The Eight reminded me a lot of G"odel, Escher, Bach: An Eternal Golden Braid by Douglas Hofstadter in that it touches upon a lot of self-referential "strange loops", like the Fibbonacci series, Bach's music, the Moebius strip (the symbol for infinity and the number eight), to name a few. Like with Hofstadter's book, it's also extremely metaphorical in nature and both books borrow from Lewis Carroll. Most importantly, Hofstadter's book was primarily about the concept of coding (the device used ingeniously by Kurt G"odel to prove his famous incompleteness theorem) and that concept permeates The Eight.
Catherine Velis is a financial computer expert in a boy's club. When set steps out of line, she's sent to Algiers as "punishment". She soon realises that she's really a pawn in a big chess game where the stakes are incredibly high. The other players in the game are also assigned to respective chess pieces, and the object is to uncover the secret encoded in the Montglane Chess Service, once owned by Charlemagne and possessing a potential for incredible power. As Catherine goes about her journey, the parallel path taken by Mireille de Remi, a young girl struggling to survive in the heart of the French Revolution, is also depicted. The climax in the story occurs when their paths intersect.
The reason I compare this book to Hofstadter's classic is because the latter is in my view the most natural extension of the curiousity that The Eight invokes in you. (I consider G"odel, Escher, Bach to one of the greatest books every written and one that has profoundly influenced my research and my philosophies.) Hofstadter's book was a much more serious work into the nature of the Universe while Eight is mostly interesting as a work of fiction. While I read G"odel, Escher, Bach long before I read The Eight, if I were starting all over, I'd probably do it the other way around.
Other interesting aspects about this book include the fact that the whole plot is structured based on a famous chess game (again, similar in spirit to In Through the Looking Glass); the use of real historical people as characters (Rousseau, Voltaire, Talleyrand, Napoleon, to name a few); the use of strong females as the primary protagonists (something I always get a kick out of); and the perspectives of different characters which tell the tale of how they come in contact with the Montglane Chess Service. There has also been an interesting side effect: while I appreciated it before, it is only after reading The Eight that I've come to realise the genius in The Simpsons' Stonecutters episode.