[gizmo686]

The math behind quantum mechanics is intuitive if you view it as a generalization of probability theory to allow negative numbers. The counter-intuitive part is that the resulting system turns out to be a good model of the world.

[medlyyy]

http://www.scottaaronson.com/democritus/lec9.html

The above is a good accessible exposition of this perspective. Though it would help to have some acquaintance with ordinary probability as well as basic linear algebra.