Terence Tao has some interesting writing on the interplay between rigour and intuition: http://terrytao.wordpress.com/career-advice/there%E2%80%99s-more-to-mat

Terence Tao has some interesting writing on the interplay between rigour and intuition: http://terrytao.wordpress.com/career-advice/there%E2%80%99s-more-to-mathematics-than-rigour-and-proofs/ http://terrytao.wordpress.com/career-advice/there%E2%80%99s-... Nevertheless, this problem is interesting because people tend to trip up on the maths. The actual behaviour, even in simulation, is very unintuitive (the mean gain from swapping envelopes does not converge to zero over time, and in fact does not converge to anything at all but oscillates wildly). It's a good introduction to the subtleties of probability theory in non-finite spaces.