As a mathematical dude, I am remarkably impressed with the
WolframAlpha iPhone app.
This is my much loved Mathematica book. It's 1470 pages and I use it as a doorstop. It weighs about 2.8kg.
It's big because it has a lot of stuff to explain. Like 3D plots, say.
This, obviously, is an iPhone. It weighs 135g.
Yes I am working on the book. I was trying to evaluate "Integrate[Ei[x]*Exp[-x],{x,0,1}]" for a proof I needed. Ok the iPhone version doesn't give you quite the power of the full web browser or a local instance of Mathematica, but it's pretty darn impressive.
Oh and the integral comes out to γ-Ei(1)/e ≈ -0.119959...