What are some interpretations of Von Neumann's quote? John Von Neumann once said to Felix Smith, "Young man, in mathematics you don't understand things. You just get used to them." This was a response to Smith's fear about the method of characteristics. 
Did he mean that with experience and practice, one obtains understanding? 

Poincare once wrote that all of mathematics is one plus one equals two, and a lot of definitions.  Speaking as a physicist, I believe the most important thing to understand about mathematics is whether those definitions are useful in describing reality (i.e., observations). I don't believe mathematicians are similarly concerned, though certainly von Neumann himself is a most prominent counter-example.
Just to be provocative, I have found Newton's calculus to be sufficient for my needs and have never understood \delta -- \epsilon proofs.  There seems to be no place for "infinity" in physics. On the other hand, nonstandard analysis has proven quite useful to me.
