Haha in my country half the computer science degrees are titled "Applied Mathematics".

Such a title makes me feel like I might come off smarter than I actually am -- I like it. Especially when considering my mathematically understanding and abilities.

I think you don't understand enough physics, maths or cs if you think there's a way to draw a neat line between any pair of them.

Saying that there's a distinction between them is different than drawing a neat line. Surely you aren't arguing that they're the same discipline instead?