My favorite von Neumann story involved a lecture he gave in German. At the end of the lecture David Hilbert's first question was, "That was very nice, but what are these 'Hilbert spaces'?"
The point is that Hilbert spaces were named after David Hilbert by von Neumann. Which lead to the odd situation where Hilbert didn't know what Hilbert spaces were.
I also recall a talk about the diverse kinds of people in math. One (I hope I don't misremember) was Hilbert, held up as an example of someone who could seem frustratingly dense -- he'd ask many questions during a talk. But once he started wrapping his mind around things, he could see very profoundly.
In contrast, the other was a fast calculator like von Neumann; maybe it was von Neumann. The point of the talk was that there's no single type who does good mathematical work. And the moral was that you shouldn't feel bad if you feel confused and foggy while others seem quicker on the uptake. This could also describe Hilbert, Einstein and Grothendieck.
(I hope it's clear that my knowledge of famous mathematicians is very sketchy, based on half-listened talks and random snatches from books...)
