Some nice quotes from Satoshi Nakamoto's 2008 white paper.
On the goal:
What is needed is an electronic payment system based on cryptographic proof instead of trust.
On mining difficulty:
The work required is exponential in the number of zero bits required, and can be verified by executing a single hash.
On incentives:
[An attacker with majority CPU power] ought to find it more profitable to play by the rules, such rules that favour him with more new coins than everyone else combined, than to undermine the system and the validity of his own wealth.
Beautifully written paper.