I, and from conversations, I think most professional mathematicians, have had the experience of working on a mathematical problem, going to bed clueless about how to solve it, and waking up with the solution (a correct proof in this case).
A surprising lot of what we attribute to conscious discursive reason is actually done by the unconscious part of the mind. (Personally I’m an Eccelsian dualist: although the mind arises from brain actitivity, it is not the same thing.)
Yes, brain activity is not the same as “mind.” Actually, the real puzzle is what is consciousness? Again, based on brain activity but not the same as brain activity.