Read Greg Egan's collection of short stories - Luminous. Greg Egan's book Permutation City is probably one of the best novels ever to look at "copies" - human intelligences running on computer systems.
Luminous has some great stories. A lot have a mathematical feel. Probably the best concerns what happens when mathematicians discover that simple maths "breaks down" at very large numbers, 2+2 no longer equals 4. Egan has to be one of the best SF writers around, combining great ideas, avoiding space operatics, and a wonderfully rich use of language.
***Imported from old blog***