"But to people not already familiar with what’s going on the same patterns are not very illuminating; they are often even misleading. The language is not alive

"But to people not already familiar with what’s going on the same patterns are not very illuminating; they are often even misleading. The language is not alive except to those who use it." struck me as significant, and "The standard of correctness and completeness necessary to get a computer program to work at all is a couple of orders of magnitude higher than the mathematical community’s standard of valid proofs." is the closest I've ever seen to someone stating the one of the most important differences there.