I read logicalee's comment as a reference to the way most (all?) branches of mathematics may be built using sets and their axioms. Set theory boils down to "in the set" and "not in the set", ie. black and white.
This is not entirely true. There are many proofs that begin by assuming CH. There are also two ways of interpreting "need CH to prove". One way is that the thing you are trying to prove is equivalent to CH, which is an interesting/useful result. Another way to interpret it is that you can not come up with another way of proving it. In the latter case, the CH based proof justifies that your proposition is not inconsistent, and may even lead you (or others) to proof that it is true regardless of CH. If I recall correctly some statements have been proved by proving the statement when CH is true, and also when CH is false.
And when you're math as a human endeavor, you can also add "provable but not yet proven" and "proven independent"
So, learn some stuff, see how far from black and white higher math can be.