[gaze]

I think just as much as it's important to have intuition is to have a healthy relationship with your intuition. Knowing when to trust it and when not to. Intuition often happily leads you very far down the wrong path. Math can, too, obviously, but doing math properly involves many self checks. You frame the problem in many different ways and can see if they line up. Your intuition is just the way you see the world. If the way you see the world happens to be wrong, you'll think the wrong thing. For instance, I might intuitively think that if I digitize a band limited analog signal I'm throwing something useful away... that you're throwing away the data between the samples. There's clearly wiggles there... those wiggles must encode something! It turns out though that a digitally sampled band limited signal can be perfectly reproduced. Perfectly. That's totally counter-intuitive, by which I mean there's little real world experience that would tell you otherwise!

So, I think you should think about intuition, math, whatever else you have in your pocket as tools. They give the right answer when used correctly and sometimes give the wrong answer even when you're sure you're using them correctly. I think though that intuition CAN be more insidious because it's what you've experienced! It HAS to be true, you think.