"...unless you are one of the very, very rare people who sees the maths in their mind. I suspect Pease is one. "

I've never met one of these types... but one guy that works with me had a friend in the technical high school that from time to time had an argument with the teacher why his exercises where without calculations, just with the *correct* answer.

He said that usually his friend would say to the teacher that calculations where unnecessary, since the exercise (something like circuit analysys, with transistors, RLC parts...) was too simple and it was clear as crystal since with the given values and voltage dropouts involved the answer was already there.

I think that usually a teacher don't take the time to ask that kind of person HOW they do it. Of course that they have a special tallent, but usually they have some "mind trick" that can be thaught to the mere humans :-)