Intuition is very often a direct result of experience--- I still remember my math professors all chanting various mantras about training my 'mathematical intuit

Intuition is very often a direct result of experience--- I still remember my math professors all chanting various mantras about training my 'mathematical intuition' and over the years, I'd have to agree with them. I don't think in terms on one versus the other, if you are not using both, something is wrong. Easy to understand if you don't have any intuition, but if you do and you ignore it for the sake of 'rationality', I'm not sure that would in fact be rational! We get our ideas from a lot of different places, some more off the wall than others--- once we have them we can examine them and proceed or discard based on some presumably rational evaluation. Is intuition as valuable as rational thinking? You betcha!