I cannot recommend On Numbers and Games by John H. Conway enough. He demonstrates the surreal numbers by proof which is a wonderful introduction to proofs. The

I cannot recommend On Numbers and Games by John H. Conway enough. He demonstrates the surreal numbers by proof which is a wonderful introduction to proofs. The latter section of the book is highly entertaining. He also worked on cool stuff in the sphere-packing problem: http://www.amazon.com/Packings-Lattices-Grundlehren-mathematischen-Wissenschaften/dp/0387985859 http://www.amazon.com/Packings-Lattices-Grundlehren-mathemat... I really appreciate is writing and teaching style. He likes to bring his readers and listeners up to his level.