[brownbat]

Yeah, if a "natural language" explanation is just writing out mechanical mathematical steps or formulae in clumsy english, it's completely missing the point.

Use natural language for what it's good at. Where did this mathematical idea originate? Who introduced it? What was the problem this mathematical idea helped address? How much does it help address that problem (assuming the why and how are beyond the layman, just describe how helpful it was.)

The Quicksort intro by gohrt is a perfect example.

You're not using the natural language to do away with the thorough mathematical explanation, you're giving the lay reader an idea of why the concept is important, why they should care, in the most general sense.