intuitively obvious

Thought by someone who knows what it is, to be completly transparent. The concept in question, however, is usually mind-numbingly difficult to comprehend. Things that are intuitively obvious are often left as an exercise for the reader. The authors of such utterances will be smoten when Armageddon comes.

(usually Mathematics:)

Something is intuitively obvious if all mathematicians, most of them, some of them or the author would expect that something to be true. For instance, it is intuitively obvious that pi is normal and that P!=NP. It is probably not intuitively obvious that Fermat's last theorem is true (nor is it obvious that it is false).

Proving that something which is intuitively obvious is in fact true might be hard; it may even be impossible for us (although for obvious reasons we have no examples of this). The depth of the intuition required varies tremendously; some things termed intuitively obvious aren't.

For obvious reasons, the phrase is somewhat notorious, and not liked by all.

In "proper" mathematical use, only axioms should be called intuitively obvious. Everything else must be proven rigorously. However, I, being a mathematician of sorts, look at a simple word problem, and think, "you just do this and the answer jumps out at you. Why can't you see it?"

Or, in problems with a little more information than is strictly required, "what do I do with this number?"
"You just ignore it! Why is it so difficult to understand that someone might give an extra number for you to worry about?!"
It can be very frustrating when someone you are trying to talk to cannot see what is intuitively obvious to you.

I never understood why word problems are so often considered the most difficult part of mathematics, when they are a step away from the abstraction that makes math hard.