Sure. Speak French without learning French. Or maybe learn French by reading a picture book. I sympathize with the author because there is a great deal of room

Sure. Speak French without learning French. Or maybe learn French by reading a picture book. I sympathize with the author because there is a great deal of room for improvement in the language of math, which may let us model the world on a computer much more easily. One example: Using Robinson infinitesimals allows you very easily to write code for forward mode exact differentiation (not symbolic, not approximate). But justifying these simplifications is hard. The question is how much math can be simplified by analogous means without wrecking the foundations. Another example: Many really useful systems have to deal with uncertainty. I have yet to see a system that allows programmers to easily build such models. I have seen some nice ideas probability monads, Bayesian networks, etc. But how many non-specialists are prepared to use such tools? Happy to have HNers prove me wrong on this one.