The Lost Colony (Artemis Fowl, #5)

Ten thousand years ago, humans and fairies fought a great battle for the magical island of Ireland. When it became clear that they could not win, all of the faeries moved below ground—all except for the 8th family, the demons. Rather than surrender, they used a magical time spell to take their colony out of time and into Limbo. There they have lived for decades, planning their violent revenge on humans.

Now the time spell is unraveling, and demons are beginning to materialize without warning on Earth. If humans were to find out about them, all faeries would be exposed. To protect themselves, the faeries must predict when the next demon will materialize. But in order to do so, they will have to decipher temporal equations so complicated, even a great brain like Foaly can't understand them. But he knows someone who can: Artemis Fowl.

So when a confused and frightened demon imp pops appears in a Sicilian theater, Artemis is there to meet him. But he is not alone. Someone else has unlocked the secrets of the fairy world and managed to solve complex mathematical problems that only a genius could. And she is only twelve years old...