"Intuition is the root of all superstition." E.T. Bell
I've pointed out how understandind abstraction shows the the commonalities and differences between all knowledge. The differences come from whether we want to be vague or not. As the video below this 'quote for the day' points out, the foundations of mathematics . . . really all the way to the early 1800s with the non-euclidean geometries . . . have become problematical. The different schools that have sprung up after 1931's publishing of Kurt Godel's incompleteness theorems don't necessarily address the issue of conception of mathematical concepts. But, occasionally, mathematicians do wonder about the issue. They often use the word 'intuition' for the idea that sometimes mathematicians don't understand where and how they get their mathematical concepts.
The use of intuition by the mathematicians here is a far cry from the way the supernatural religious use vagueness(see my logical disproof of the existence of god post way down(7/12/11) to keep from being disproved. Mathematicians just point out there is vagueness as a placeholder till they can give rigorous conception of the problem.
Of course, we come from ignorance, and sometimes people are born to it and don't like change.