Interestingly, this guide states that the intuitive understanding of maths is only suitable at the school level but not for the university.
In his recently published book "Mathematica: A Secret World of Intuition and Curiosity", David Bessis argues that the intuition is the "secret" of understanding maths at all levels.
Not sure what conclusion to draw from here, but my (rather dated) experience with university maths tells me that the intuition is a powerful tool in developing the understanding of the subject.
I think he's saying here that intuition is sufficient for high school math, but not sufficient for college. That's not to say that it isn't necessary, only that it isn't sufficient.
Easier to do in a helmet than in a windshield, I suppose.