With all due respect to Dijkstra, this is so narrow-minded. I love intuition in mathematics, primarily coming from spatial or geometric reasoning. Then it's tim

With all due respect to Dijkstra, this is so narrow-minded. I love intuition in mathematics, primarily coming from spatial or geometric reasoning. Then it's time to put it into algebraic or symbolic terms, but that's pinning a butterfly to a board to show you actually caught it. I like point (ii) above, as learning to let the rules of the game guide your writing is a very powerful technique indeed. But teaching math formally without appeal to intuition is what a lot of people do and it's boring and unpleasant to me. It doesn't simplify, it merely traces lines in the sand or on a page without taking the trouble to look up and appreciate the larger picture (sometimes meaning literal picture). It's clear that Dijkstra & I appreciate very different parts of mathematics :)