On the other hand, as someone who knows a bit of math, I love those Wikipedia articles that get straight to the point, and hate those where I first have to dig through a pile of (to me) useless "intuition".

I'm not sure if it is really possible to learn/teach math (like actual math, not just some loose intuitions, because those don't really help you with anything) without going through notation and prior knowledge. Notation exists for a reason.