We know that FLT is true because Andrew Wiles has proven it. We don't know that RH is true. We have strong reasons to believe it is true since we have discovere

We know that FLT is true because Andrew Wiles has proven it. We don't know that RH is true. We have strong reasons to believe it is true since we have discovered directly a large number of roots on Re(z) = 1/2 and none anywhere else. I do believe intuition exists in the process of doing mathematics, but I don't think either of these are good examples.