathematical among them is the final chapter whose narrative line has the structure of a Möbius strip. (See also here and here.) But, since the main mathematical content is contained in the introduction, I will focus the rest of this review there. The most mathematically fascinating part of the introduction is the suggestion that the compression algorithm used to encode the book appears to be impossibly powerful by today's standards, let alone what one might have known in 800BC:
The first "interpretation" is that the story had to have been composed itself in a way that allowed for greater compression, by repeated use of elements, words, plot devices or whatever. This would have put restrictions on how the story could have been composed, but would have produced a greater compression in the end than would initially seem possible for a book of that length. This is an interesting idea, though not a mind blowing one. (For instance, I already know from experience that I can affect the size of the pictures taken by my digital camera by composing it carefully and avoiding the fine details or frequently changing patterns that would not compress well.) The second "interpretation" is a bit more interesting: that they have not decrypted the books at all, but rather have merely imposed structure on the noise. This would be a bit like the facilitated communication controversy (where the facilitators appear to have been actually creating the messages from the people they were supposed to be interpreting) or like an algorithm that appears to produce an interesting signal that turns out to have actually just been a consequence of numerical approximation. But, my favorite is the last "interpretation". It is suggested that the book may be able to have been compressed so compactly because it actually arises naturally as a mathematical structure. For instance, although the decimal expansion of the number π is infinitely long and contains no recognizable patterns, we can compactly write down an algorithm which would produce those digits. The introduction even names a movement of philosophers (including Kurt Gödel) who believe in such "hidden messages":
This immediately reminds me of Carl Sagan's Contact in which a hidden message is found in the number π. In addition to Gödel, the introduction briefly mentions Alan Turing as the subject of another coded message that Mason dealt with in preparation for the lost books.

More information about this work can be found at www.amazon.com. 
(Note: This is just one work of mathematical fiction from the list. To see the entire list or to see more works of mathematical fiction, return to the Homepage.) 

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Exciting News: The 1,600th entry was recently added to this database of mathematical fiction! Also, for those of you interested in nonfictional math books let me (shamelessly) plug the recent release of the second edition of my soliton theory textbook.
(Maintained by Alex Kasman, College of Charleston)